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.
In[856]:= ClearAll[f];
Parameter Inputs
Elasticity of Substitution
In[857]:= sigma=4;
Tariff Rate
In[858]:= t=0.20;
Data Inputs - Initial Equilibrium Values
Domestic Duopoly (X and Y) and 1 Foreign Firm (F)
Consumer expenditures in the single market
In[859]:= vx0=25;
In[860]:= vy0=25;
In[861]:= vf0=50;
Calculated or Normalized Initial Equilibrium Values
Prices
In[862]:= px0=1;
In[863]:= py0=1;
In[864]:= pf0=1;
Quantities
In[865]:= qx0=vx0/px0;
In[866]:= qy0=vy0/py0;
In[867]:= qf0=vf0/(pf0 (1+t));
Calibration of Parameters Based on the Initial Equilibrium
Initial Marginal Costs
In[868]:= mx0=px0 (1-1/(sigma-((sigma-1) vx0)/(vx0+vy0+vf0)));
In[869]:= my0=py0 (1-1/(sigma-((sigma-1) vy0)/(vx0+vy0+vf0)));
In[870]:= mf0=pf0 (1-1/(sigma-((sigma-1) vf0)/(vx0+vy0+vf0)));
In[871]:= bf=(vf0 ((pf0 (1+t))/px0)^(sigma-1))/vx0;
In[872]:= by=(vy0 (py0/px0)^(sigma-1))/vx0;
In[873]:= P0=(px0^(1-sigma)+by py0^(1-sigma)+bf (pf0 (1+t))^(1-sigma))^(1/(1-sigma));
In[874]:= k=qx0 P0^(-sigma+1) px0^sigma;
New Equilibrium Values with Merger of X and F, No Efficiencies
In[875]:= sharex=(px/P)^(1-sigma);
In[876]:= sharey=(py/P)^(1-sigma) by;
In[877]:= sharef=((pf (1+t))/P)^(1-sigma) bf;
In[878]:= P=(px^(1-sigma)+by py^(1-sigma)+bf (pf (1+t))^(1-sigma))^(1/(1-sigma));
In[879]:= EqnX1=px==(px-mx0) (sigma-(sigma-1) sharex)-(pf-mf0) (sigma-1) sharex ((pf (1+t))/px)^-sigma bf;
In[880]:= EqnY1=py==(py-my0) (sigma-(sigma-1) sharey);
In[881]:= EqnF1=pf==(pf-mf0) (sigma-(sigma-1) sharef)-((px-mx0) (sigma-1) sharef (px/(pf (1+t)))^-sigma)/bf;
In[882]:= FindRoot[{EqnX1,EqnY1,EqnF1},{px,px0},{py,py0},{pf,pf0}]
Out[882]= {px->1.28191,py->1.04721,pf->1.20465}
In[883]:= px1=px/.%;
In[884]:= py1=py/.%%;
In[885]:= pf1=pf/.%%%;
In[886]:= P1=(px1^(1-sigma)+by py1^(1-sigma)+bf (pf1 (1+t))^(1-sigma))^(1/(1-sigma));
In[887]:= qx1=k P1^(sigma-1) px1^-sigma;
In[888]:= qy1=k P1^(sigma-1) py1^-sigma by;
In[889]:= qf1=k P1^(sigma-1) (pf1 (1+t))^-sigma bf;
Percent Changes in Consumer Prices, No Efficiencies
In[890]:= ((px1-px0) 100)/px0
Out[890]= 28.1909
In[891]:= ((py1-py0) 100)/py0
Out[891]= 4.72103
In[892]:= ((pf1 (1+t)-pf0 (1+t)) 100)/(pf0 (1+t))
Out[892]= 20.4645
In[893]:= ((P1-P0) 100)/P0
Out[893]= 17.1243
Percent Changes in Quantities and Employment, No Efficiencies
Domestic Shipments
In[894]:= ((qx1-qx0) 100)/qx0
Out[894]= -40.5006
In[895]:= ((qy1-qy0) 100)/qy0
Out[895]= 33.5997
Imports
In[896]:= ((qf1-qf0) 100)/qf0
Out[896]= -23.7036
Domestic Employment
In[897]:= (((qx1+qy1)-(qx0+qy0)) 100)/(qx0+qy0)
Out[897]= -3.45048
New Equilibrium Values with Merger of X and F, With Efficiencies
Adopting best practices through IP transfer
In[898]:= mx3=Min[mx0,mf0];
In[899]:= mf3=Min[mx0,mf0];
In[900]:= my3=my0;
In[901]:= P3=(px3^(1-sigma)+by py3^(1-sigma)+bf (pf3 (1+t))^(1-sigma))^(1/(1-sigma));
In[902]:= sharex3=(px3/P3)^(1-sigma);
In[903]:= sharey3=(py3/P3)^(1-sigma) by;
In[904]:= sharef3=((pf3 (1+t))/P3)^(1-sigma) bf;
In[905]:= EqnX3=px3==(px3-mx3) (sigma-(sigma-1) sharex3)-(pf3-mf0) (sigma-1) sharex3 ((pf3 (1+t))/px3)^-sigma bf;
In[906]:= EqnY3=py3==(py3-my3) (sigma-(sigma-1) sharey3);
In[907]:= EqnF3=pf3==(pf3-mf3) (sigma-(sigma-1) sharef3)-((px3-mx0) (sigma-1) sharef3 (px3/(pf3 (1+t)))^-sigma)/bf;
In[908]:= FindRoot[{EqnX3,EqnY3,EqnF3},{px3,px0},{py3,py0},{pf3,pf0}]
Out[908]= {px3->1.13128,py3->1.03405,pf3->1.18893}
In[909]:= px4=px3/.%;
In[910]:= py4=py3/.%%;
In[911]:= pf4=pf3/.%%%;
In[912]:= P4=(px4^(1-sigma)+by py4^(1-sigma)+bf (pf4 (1+t))^(1-sigma))^(1/(1-sigma));
In[913]:= qx4=k P4^(sigma-1) px4^-sigma;
In[914]:= qy4=k P4^(sigma-1) py4^-sigma by;
In[915]:= qf4=k P4^(sigma-1) (pf4 (1+t))^-sigma bf;
Percent Changes in Consumer Prices, With Efficiencies
In[916]:= ((px4-px0) 100)/px0
Out[916]= 13.1283
In[917]:= ((py4-py0) 100)/py0
Out[917]= 3.40513
In[918]:= ((pf4(1+t)-pf0 (1+t)) 100)/(pf0 (1+t))
Out[918]= 18.8927
In[919]:= ((P4-P0) 100)/P0
Out[919]= 12.8243
Percent Changes in Quantities and Employment, With Efficiencies
Domestic Shipments
In[920]:= ((qx4-qx0) 100)/qx0
Out[920]= -12.3155
In[921]:= ((qy4-qy0) 100)/qy0
Out[921]= 25.6146
Imports
In[922]:= ((qf4-qf0) 100)/qf0
Out[922]= -28.1234
Domestic Employment
In[923]:= (((qx4+qy4)-(qx0+qy0)) 100)/(qx0+qy0)
Out[923]= 6.64954
New Equilibrium Values without Merger, With Greenfield Investment
In[924]:= hc=Min[1.10,1+t];
In[925]:= mf5=mf0 hc;
In[926]:= my5=my0;
In[927]:= mx5=mx0;
In[928]:= P5=(px5^(1-sigma)+by py5^(1-sigma)+bf pf5^(1-sigma))^(1/(1-sigma));
In[929]:= sharex5=(px5/P5)^(1-sigma);
In[930]:= sharey5=(py5/P5)^(1-sigma) by;
In[931]:= sharef5=(pf5 /P5)^(1-sigma) bf;
In[932]:= EqnX5=px5==(px5-mx5) (sigma-(sigma-1) sharex5);
In[933]:= EqnY5=py5==(py5-my5) (sigma-(sigma-1) sharey5);
In[934]:= EqnF5=pf5==(pf5-mf5) (sigma-(sigma-1) sharef5);
In[935]:= FindRoot[{EqnX5,EqnY5,EqnF5},{px5,px0},{py5,py0},{pf5,pf0}]
Out[935]= {px5->0.992698,py5->0.992698,pf5->1.13461}
In[936]:= px6=px5/.%;
In[937]:= py6=py5/.%%;
In[938]:= pf6=pf5/.%%%;
In[939]:= P6=(px6^(1-sigma)+by py6^(1-sigma)+bf pf6^(1-sigma))^(1/(1-sigma));
In[940]:= qx6=k P6^(sigma-1) px6^-sigma;
In[941]:= qy6=k P6^(sigma-1) py6^-sigma by;
In[942]:= qf6=k P6^(sigma-1) pf6^-sigma bf;
Percent Changes in Consumer Prices, With Greenfield Investment
In[943]:= ((px6-px0) 100)/px0
Out[943]= -0.730197
In[944]:= ((py6-py0) 100)/py0
Out[944]= -0.730197
In[945]:= ((pf6-pf0 (1+t)) 100)/(pf0 (1+t))
Out[945]= -5.44909
In[946]:= ((P6-P0) 100)/P0
Out[946]= -3.20443
Percent Changes in Quantities and Employment, With Greenfield Investment
Domestic Shipments 
In[947]:= ((qx6-qx0) 100)/qx0
Out[947]= -6.61056
In[948]:= ((qy6-qy0) 100)/qy0
Out[948]= -6.61056
Imports
In[949]:= ((0-(qf0)) 100)/(qf0)
Out[949]= -100.
Domestic Employment
In[950]:= (((qf6+qx6+qy6)-(qx0+qy0)) 100)/(qx0+qy0)
Out[950]= 87.9527