Appendix E: Economic Model

Model Overview

Chapter 8 uses an industry-specific partial equilibrium model of the global rice market to simulate the effects of country-specific policies on the industry and consumers in the United States and other major rice-producing and -consuming countries. The prospective model is calibrated to 2023 trade data with two types of rice (aromatic and nonaromatic), two stages of processing (paddy and milled rice), and 185 countries aggregated into 18 country groups (16 individual countries and two aggregate groups). The model is used to analyze the impacts of tariffs, export bans, tariff-rate quotas (TRQs), export charges, minimum support prices, and government-to-government contracts.[1]

Table E.1 List of countries included in the rice model

Group

Countries

Individual countries in the model

Bangladesh, Brazil, Burma, Cambodia, China, India, Indonesia, Japan, Pakistan, Paraguay, Philippines, South Korea, Thailand, United States, Uruguay, Vietnam

Aggregate groups

Other developed countries, other developing countries

Source: Compiled by the USITC.

Supply Structure

In the following three sections, the subscripts i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@ , j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@ , k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@ , and f MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOzaaaa@36F8@  denote the type of rice (aromatic or nonaromatic), exporting country, importing country, and factor input in the production of paddy rice, respectively.

The model assumes a perfectly competitive global rice market where each country produces a unique variety of rice with characteristics that differentiate it from rice produced in other countries. Four countries—India, Pakistan, Thailand, and Vietnam—produce aromatic rice in addition to nonaromatic rice and produce a unique variety of each type. The production process consists of two steps: rice farming and milling (processing). Trade can occur after either step in the production process. That is, rice can be traded as paddy rice and then processed in the destination country or processed in the source country and traded as milled rice. The supply of paddy rice in metric tons ( Q ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyua8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaaaaa@391A@  ) from each country is determined by the equation below.

Q ij = α ij p ij 1+ ω ij θ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyua8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaGcpeGaeyyp a0JaeqySde2damaaBaaaleaapeGaamyAaiaadQgaa8aabeaak8qada qadaWdaeaapeGaamiCa8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqa baGcpeWaaeWaa8aabaWdbiaaigdacqGHRaWkcqaHjpWDpaWaaSbaaS qaa8qacaWGPbGaamOAaaWdaeqaaaGcpeGaayjkaiaawMcaaaGaayjk aiaawMcaa8aadaahaaWcbeqaa8qacqaH4oqCpaWaaSbaaWqaa8qaca WGPbGaamOAaaWdaeqaaaaaaaa@4EB5@

 

p ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiCa8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaaaaa@3939@  is the producer price of paddy rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  in country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@ ; ω ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyYdC3damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@3A11@  are general ad valorem production subsidies for rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  produced in country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@ ; and θ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiUde3damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@39FA@  is the elasticity of supply for paddy rice. The calibrated supply shift parameter ( α ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqySde2damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@39E3@  ) captures country-specific factors for each rice type that shift the supply curve.

In the model, eight factor inputs are used in paddy rice farming: fertilizer, pesticides, energy, water, seed, land, labor, and capital. The quantity of each factor input f MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOzaaaa@36F8@  used to produce one unit of paddy rice quantity ( Q ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyua8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaaaaa@391A@  ) in country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  is represented by g ijf MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4za8aadaWgaaWcbaWdbiaadMgacaWGQbGaamOzaaWdaeqaaaaa @3A1B@ . The price of each unit of factor input f MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOzaaaa@36F8@  in country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  used in the farming of rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  is w ijf MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Da8aadaWgaaWcbaWdbiaadMgacaWGQbGaamOzaaWdaeqaaaaa @3A2B@ . The first equation below represents each factor input’s share of the total cost of production of paddy rice, where f=1 F ψ ijf =1 MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Waaubmaeqal8aabaWdbiaadAgacqGH9aqpcaaIXaaapaqaa8qacaWG gbaan8aabaWdbiabgUIiYdaakiabeI8a59aadaWgaaWcbaWdbiaadM gacaWGQbGaamOzaaWdaeqaaOWdbiabg2da9iaaigdaaaa@42E6@  and F MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOraaaa@36D8@  is the total number of factors used in the production of paddy rice. The cost shares of factor input f MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOzaaaa@36F8@  in the production of paddy rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  in country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  ( ψ ijf MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiYdK3damaaBaaaleaapeGaamyAaiaadQgacaWGMbaapaqabaaa aa@3AFD@  ) comes from the Cobb-Douglas production function for paddy rice in the second equation below.

ψ ijf = w ijf g ijf f=1 F w ijf g ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiYdK3damaaBaaaleaapeGaamyAaiaadQgacaWGMbaapaqabaGc peGaeyypa0ZaaSaaa8aabaWdbiaadEhapaWaaSbaaSqaa8qacaWGPb GaamOAaiaadAgaa8aabeaak8qacaWGNbWdamaaBaaaleaapeGaamyA aiaadQgacaWGMbaapaqabaaakeaapeWaaeWaa8aabaWdbmaavadabe Wcpaqaa8qacaWGMbGaeyypa0JaaGymaaWdaeaapeGaamOraaqdpaqa a8qacqGHris5aaGccaWG3bWdamaaBaaaleaapeGaamyAaiaadQgaca WGMbaapaqabaGcpeGaam4za8aadaWgaaWcbaWdbiaadMgacaWGQbaa paqabaaak8qacaGLOaGaayzkaaaaaaaa@53B0@

 

Q ij =A f=1 F g ijf ψ ijf MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyua8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaGcpeGaeyyp a0JaamyqamaawahabeWcpaqaa8qacaWGMbGaeyypa0JaaGymaaWdae aapeGaamOraaqdpaqaa8qacqGHris5aaGccaWGNbWdamaaDaaaleaa peGaamyAaiaadQgacaWGMbaapaqaa8qacqaHipqEpaWaaSbaaWqaa8 qacaWGPbGaamOAaiaadAgaa8aabeaaaaaaaa@4A38@

 

In the model, the processing of paddy rice into milled rice is represented by the Leontief production function with two inputs, paddy rice ( Q ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyua8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaaaaa@391A@  ) and all the value-added resources used in the milling process, K ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4sa8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaaaaa@3914@  in the equation below.

m ij =min λ ij Q ij ,  K ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyBa8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaGcpeGaeyyp a0JaamyBaiaadMgacaWGUbWaaiWaa8aabaWdbiabeU7aS9aadaWgaa WcbaWdbiaadMgacaWGQbaapaqabaGcpeGaamyua8aadaWgaaWcbaWd biaadMgacaWGQbaapaqabaGcpeGaaiilaiaacckacaWGlbWdamaaBa aaleaapeGaamyAaiaadQgaa8aabeaaaOWdbiaawUhacaGL9baaaaa@4B9A@

 

h ij = p ij Q ij + ν ij K ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiAa8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaGcpeGaeyyp a0JaamiCa8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaGcpeGaam yua8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaGcpeGaey4kaSIa eqyVd42damaaBaaaleaapeGaamyAaiaadQgaa8aabeaak8qacaWGlb WdamaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@48B0@

 

λ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4UdW2damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@39F8@  is the milling quantity recovery rate for rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  in country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@ , and the quantity of milled rice produced is m ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyBa8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaaaaa@3936@ . h ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamiAa8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaaaaa@3931@  is the total cost of milling, and ν ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyVd42damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@39FC@  is the fixed value added to paddy rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  of milling in country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@ .

Demand Structure

The model has a nested constant elasticity of substitution (CES) demand structure. Consumers choose the types and sources of rice among which to allocate their total expenditure on rice. The consumers’ decision is determined by maximizing their CES utility function subject to their budget constraint. The aggregate utility function for country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  is represented by the following three equations where J MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOsaaaa@36DC@  and I MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamysaaaa@36DB@  are the total number of source countries and rice types, respectively.

max  U k q ijk = i=1 I γ ik u ik ϕ1 ϕ ϕ 1ϕ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyBaiaadggacaWG4bGaaiiOaiaadwfapaWaaSbaaSqaa8qacaWG RbaapaqabaGcpeWaaeWaa8aabaWdbiaadghapaWaaSbaaSqaa8qaca WGPbGaamOAaiaadUgaa8aabeaaaOWdbiaawIcacaGLPaaacqGH9aqp daGfWbqabSWdaeaapeGaamyAaiabg2da9iaaigdaa8aabaWdbiaadM eaa0WdaeaapeGaeyyeIuoaaOWaaeWaa8aabaWdbiabeo7aN9aadaWg aaWcbaWdbiaadMgacaWGRbaapaqabaGcpeGaamyDa8aadaqhaaWcba WdbiaadMgacaWGRbaapaqaa8qadaWcaaWdaeaapeGaeqy1dyMaeyOe I0IaaGymaaWdaeaapeGaeqy1dygaaaaaaOGaayjkaiaawMcaa8aada ahaaWcbeqaa8qadaWcaaWdaeaapeGaeqy1dygapaqaa8qacaaIXaGa eyOeI0Iaeqy1dygaaaaaaaa@5D9D@

 

s.t   u ik = j=1 J β ijk q ijk σ1 σ σ 1σ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Caiaac6cacaWG0bGaaiiOaiaacckacaWG1bWdamaaBaaaleaa peGaamyAaiaadUgaa8aabeaak8qacqGH9aqpdaGfWbqabSWdaeaape GaamOAaiabg2da9iaaigdaa8aabaWdbiaadQeaa0WdaeaapeGaeyye IuoaaOWaaeWaa8aabaWdbiabek7aI9aadaWgaaWcbaWdbiaadMgaca WGQbGaam4AaaWdaeqaaOWdbiaadghapaWaa0baaSqaa8qacaWGPbGa amOAaiaadUgaa8aabaWdbmaalaaapaqaa8qacqaHdpWCcqGHsislca aIXaaapaqaa8qacqaHdpWCaaaaaaGccaGLOaGaayzkaaWdamaaCaaa leqabaWdbmaalaaapaqaa8qacqaHdpWCa8aabaWdbiaaigdacqGHsi slcqaHdpWCaaaaaaaa@5B80@

 

and  s.t.   E k = i=1 I j=1 J d ijk q ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyyaiaad6gacaWGKbGaaiiOaiaacckacaWGZbGaaiOlaiaadsha caGGUaGaaiiOaiaacckacaWGfbWdamaaBaaaleaapeGaam4AaaWdae qaaOWdbiabg2da9maawahabeWcpaqaa8qacaWGPbGaeyypa0JaaGym aaWdaeaapeGaamysaaqdpaqaa8qacqGHris5aaGcdaGfWbqabSWdae aapeGaamOAaiabg2da9iaaigdaa8aabaWdbiaadQeaa0WdaeaapeGa eyyeIuoaaOGaamiza8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4Aaa WdaeqaaOWdbiaadghapaWaaSbaaSqaa8qacaWGPbGaamOAaiaadUga a8aabeaaaaa@588D@

 

In the above equations, β ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamyAaiaadQgacaWGRbaapaqabaaa aa@3AD5@  is the calibrated demand preference parameter of consumers for the rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  imported by country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  from country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  and γ ik MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4SdC2damaaBaaaleaapeGaamyAaiaadUgaa8aabeaaaaa@39EC@  is the calibrated demand preference parameter for country composite rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  in country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@ . σ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdmhaaa@37D0@  is the elasticity of substitution between sources of each rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@ , and ϕ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeqy1dygaaa@37D5@  is the elasticity of substitution between nonaromatic and aromatic types of rice. The budget constraint for country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  is that total expenditure ( E k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyra8aadaWgaaWcbaWdbiaadUgaa8aabeaaaaa@3821@  ) must equal the quantity of rice supplied ( q ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyCa8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaaaa @3A2A@  ) multiplied by the delivered price of rice ( d ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiza8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaaaa @3A1D@  ) type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  from source country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  to destination country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@ . The delivered prices are a function of the producer prices, policy-induced price shifters, and location of paddy rice milling defined by the equation below.

d ijk = 1 μ ijk p ij λ ij + ν ij + μ ijk p ij λ ik + ν ik 1+ τ ijk 1 δ ik 1+ r ijk 1+ ξ ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiza8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaOWd biabg2da9maabmaapaqaa8qadaqadaWdaeaapeGaaGymaiabgkHiTi abeY7aT9aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaaGc peGaayjkaiaawMcaamaabmaapaqaa8qadaWcaaWdaeaapeGaamiCa8 aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaaakeaapeGaeq4UdW2d amaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaGcpeGaey4kaSIaeq yVd42damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaOWdbiaawIca caGLPaaacqGHRaWkcqaH8oqBpaWaaSbaaSqaa8qacaWGPbGaamOAai aadUgaa8aabeaak8qadaqadaWdaeaapeWaaSaaa8aabaWdbiaadcha paWaaSbaaSqaa8qacaWGPbGaamOAaaWdaeqaaaGcbaWdbiabeU7aS9 aadaWgaaWcbaWdbiaadMgacaWGRbaapaqabaaaaOWdbiabgUcaRiab e27aU9aadaWgaaWcbaWdbiaadMgacaWGRbaapaqabaaak8qacaGLOa GaayzkaaaacaGLOaGaayzkaaWaaeWaa8aabaWdbiaaigdacqGHRaWk cqaHepaDpaWaaSbaaSqaa8qacaWGPbGaamOAaiaadUgaa8aabeaaaO WdbiaawIcacaGLPaaadaqadaWdaeaapeGaaGymaiabgkHiTiabes7a K9aadaWgaaWcbaWdbiaadMgacaWGRbaapaqabaaak8qacaGLOaGaay zkaaWaaeWaa8aabaWdbiaaigdacqGHRaWkcaWGYbWdamaaBaaaleaa peGaamyAaiaadQgacaWGRbaapaqabaaak8qacaGLOaGaayzkaaWaae Waa8aabaWdbiaaigdacqGHRaWkcqaH+oaEpaWaaSbaaSqaa8qacaWG PbGaamOAaiaadUgaa8aabeaaaOWdbiaawIcacaGLPaaaaaa@8679@

 

All policy-induced price shifters are included as ad valorem rates. τ ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiXdq3damaaBaaaleaapeGaamyAaiaadQgacaWGRbaapaqabaaa aa@3AF9@  is the tariff rate applied by country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  to imports from country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  of rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@ ; δ ik MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiTdq2damaaBaaaleaapeGaamyAaiaadUgaa8aabeaaaaa@39EA@  is the consumption subsidy in country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  for rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@ ; and ξ ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOVdG3damaaBaaaleaapeGaamyAaiaadQgacaWGRbaapaqabaaa aa@3AF7@  are the export charges applied by country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  on its exports to country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  of rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@ . The quota rent rate ( r ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOCa8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaaaa @3A2B@  ) is the cost of quota policies, including export quotas and import quotas. The quota policies cause a discrepancy between supply and demand that can result in higher prices. The quota rent rate behaves like a tariff except, instead of the government receiving revenue, the exporting producers restricted by the quota receive economic rents from higher prices. The rent rate is endogenous in the model and is required for all counterfactuals, including those that do not directly simulate changes to quota policies. All counterfactuals shift the equilibrium and affect the size of the discrepancy between supply and demand caused by the import and export quotas.

Outside of the policy-induced price shifters, delivered prices also include differences depending on where the paddy rice is processed. μ ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiVd02damaaBaaaleaapeGaamyAaiaadQgacaWGRbaapaqabaaa aa@3AEA@  is the share of rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  exported from country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  to country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  that is paddy rice; λ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4UdW2damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@39F8@  and λ ik MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4UdW2damaaBaaaleaapeGaamyAaiaadUgaa8aabeaaaaa@39F9@  are the milling recovery rates of rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  for countries j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  and k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@ , respectively; and ν ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyVd42damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@39FC@  and ν ik MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqyVd42damaaBaaaleaapeGaamyAaiaadUgaa8aabeaaaaa@39FD@  are the fixed milling costs of paddy rice in countries j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  and k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@ , respectively.

The demand function for rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  exported from country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  to country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  implied by country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  ’s utility function is defined below.

q ijk = E k Z k η+ϕ P ik σϕ d ijk σ β ijk γ ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyCa8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaOWd biabg2da9iaadweapaWaaSbaaSqaa8qacaWGRbaapaqabaGcpeWaae Waa8aabaWdbiaadQfapaWaaSbaaSqaa8qacaWGRbaapaqabaaak8qa caGLOaGaayzkaaWdamaaCaaaleqabaWdbiabeE7aOjabgUcaRiabew 9aMbaakmaabmaapaqaa8qacaWGqbWdamaaBaaaleaapeGaamyAaiaa dUgaa8aabeaaaOWdbiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaeq 4WdmNaeyOeI0Iaeqy1dygaaOWaaeWaa8aabaWdbiaadsgapaWaaSba aSqaa8qacaWGPbGaamOAaiaadUgaa8aabeaaaOWdbiaawIcacaGLPa aapaWaaWbaaSqabeaapeGaeyOeI0Iaeq4WdmhaaOGaeqOSdi2damaa BaaaleaapeGaamyAaiaadQgacaWGRbaapaqabaGcpeGaeq4SdC2dam aaBaaaleaapeGaamyAaiaadQgacaWGRbaapaqabaaaaa@6234@

 

The parameter η MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4TdGgaaa@37B9@  is the price elasticity of total industry demand, and the CES price index in the inner nest for the two different composite rice types in country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  ( P ik MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiua8aadaWgaaWcbaWdbiaadMgacaWGRbaapaqabaaaaa@391A@  ) is represented by the following equation.

P ik = j=1 J β ijk d ijk 1σ 1 1σ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiua8aadaWgaaWcbaWdbiaadMgacaWGRbaapaqabaGcpeGaeyyp a0ZaaeWaa8aabaWdbmaawahabeWcpaqaa8qacaWGQbGaeyypa0JaaG ymaaWdaeaapeGaamOsaaqdpaqaa8qacqGHris5aaGccqaHYoGypaWa aSbaaSqaa8qacaWGPbGaamOAaiaadUgaa8aabeaak8qadaqadaWdae aapeGaamiza8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqa aaGcpeGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0 Iaeq4WdmhaaaGccaGLOaGaayzkaaWdamaaCaaaleqabaWdbmaalaaa paqaa8qacaaIXaaapaqaa8qacaaIXaGaeyOeI0Iaeq4Wdmhaaaaaaa a@5547@

 

The CES price index in the outer nest ( Z k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOwa8aadaWgaaWcbaWdbiaadUgaa8aabeaaaaa@3836@  ), which represents the average consumer price for all rice in country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@ , is defined below.

Z k = i=1 I γ ik P ik 1ϕ 1 1ϕ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOwa8aadaWgaaWcbaWdbiaadUgaa8aabeaak8qacqGH9aqpdaqa daWdaeaapeWaaybCaeqal8aabaWdbiaadMgacqGH9aqpcaaIXaaapa qaa8qacaWGjbaan8aabaWdbiabggHiLdaakiabeo7aN9aadaWgaaWc baWdbiaadMgacaWGRbaapaqabaGcpeWaaeWaa8aabaWdbiaadcfapa WaaSbaaSqaa8qacaWGPbGaam4AaaWdaeqaaaGcpeGaayjkaiaawMca a8aadaahaaWcbeqaa8qacaaIXaGaeyOeI0Iaeqy1dygaaaGccaGLOa GaayzkaaWdamaaCaaaleqabaWdbmaalaaapaqaa8qacaaIXaaapaqa a8qacaaIXaGaeyOeI0Iaeqy1dygaaaaaaaa@527F@

 

The global demand for each paddy rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  supplied by country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  is represented by the following equation, where K MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4saaaa@36DD@  is the total number of importing countries.

G ij = k=1 K q ijk 1 μ ijk λ ij + μ ijk λ ik MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4ra8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaGcpeGaeyyp a0ZaaybCaeqal8aabaWdbiaadUgacqGH9aqpcaaIXaaapaqaa8qaca WGlbaan8aabaWdbiabggHiLdaakmaalaaapaqaa8qacaWGXbWdamaa BaaaleaapeGaamyAaiaadQgacaWGRbaapaqabaaakeaapeWaaeWaa8 aabaWdbiaaigdacqGHsislcqaH8oqBpaWaaSbaaSqaa8qacaWGPbGa amOAaiaadUgaa8aabeaaaOWdbiaawIcacaGLPaaacqaH7oaBpaWaaS baaSqaa8qacaWGPbGaamOAaaWdaeqaaOWdbiabgUcaRiabeY7aT9aa daWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaOWdbiabeU7aS9 aadaWgaaWcbaWdbiaadMgacaWGRbaapaqabaaaaaaa@5AD9@

 

The market clearing condition is defined by the following equation.

G ij = Q ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4ra8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaGcpeGaeyyp a0Jaamyua8aadaWgaaWcbaWdbiaadMgacaWGQbaapaqabaaaaa@3D3D@

 

Some countries in the model have import quotas or export controls. In these cases, the bilateral trade flows that are subject to the quotas must also satisfy the market clearing conditions in the equations below. T ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiva8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaaaa @3A0D@  are the binding TRQ quantities applied by country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  to imports of rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  from country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@ , and C ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaaaa @39FC@  are the quantitative export controls applied by country j MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOAaaaa@36FC@  to its exports of rice type i MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaaaa@36FB@  to country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@ . In certain instances (e.g., India exporting to Japan), one country has an export quota and the other has an import quota. In these cases, the model assumes that the export control is binding.[2]

T ijk = q ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiva8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaOWd biabg2da9iaadghapaWaaSbaaSqaa8qacaWGPbGaamOAaiaadUgaa8 aabeaaaaa@3F4A@

 

C ijk = q ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4qa8aadaWgaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeqaaOWd biabg2da9iaadghapaWaaSbaaSqaa8qacaWGPbGaamOAaiaadUgaa8 aabeaaaaa@3F39@

 

Data Description

The model uses producer prices and bilateral trade in quantities as the main inputs along with many parameters. The bilateral trade data come from the Global Trade Analytics Suite (GTAS).[3] The 6-digit level of the Harmonized Commodity Description and Coding System (HS) includes four categories of rice (table E.2).

Table E.2 Harmonized Commodity Description and Coding System (HS) codes and descriptions for rice

HS 6-digit code

Description

100610

Rice in the husk (paddy or rough)

100620

Husked (brown) rice

100630

Semi-milled or wholly milled rice, whether or not polished or glazed

100640

Broken rice

Source: S&P Global, GTAS database, accessed August 30, 2024.

The parameter μ ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiVd02damaaBaaaleaapeGaamyAaiaadQgacaWGRbaapaqabaaa aa@3AEA@ , which represents the share of total rice trade that is paddy rice (described by the HS as rice in the husk), is calculated from the trade data by dividing the quantity of trade classified under HS code 100610 in metric tons by the total rice traded. Once the share parameter is determined, all rice trade is aggregated into one HS 4-digit group (1006). Additionally, the model uses production data in combination with the trade data to calculate domestic shipments of each rice type ( q i,j=k,k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyCa8aadaWgaaWcbaWdbiaadMgacaGGSaGaamOAaiabg2da9iaa dUgacaGGSaGaam4AaaWdaeqaaaaa@3D80@  ). The production data come from the U.S. Department of Agriculture (USDA) Production, Supply and Distribution (PSD) Online database.[4] Domestic shipments are calculated by subtracting each country’s exports from its production.[5] Four countries examined for this report produce aromatic rice: India, Pakistan, Thailand, and Vietnam. Neither the PSD Online production data nor the HS classifications for trade data disaggregate aromatic and nonaromatic rice. To disaggregate the data, the model uses share parameters from the RiceFlow model used in the 2015 U.S. International Trade Commission (Commission) report on rice.[6] These parameters provide the share of production in each country that is aromatic and the share of each bilateral trade flow that is aromatic.[7] Where more recent data were available, these shares were updated using country-specific information and sources.[8] The table below provides the aromatic share of production data that were used in the model for this report.[9]

Table E.3 Aromatic share of production data

Country

Aromatic share of production

Source

Year of data

India

0.096

India Grains and Feed Annual Report

2023

Pakistan

0.350

RiceFlow

2013

Thailand

0.350

S&P Export Data and the Government of Thailand Office of Agricultural Economics

2023

Vietnam

0.20

United States Department of Agriculture, United States government official

2023

Source: Durand-Morat and Wailes, RiceFlow, accessed various dates; USDA, accessed various dates; Government of Thailand Office of Agricultural Economics, accessed March 2024; interview with foreign government official, accessed September 20, 2024; S&P Global, Total exports, HS heading 1006, rice, accessed August 30, 2024.

The PSD Online production data provide the production of both paddy and milled rice for each country. The milling quantity recover rates ( λ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4UdW2damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@39F8@  and λ ik MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4UdW2damaaBaaaleaapeGaamyAaiaadUgaa8aabeaaaaa@39F9@  ) are calculated by dividing each country’s milled production by its paddy rice production.

Producer prices for nonaromatic paddy rice data come from the Food and Agriculture Organization of the United Nations (FAO) FAOSTAT database and data from the RiceFlow model.[10] The annual producer prices of paddy rice are only available for the 2022 calendar year, so the model proxies the 2023 producer price data with the 2022 data. The table provides the prices, source, and year of data.

Table E.4 Producer price of rice data

In dollars; FAO = Food and Agriculture Organization; — (em dash) = not applicable; mt = metric tons.

Trading partner

Nonaromatic producer price ($/mt)

Source nonaromatic

Year of nonaromatic data

Bangladesh

220.40

FAO/RiceFlow (imputed value)

Brazil

279.10

FAO

2022

Burma

179.22

FAO/RiceFlow (imputed value)

Cambodia

267.17

FAO/RiceFlow (imputed value)

China

413.10

FAO

2022

India

222.96

FAO/RiceFlow (imputed value)

Indonesia

392.39

FAO

2022

Japan

1413.20

FAO

2022

Pakistan

735.10

FAO

2022

Paraguay

354.00

FAO/RiceFlow (imputed value)

Philippines

320.10

FAO

2022

South Korea

1803.90

FAO

2022

Thailand

299.20

FAO

2022

United States

427.69

FAO

2022

Uruguay

235.00

FAO

2022

Vietnam

311.40

FAO

2022

Developed group

331.35

FAO (average of developed)

2022

Developing group

303.81

FAO (average of developing)

2022

Source: FAO, FAOSTAT database, “Producer Price”, accessed various dates; USITC imputed value using data from FAO, “Producer Price,” FAOSTAT database and Durand-Morat and Wailes, RiceFlow, accessed various dates.

Not all individual countries have producer prices available in the FAOSTAT database. For those without producer price data available, producer prices from the 2015 Commission report are used and scaled up by the average price increase from 2015 to 2022 for the countries where 2022 producer price data are available. The producer price of aromatic rice is calculated by scaling up the 2022 producer prices of nonaromatic rice from FAOSTAT, using the relative difference between aromatic and nonaromatic rice prices in the 2015 Commission report that used the RiceFlow model.[11] The producer prices for the aggregated developing-country and developed-country groups are the simple average of FAO producer prices in the developed and developing countries.

On the supply side, the model uses the factor input shares of total production costs ( ψ ijf MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiYdK3damaaBaaaleaapeGaamyAaiaadQgacaWGMbaapaqabaaa aa@3AFD@  ) as inputs. These shares are from various country-specific sources, and where no cost-of-production data more recent than 2013 are available, the cost shares from the 2015 RiceFlow model are used.[12] The table below lists the countries, sources, and year of the cost shares used.

Table E.5 Sources and year of most recent cost shares of production data

Trading partner

Source

Year

Bangladesh

RiceFlow

2013

Brazil

RiceFlow

2013

Burma

RiceFlow

2013

Cambodia

RiceFlow

2013

China

RiceFlow

2013

India

Government of India

2021

Indonesia

Khoiriyah et al. (2023)

2023

Japan

Government of Japan Ministry of Agriculture, Forestry and Fisheries

2024

Pakistan

Government of Pakistan

2022

Paraguay

RiceFlow

2013

Philippines

RiceFlow

2013

South Korea

Statistics Korea

2024

Thailand

Fakkong and Suwanmaneepong (2016)

2016

United States

United States Department of Agriculture

2023

Uruguay

Asociación Cultivadores de Arroz

2023

Vietnam

RiceFlow

2013

Developed Group

RiceFlow

2013

Developing Group

RiceFlow

2013

Source: Durand-Morat, Alvaro and Weiles, RiceFlow, accessed various dates; USDA, ARMS, accessed August, 2024; Government of India, “Cost of Cultivation/Production Estimates,” accessed April 6, 2024; Government of Pakistan, “Rice Paddy Policy Analysis for 2022–23 Crop,” accessed October 29, 2024, Fakkong and Suwanmaneepong (2016), “Determinants of Profitability of Rice Farming in Peri-Urban Area, Bangkok, Thailand,” accessed various dates; Asociación Cultivadores de Arroz, “Costos productivos,” accessed various dates.

The model contains five elasticity values: the Armington elasticity of substitution between country sources within the two rice composites ( σ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdmhaaa@37D0@  ), elasticity of substitution between the two rice composites ( ϕ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeqy1dygaaa@37D5@  ), elasticity of total industry demand ( η MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4TdGgaaa@37B9@  ), elasticity of supply for paddy rice ( θ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiUde3damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@39FA@  ), and the price elasticity of supply for land ( ϵ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr hAXaqeguuDJXwAKbstHrhAG8KBLbacfiaeaaaaaaaaa8qacqWF1pG8 paWaaSbaaSqaa8qacaWGPbGaamOAaaWdaeqaaaaa@443F@  ). The elasticity values are listed in the table below.

Table E.6 Elasticity estimates

Elasticity

Value

Source

           σ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Wdmhaaa@37D0@

5

GTAP

           ϕ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeqy1dygaaa@37D5@

3

Commission estimate, assuming the elasticity of substitution between composites will be less than within composites

           η MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4TdGgaaa@37B9@

−1

Commission estimate

           ϵ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr hAXaqeguuDJXwAKbstHrhAG8KBLbacfiaeaaaaaaaaa8qacqWF1pG8 paWaaSbaaSqaa8qacaWGPbGaamOAaaWdaeqaaaaa@443F@

0.5

Commission estimate

           θ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiUde3damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@39FA@

Varies

Calibrated by the model in the section below

Source: Aguiar, A., Chepeliev, M., Corong, E., & van der Mensbrugghe, D. (2023). “The Global Trade AnalysisProject (GTAP) Data Base: Version 11,” accessed August 2023.

The model also uses tariff data from the United Nations Conference on Trade and Development Trade Analysis Information System accessed through the World Integrated Trade Solution database.[13] Average tariff levels between pairs of countries are computed as a simple average of the ad valorem equivalent tariffs for all Harmonized Tariff Schedule of the United States (HTS) 8-digit products relating to rice.[14] Most-favored-nation tariff rates are used by default, but in cases where two countries have a trade agreement, the preferential rate is used instead.

The tariff rates used for the developed- and developing-country groups are the trade-weighted average of the tariff rates for the countries included in the groups. These tariff rates are in turn calculated as a simple average of tariffs applied by a given developed or developing country at the HTS 8-digit level. For the European Union and Colombia, which have TRQ policies, ad valorem equivalent rates are calculated by computing the total revenue from out-of-quota imports and dividing this revenue by the total value of imported rice.

The TRQ information used for Japan in the model comes from USDA Global Agricultural Information Network reports.[15] The model does not use current production subsidies because of a lack of concrete data for countries included in the model. The information on India’s export ban and government-to-government contracts comes from governmental notices.[16]

For the quantitative assessment of food security, the model produces the change in daily caloric intake using the change in quantity of rice consumption. The model uses this change to calculate the percentage change in the USDA Economic Research Service calorie gap index for the individual developing countries in the model and the developing-country aggregate group.[17]

Model Calibration

The model uses the baseline data and exogenous parameters described in the section above to calibrate some of the supply and demand parameters and elasticities. The factor input cost shares of production, including the cost share of land rents ( χ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4Xdm2damaaBaaaleaapeGaamyAaiaadQgaa8aabeaaaaa@39FB@  ), are exogenous and remain constant. Additionally, all elasticities are exogenous and remain constant in the model, other than the elasticity of supply for paddy rice, which is calibrated according to the following equation. ϵ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamrr1ngBPrwtHr hAXaqeguuDJXwAKbstHrhAG8KBLbacfiaeaaaaaaaaa8qacqWF1pG8 paWaaSbaaSqaa8qacaWGPbGaamOAaaWdaeqaaaaa@443F@  is the elasticity of supply of land for paddy rice production.

θ ij = 1 χ ij + ϵ ij χ ij χ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqiUde3damaaBaaaleaapeGaamyAaiaadQgaa8aabeaak8qacqGH 9aqpdaWcaaWdaeaapeGaaGymaiabgkHiTiabeE8aJ9aadaWgaaWcba WdbiaadMgacaWGQbaapaqabaGcpeGaey4kaSYefv3ySLgznfgDOfda ryqr1ngBPrginfgDObYtUvgaiuGacqWF1pG8paWaaSbaaSqaa8qaca WGPbGaamOAaaWdaeqaaOWdbiabeE8aJ9aadaWgaaWcbaWdbiaadMga caWGQbaapaqabaaakeaapeGaeq4Xdm2damaaBaaaleaapeGaamyAai aadQgaa8aabeaaaaaaaa@581D@

 

In the following equations, the superscript “ * MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaaiOkaaaa@36BB@  ” denotes initial values. The supply initial shift parameter ( α ij * MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqySde2damaaDaaaleaapeGaamyAaiaadQgaa8aabaWdbiaacQca aaaaaa@3AA2@  ) is calibrated according to the equation below.

α ij * = q ij * p ij * 1+ ω ij * θ ij MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqySde2damaaDaaaleaapeGaamyAaiaadQgaa8aabaWdbiaacQca aaGccqGH9aqpcaWGXbWdamaaDaaaleaapeGaamyAaiaadQgaa8aaba WdbiaacQcaaaGcdaqadaWdaeaapeGaamiCa8aadaqhaaWcbaWdbiaa dMgacaWGQbaapaqaa8qacaGGQaaaaOWaaeWaa8aabaWdbiaaigdacq GHRaWkcqaHjpWDpaWaa0baaSqaa8qacaWGPbGaamOAaaWdaeaapeGa aiOkaaaaaOGaayjkaiaawMcaaaGaayjkaiaawMcaa8aadaahaaWcbe qaa8qacqGHsislcqaH4oqCpaWaaSbaaWqaa8qacaWGPbGaamOAaaWd aeqaaaaaaaa@527E@

 

The model uses initial delivered prices, which are a function of data inputs, including the producer prices, milling quantity recovery rates and costs, and the costs imposed by government policies, to calibrate the inner nest demand shift parameter ( β ijk MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamyAaiaadQgacaWGRbaapaqabaaa aa@3AD5@  ).

β ijk = d ijk * d i,j=k,k * σ q ijk * q i,j=k,k * MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaeqOSdi2damaaBaaaleaapeGaamyAaiaadQgacaWGRbaapaqabaGc peGaeyypa0ZaaSaaa8aabaWdbmaabmaapaqaa8qadaWcaaWdaeaape Gaamiza8aadaqhaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeaapeGa aiOkaaaaaOWdaeaapeGaamiza8aadaqhaaWcbaWdbiaadMgacaGGSa GaamOAaiabg2da9iaadUgacaGGSaGaam4AaaWdaeaapeGaaiOkaaaa aaaakiaawIcacaGLPaaapaWaaWbaaSqabeaapeGaeq4WdmhaaOGaam yCa8aadaqhaaWcbaWdbiaadMgacaWGQbGaam4AaaWdaeaapeGaaiOk aaaaaOWdaeaapeGaamyCa8aadaqhaaWcbaWdbiaadMgacaGGSaGaam OAaiabg2da9iaadUgacaGGSaGaam4AaaWdaeaapeGaaiOkaaaaaaaa aa@5A72@

 

Countries in the model do not always have domestic production for aromatic rice. When this is the case, the demand shift parameter above becomes undefined. In these cases, the model normalizes the demand shift parameter around aromatic rice imports from India rather than the domestic shipments of aromatic rice, which would be zero for countries with no aromatic rice production.

The outer nest demand shift parameter is calibrated according to the following equation. Subscripts “ i=n MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaiabg2da9iaad6gaaaa@38F4@  ” and “ i = a MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamyAaiaacckacqGH9aqpcaGGGcGaamyyaaaa@3B2F@  ” denote nonaromatic and aromatic rice types, respectively.

γ ik = j=1 J v i=a,jk * P i=a,k * P i=n,k * ϕ1 j=1 J v i=n,jk * MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaeq4SdC2damaaBaaaleaapeGaamyAaiaadUgaa8aabeaak8qacqGH 9aqpdaWcaaWdaeaapeWaaeWaa8aabaWdbmaavadabeWcpaqaa8qaca WGQbGaeyypa0JaaGymaaWdaeaapeGaamOsaaqdpaqaa8qacqGHris5 aaGccaWG2bWdamaaDaaaleaapeGaamyAaiabg2da9iaadggacaGGSa GaamOAaiaadUgaa8aabaWdbiaacQcaaaaakiaawIcacaGLPaaadaqa daWdaeaapeWaaSaaa8aabaWdbiaadcfapaWaa0baaSqaa8qacaWGPb Gaeyypa0JaamyyaiaacYcacaWGRbaapaqaa8qacaGGQaaaaaGcpaqa a8qacaWGqbWdamaaDaaaleaapeGaamyAaiabg2da9iaad6gacaGGSa Gaam4AaaWdaeaapeGaaiOkaaaaaaaakiaawIcacaGLPaaapaWaaWba aSqabeaapeGaeqy1dyMaeyOeI0IaaGymaaaaaOWdaeaapeWaaubmae qal8aabaWdbiaadQgacqGH9aqpcaaIXaaapaqaa8qacaWGkbaan8aa baWdbiabggHiLdaakiaadAhapaWaa0baaSqaa8qacaWGPbGaeyypa0 JaamOBaiaacYcacaWGQbGaam4AaaWdaeaapeGaaiOkaaaaaaaaaa@6A9E@

 

The aggregate expenditure on rice by each country k MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaam4Aaaaa@36FD@  is calibrated using the equation below. The model assumes that expenditure on rice remains constant.

E k = q ijk * Z k * ηϕ P i=n,k * ϕσ d i=n,j=k,k * σ MathType@MTEF@5@5@+= feaahGart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyra8aadaWgaaWcbaWdbiaadUgaa8aabeaak8qacqGH9aqpcaWG XbWdamaaDaaaleaapeGaamyAaiaadQgacaWGRbaapaqaa8qacaGGQa aaaOWaaeWaa8aabaWdbiaadQfapaWaa0baaSqaa8qacaWGRbaapaqa a8qacaGGQaaaaaGccaGLOaGaayzkaaWdamaaCaaaleqabaWdbiabgk HiTiabeE7aOjabgkHiTiabew9aMbaakmaabmaapaqaa8qacaWGqbWd amaaDaaaleaapeGaamyAaiabg2da9iaad6gacaGGSaGaam4AaaWdae aapeGaaiOkaaaaaOGaayjkaiaawMcaa8aadaahaaWcbeqaa8qacqaH vpGzcqGHsislcqaHdpWCaaGcdaqadaWdaeaapeGaamiza8aadaqhaa WcbaWdbiaadMgacqGH9aqpcaWGUbGaaiilaiaadQgacqGH9aqpcaWG RbGaaiilaiaadUgaa8aabaWdbiaacQcaaaaakiaawIcacaGLPaaapa WaaWbaaSqabeaapeGaeq4Wdmhaaaaa@6339@

 

Bibliography

Aguiar, A., Chepeliev, M., Corong, E., & van der Mensbrugghe, D. (2023). “The Global Trade Analysis Project (GTAP) Data Base: Version 11.” Journal of Global Economic Analysis7(2).https://doi.org/10.21642/JGEA.070201AF

Asociación Cultivadores de Arroz (ACA). “Costos productivos.” Arroz, December 2023. https://www.aca.com.uy/revista-no-108/.

Bangladesh Rice Research Institute (BRRI). “Estimation of Costs and Returns of MV Rice Cultivation at the Farm Level.” In Anual Report of the Bangladesh Rice Resarch Institute 2022–2023. Bangladesh Rice Research Institute, November 2023. https://brri.portal.gov.bd/sites/default/files/files/brri.portal.gov.bd/page/6d86d72e_953c_4f74_9157_3cfeaa80c2b1/2023-11-19-08-40-31f6f535f0ea30e2192859843fa4e4e1.pdf.

Durand-Morat, Alvaro, and Eric Wailes. “RiceFlow: A Multi-Region, Multi-Product, Spatial Partial Equilibrium Model of the World Rice Economy.” Department of Agricultural Economics and Agribusiness, University of Arkansas, July 2010.

Fakkhong, Sasima, and Suneeporn Suwanmaneepong. “Determinants of Profitability of Rice Farming in Peri-Urban Area, Bangkok, Thailand.” Presentation at the Asian Conference on the Social Sciences, Japan, 2016. https://papers.iafor.org/wp-content/uploads/papers/acss2016/ACSS2016_27913.pdf.

Food and Agriculture Organization of the United Nations (FAO). FAOSTAT database. “Producer Prices.” Accessed various dates. https://www.fao.org/faostat/en/#data/PP.

Government of India. Ministry of Agriculture and Farmers Welfare (MAFW). “Cost of Cultivation/Production Estimates.” Cost of Cultivation/Production Estimates.” April 6, 2024. https://desagri.gov.in/document-report-category/cost-of-cultivation-production-estimates/.

Government of Japan. 農林水産省 [Ministry of Agriculture, Forestry and Fisheries]. “農産物生産費統計 [Agricultural Production Cost Statistics].” December 12, 2024. https://www.maff.go.jp/j/tokei/kouhyou/noukei/seisanhi_nousan/index.html#y.

Government of Pakistan. Rice Paddy Policy Analysis for 2022–23 Crop. API Series 284. Agricultural Policy Institute, July 2022. https://api.gov.pk/SiteImage/Policy/Rice%20Policy%202022-23.pdf.

Government of Thailand. Office of Agricultural Economics. Agricultural Statistics of Thailand 2023. March 2024. https://www.oae.go.th/assets/portals/1/files/jounal/2567/statistic2566.pdf.

Khoiriyah, Nikmatul, Mellysa Isnaini, Atiek Iriany, and David Forgenie. “Analyzing The Cost of Paddy Rice Labor in Indonesia: A Case Study in Ten Tons Syngenta Project.” JSEP (Journal of Social and Agricultural Economics) 16, no. 2 (August 19, 2023): 189–204. https://doi.org/10.19184/jsep.v16i2.38160.

Kookkaew, Pathompong. “Cost and Return on Investment from Rice RD41 Farming of the Farmers in Samchuk District, Suphanburi Province, Thailand.” Paper presented at the 48th Annual International Academic Conference, Copenhagen, January 2019. https://doi.org/10.20472/IAC.2019.048.028.

Sarangi, Kumar. “Export of Non-Basmati White Rice (under HS Code 1006 30 90) to Nepal, Cameroon, Côte d’Ivoire, Republic of Guinea, Malaysia, Philippines and Seychelles.” Ministry of Commerce and Industry, Government of India, October 18, 2023. https://content.dgft.gov.in/Website/dgftprod/4c606476-77fb-458a-926f-59b00cd1d77a/DGFT%20Notification%20No.%2037-2023%20dated%2018.10.2023-English.pdf.

S&P Global Market Intelligence. Total exports and general imports, Harmonized System (HS) chapter 10, cereals. “Global Trade Atlas (GTA) database.” accessed various dates. https://connect.ihsmarkit.com/gtas/gta/standard-reports/.

United Nations Conference on Trade and Development (UNCTAD). Trade Analysis Information System (TRAINS). “Tariff-View and Export Raw Data.” World Bank. World Integrated Trade Solution (WITS) database. Accessed various dates. https://wits.worldbank.org/WITS/WITS/Restricted/Login.aspx.

U.S. Department of Agriculture (USDA). Economic Research Service (ERS) and National Agricultural Statistics Service (NASS). “Agricultural Resource Management Survey (ARMS).” Accessed August, 2024. https://www.nass.usda.gov/Surveys/Guide_to_NASS_Surveys/Ag_Resource_Management/

U.S. Department of Agriculture (USDA). Foreign Agricultural Service (FAS). Grain and Feed Annual: Japan. JA2024-0014. March 20, 2024. https://apps.fas.usda.gov/newgainapi/api/Report/DownloadReportByFileName?fileName=Grain%20and%20Feed%20Annual_Tokyo_Japan_JA2024-0014.pdf.

U.S. Department of Agriculture (USDA). Foreign Agricultural Service (FAS). Grain and Feed Annual: India. GAIN Report IN2024-0016. March 29, 2024. https://apps.fas.usda.gov/newgainapi/api/Report/DownloadReportByFileName?fileName=Grain%20and%20Feed%20Annual_New%20Delhi_India_IN2024-0016.pdf.

U.S. Department of Agriculture (USDA). Foreign Agricultural Service (FAS). “Global Food Security Snapshot.” Accessed various dates. https://fas.usda.gov/data/global-food-security-spotlight.

U.S. Department of Agriculture (USDA). Foreign Agricultural Service (FAS). .” Production, Supply, and Distribution (PSD) Online database. “Grains . Accessed various dates. https://apps.fas.usda.gov/psdonline/app/index.html#/app/home.

U.S. International Trade Commission (USITC). Rice: Global Competitiveness of the U.S. Industry. Publication number 4530. April 2015. https://www.usitc.gov/publications/332/pub4530.pdf.

통계청 [Statistics Korea]. “2023년산 논벼() 생산비조사 결과 [Results of the 2023 Rice Paddy Production Cost Survey].” December 12, 2024. https://kostat.go.kr/board.es?mid=a10301080600&bid=227&act=view&list_no=430131


 



[1] In addition to the policies modeled in this report, the model could be used to analyze the impacts of consumption and production subsidies. These production and consumption subsidy policies are not used for counterfactual simulations because of a lack of consistent data on the value of the subsidies for the countries in the model.

[2] In simulation 6, we do not remove the out-of-quota tariff rate to isolate the effects of strictly import tariff policies.

[3] S&P Global, Total exports, HS heading 1006, rice, accessed August 30, 2024.

[4] USDA, FAS, PSD Online database, “Grains,” accessed various dates.

[5] The annual trade data are based on the calendar year, and the production data are based on the marketing year, which varies by country. The model assumes that the marketing year dates align with the calendar year dates for all countries.

[6] USITC, Rice: Global Competitiveness, 2015; Durand-Morat and Wailes, “RiceFlow: A Multi-Region, Multi-Product, Spatial Partial Equilibrium Model,”, July 2010.

[7] For countries that do not produce aromatic rice, the aromatic share of production is set to zero. For countries that do not import aromatic rice from a specific country, the aromatic share of bilateral trade is set to zero.

[8] S&P Global, Total exports, HS heading 1006, rice, accessed August 30, 2024; Government of Thailand, Office of Agricultural Economics, Agricultural Statistics of Thailand 2023, March 2024; USDA, FAS, Grain and Feed Annual: India 2024, March 29, 2024; U.S. government official, interview by USITC staff, September 20, 2024.

[9] The aromatic shares of each bilateral trade flow are not reported in this appendix because of the large number of shares.

[10] FAO, FAOSTAT database, “Producer Prices,” accessed various dates; Durand-Morat and Wailes, “RiceFlow: A Multi-Region, Multi-Product, Spatial Partial Equilibrium Model,” July 2010.

[11] USITC, Rice: Global Competitiveness, 2015.

[12] Kookkaew, “Cost and Return on Investment,” January 2019, 91; Government of India, MAFW, “Cost of Cultivation/Production Estimates,” April 6, 2024; ACA, “Costos productivos,” December 2023, 30; BRRI, “Estimation of Costs and Returns,” November 2023, 245; Government of Pakistan, “Rice Paddy Policy Analysis for 2022–23 Crop,” accessed October 29, 2024, 13; Durand-Morat and Wailes, “RiceFlow: A Multi-Region, Multi-Product, Spatial Partial Equilibrium Model of the World Rice Economy,” July 2010; Fakkhong and Suwanmaneepong, “Determinants of Profitability of Rice Farming in Peri-Urban Area, Bangkok, Thailand,” 2016; 통계청 [Statistics Korea], “2023년산 논벼() 생산비조사 결과 [Results of the 2023 Rice Paddy Production Cost Survey],” December 12, 2024; MAFF, “農産物生産費統計 [Agricultural Production Cost Statistics],” December 12, 2024; Khoiriyah et al., “Analyzing The Cost of Paddy Rice Labor in Indonesia,” August 19, 2023, 195–198; USDA, ERS and NASS, “Agricultural Resource Management Survey (ARMS),” accessed August, 2024.

[13] WITS database, “Tariff-View and Export Raw Data,” accessed August 16, 2024.

[14] As a robustness check, tariffs were also computed as a trade-weighted average of the rates between two countries. The use of this alternative tariff computation method did not have any noticeable impact on results.

[15] USDA, FAS, Japan: Grain and Feed Annual, March 20, 2024.

[16] Kumar Sarangi, written letter to the government of India, Ministry of Commerce and Industry, October 18, 2023.

[17] USDA, FAS, “Global Food Security Snapshot,” accessed various dates.