Bertrand Model for New Entry of Subject Imports
D. Riker, 05/13/19 version
This partial equilibrium (PE) model of tariff changes when there is new entry of subject imports. The model is described in detail in Riker, D. An Industry-Specific Model with New Entry. USITC Economics Working Paper 2019-02-A.
  
The user can modify data inputs, elasticity values, and tariff rates 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[93]:= ClearAll[f];
Parameter Inputs
Elasticity of Substitution (Non-Nested CES)
In[94]:= sigma=4;
Initial Tariff Factor
In[95]:= td0=1;
In[96]:= tr0=1;
In[97]:= tn0=1;
Revised Tariff Factor
In[98]:= ts1=1;
In[99]:= td1=1;
In[100]:= tr1=1;
In[101]:= tn1=1;
Data Inputs: Initial Equilibrium Values
Values
In[102]:= vd0=50;
In[103]:= vr0=25;
In[104]:= vn0=25;
Normalized or Calculated Initial Equilibrium Values
Prices
In[105]:= pd0=1;
In[106]:= pr0=1;
In[107]:= pn0=1;
Market Shares
In[108]:= sd0=vd0/(vd0+vn0+vr0);
In[109]:= sn0=vn0/(vd0+vn0+vr0);
In[110]:= sr0=vr0/(vd0+vn0+vr0);
Calibration of Constant Marginal Costs
In[111]:= cd=pd0 (1+1/((sigma-1) sd0-sigma));
In[112]:= cr=pr0 (1+1/((sigma-1) sr0-sigma));
In[113]:= cn=pn0 (1+1/((sigma-1) sn0-sigma));
Imputation of Marginal Costs
In[114]:= cs=cr;
New Equilibrium Values
In[115]:= sd=(pd td1)^(1-sigma)/((pd td1)^(1-sigma)+(ps ts1)^(1-sigma)+(pr tr1)^(1-sigma)+(pn tn1)^(1-sigma));
In[116]:= ss=(ps ts1)^(1-sigma)/((pd td1)^(1-sigma)+(ps ts1)^(1-sigma)+(pr tr1)^(1-sigma)+(pn tn1)^(1-sigma));
In[117]:= sr=(pr tr1)^(1-sigma)/((pd td1)^(1-sigma)+(ps ts1)^(1-sigma)+(pr tr1)^(1-sigma)+(pn tn1)^(1-sigma));
In[118]:= sn=(pn tn1)^(1-sigma)/((pd td1)^(1-sigma)+(ps ts1)^(1-sigma)+(pr tr1)^(1-sigma)+(pn tn1)^(1-sigma));
In[119]:= FOCd=pd+(pd-cd) ((sigma-1) sd-sigma)==0;
In[120]:= FOCs=ps+(ps-cs) ((sigma-1) ss-sigma)==0;
In[121]:= FOCr=pr+(pr-cr) ((sigma-1) sr-sigma)==0;
In[122]:= FOCn=pn+(pn-cn) ((sigma-1) sn-sigma)==0;
In[123]:= FindRoot[{FOCd,FOCs,FOCr,FOCn},{pd,pd0},{ps,pr0},{pr,pr0},{pn,pn0}]
Out[123]= {pd->0.891652,ps->0.991457,pr->0.991457,pn->0.991457}
In[124]:= pd1=pd/.%;
In[125]:= ps1=ps/.%%;
In[126]:= pr1=pr/.%%%;
In[127]:= pn1=pn/.%%%%;
Percent Changes in Prices
% Change in the Price of Domestic Shipments
In[128]:= ((pd1-pd0) 100)/pd0
Out[128]= -10.8348
% Change in the Price of Type "r" Imports (reference group)
In[129]:= ((pr1-pr0) 100)/pr0
Out[129]= -0.854268
% Change in the Price of Type "n" Imports (non-subject, not in reference group)
In[130]:= ((pn1-pn0) 100)/pn0
Out[130]= -0.854268
Change in Value of Imports and Domestic Shipments
In[131]:= vs1=(vd0+vr0+vn0)*((ps1 ts1)^(1-sigma)/((pd1 td1)^(1-sigma)+(ps1 ts1)^(1-sigma)+(pr1 tr1)^(1-sigma)+(pn1 tn1)^(1-sigma)))
Out[131]= 22.8583
Change in the Value of Expenditure on Subject Imports
In[132]:= dvs=vs1-0
Out[132]= 22.8583
In[133]:= vd1=(vd0+vr0+vn0)*((pd1 td1)^(1-sigma)/((pd1 td1)^(1-sigma)+(ps1 ts1)^(1-sigma)+(pr1 tr1)^(1-sigma)+(pn1 tn1)^(1-sigma)))
Out[133]= 31.4252
Change in the Value of Expenditure on Domestic Shipments
In[134]:= dvd=vd1-vd0
Out[134]= -18.5748
In[135]:= vr1=(vd0+vr0+vn0)*((pr1 tr1)^(1-sigma)/((pd1 td1)^(1-sigma)+(ps1 ts1)^(1-sigma)+(pr1 tr1)^(1-sigma)+(pn1 tn1)^(1-sigma)))
Out[135]= 22.8583
Change in the Value of Expenditure on Reference Group Imports
In[136]:= dvr=vr1-vr0
Out[136]= -2.14174
In[137]:= vn1=(vd0+vr0+vn0)*((pn1 tn1)^(1-sigma)/((pd1 td1)^(1-sigma)+(ps1 ts1)^(1-sigma)+(pr1 tr1)^(1-sigma)+(pn1 tn1)^(1-sigma)))
Out[137]= 22.8583
Change in the Value of Non - Subject Imports
In[138]:= dvn=vn1-vn0
Out[138]= -2.14174