FDI, Trade, and Pricing Model

D. Riker, 05/21/19

This partial equilibrium (PE) model of the economic impact of several different types of FDI, including foreign acquisitions, with and without technology transfer, and greenfield investment. The model is described in detail in Riker, D. FDI, Trade, and Pricing in a Bertrand Differentiated Products Model. USITC Economics Working Paper 2019-04-A.
  
The user can modify data inputs, the elasticity value, and the tariff rate in the simulation by change the values in the ORANGE - shaded lines in the notebook below tab. The spreadsheet will  update the estimated changes in economic outcomes that are reported in the GREEN - shaded cells once the user selects "Evaluate Notebook" under "Evaluation" in the Menu above.
   
This model is provided as a generic analytical tool, and the data and parameter values are fictional and illustrative. Actual data and parameter values should be supplied by the user based on the industry and market to which the model is applied. The model is the result of ongoing professional research of USITC staff and may be updated. The model is not meant to represent in any way the view of the U.S. International Trade Commission or any of its individual Commissioners. The model is posted to promote the active exchange of ideas between USITC staff and experts outside the USITC and to provide useful economic modeling tools to the public.

ClearAll[f];

Parameter Inputs

Elasticity of Substitution

sigma=4;

Tariff Rate

t=0.20;

Data Inputs - Initial Equilibrium Values

Domestic Duopoly (X and Y) and 1 Foreign Firm (F)

Consumer expenditures in the single market

vx0=25;

vy0=25;

vf0=50;

Calculated or Normalized Initial Equilibrium Values

Prices

px0=1;

py0=1;

pf0=1;

Quantities

qx0=(vx0/px0);

qy0=(vy0/py0);

qf0=(vf0/(pf0 (1+t)));

Calibration of Parameters Based on the Initial Equilibrium

Initial Marginal Costs

mx0=px0 (1-(1/(sigma-(((sigma-1) vx0)/(vx0+vy0+vf0)))));

my0=py0 (1-(1/(sigma-(((sigma-1) vy0)/(vx0+vy0+vf0)))));

mf0=pf0 (1-(1/(sigma-(((sigma-1) vf0)/(vx0+vy0+vf0)))));

bf=((vf0 (((((pf0 (1+t))/px0)))^(sigma-1)))/vx0);

by=((vy0 ((((py0/px0)))^(sigma-1)))/vx0);

P0=((((px0^(1-sigma))+by (py0^(1-sigma))+bf (((pf0 (1+t)))^(1-sigma))))^(1/(1-sigma)));

k=qx0 (P0^(-sigma+1)) (px0^sigma);

New Equilibrium Values with Merger of X and F, No Efficiencies

sharex=((((px/P)))^(1-sigma));

sharey=((((py/P)))^(1-sigma)) by;

sharef=(((((pf (1+t))/P)))^(1-sigma)) bf;

P=((((px^(1-sigma))+by (py^(1-sigma))+bf (((pf (1+t)))^(1-sigma))))^(1/(1-sigma)));

EqnX1=px==(px-mx0) (sigma-(sigma-1) sharex)-(pf-mf0) (sigma-1) sharex (((((pf (1+t))/px)))^(-sigma)) bf;

EqnY1=py==(py-my0) (sigma-(sigma-1) sharey);

EqnF1=pf==(pf-mf0) (sigma-(sigma-1) sharef)-(((px-mx0) (sigma-1) sharef((((px/(pf (1+t)))))^(-sigma)))/bf);

FindRoot[{EqnX1,EqnY1,EqnF1},{px,px0},{py,py0},{pf,pf0}]

px1=px/.%;

py1=py/.%%;

pf1=pf/.%%%;

P1=((((px1^(1-sigma))+by (py1^(1-sigma))+bf (((pf1 (1+t)))^(1-sigma))))^(1/(1-sigma)));

qx1=k (P1^(sigma-1)) (px1^(-sigma));

qy1=k (P1^(sigma-1)) (py1^(-sigma)) by;

qf1=k (P1^(sigma-1)) (((pf1 (1+t)))^(-sigma)) bf;

Percent Changes in Consumer Prices, No Efficiencies

(((px1-px0) 100)/px0)

(((py1-py0) 100)/py0)

(((pf1 (1+t)-pf0 (1+t)) 100)/(pf0 (1+t)))

(((P1-P0) 100)/P0)

Percent Changes in Quantities and Employment, No Efficiencies

Domestic Shipments

(((qx1-qx0) 100)/qx0)

(((qy1-qy0) 100)/qy0)

Imports

(((qf1-qf0) 100)/qf0)

Domestic Employment

((((qx1+qy1)-(qx0+qy0)) 100)/((qx0+qy0)))

New Equilibrium Values with Merger of X and F, With Efficiencies

Adopting best practices through IP transfer

mx3=Min[mx0,mf0];

mf3=Min[mx0,mf0];

my3=my0;

P3=((((px3^(1-sigma))+by (py3^(1-sigma))+bf (((pf3 (1+t)))^(1-sigma))))^(1/(1-sigma)));

sharex3=((((px3/P3)))^(1-sigma));

sharey3=((((py3/P3)))^(1-sigma)) by;

sharef3=(((((pf3 (1+t))/P3)))^(1-sigma)) bf;

EqnX3=px3==(px3-mx3) (sigma-(sigma-1) sharex3)-(pf3-mf0) (sigma-1) sharex3 (((((pf3 (1+t))/px3)))^(-sigma)) bf;

EqnY3=py3==(py3-my3) (sigma-(sigma-1) sharey3);

EqnF3=pf3==(pf3-mf3) (sigma-(sigma-1) sharef3)-(((px3-mx0) (sigma-1) sharef3((((px3/(pf3 (1+t)))))^(-sigma)))/bf);

FindRoot[{EqnX3,EqnY3,EqnF3},{px3,px0},{py3,py0},{pf3,pf0}]

px4=px3/.%;

py4=py3/.%%;

pf4=pf3/.%%%;

P4=((((px4^(1-sigma))+by (py4^(1-sigma))+bf (((pf4 (1+t)))^(1-sigma))))^(1/(1-sigma)));

qx4=k (P4^(sigma-1)) (px4^(-sigma));

qy4=k (P4^(sigma-1)) (py4^(-sigma)) by;

qf4=k (P4^(sigma-1)) (((pf4 (1+t)))^(-sigma)) bf;

Percent Changes in Consumer Prices, With Efficiencies

(((px4-px0) 100)/px0)

(((py4-py0) 100)/py0)

(((pf4(1+t)-pf0 (1+t)) 100)/(pf0 (1+t)))

(((P4-P0) 100)/P0)

Percent Changes in Quantities and Employment, With Efficiencies

Domestic Shipments

(((qx4-qx0) 100)/qx0)

(((qy4-qy0) 100)/qy0)

Imports

(((qf4-qf0) 100)/qf0)

Domestic Employment

((((qx4+qy4)-(qx0+qy0)) 100)/((qx0+qy0)))

New Equilibrium Values without Merger, With Greenfield Investment

hc=Min[1.10,1+t];

mf5=mf0 hc;

my5=my0;

mx5=mx0;

P5=((((px5^(1-sigma))+by (py5^(1-sigma))+bf (pf5^(1-sigma))))^(1/(1-sigma)));

sharex5=((((px5/P5)))^(1-sigma));

sharey5=((((py5/P5)))^(1-sigma)) by;

sharef5=(((((pf5 )/P5)))^(1-sigma)) bf;

EqnX5=px5==(px5-mx5) (sigma-(sigma-1) sharex5);

EqnY5=py5==(py5-my5) (sigma-(sigma-1) sharey5);

EqnF5=pf5==(pf5-mf5) (sigma-(sigma-1) sharef5);

FindRoot[{EqnX5,EqnY5,EqnF5},{px5,px0},{py5,py0},{pf5,pf0}]

px6=px5/.%;

py6=py5/.%%;

pf6=pf5/.%%%;

P6=((((px6^(1-sigma))+by (py6^(1-sigma))+bf (pf6^(1-sigma))))^(1/(1-sigma)));

qx6=k (P6^(sigma-1)) (px6^(-sigma));

qy6=k (P6^(sigma-1)) (py6^(-sigma)) by;

qf6=k (P6^(sigma-1)) (pf6^(-sigma)) bf;

Percent Changes in Consumer Prices, With Greenfield Investment

(((px6-px0) 100)/px0)

(((py6-py0) 100)/py0)

(((pf6-pf0 (1+t)) 100)/(pf0 (1+t)))

(((P6-P0) 100)/P0)

Percent Changes in Quantities and Employment, With Greenfield Investment

Domestic Shipments

(((qx6-qx0) 100)/qx0)

(((qy6-qy0) 100)/qy0)

Imports

(((0-(qf0)) 100)/((qf0)))

Domestic Employment

((((qf6+qx6+qy6)-(qx0+qy0)) 100)/((qx0+qy0)))