Import Stockpiling & Anticipated Tariff Changes
D. Riker, 08/05/19
This sector-specific partial equilibrium (PE) model quantifies the reaction of imports to an anticipated future tariff increase. If it is economical to stockpile, there will be a surge of imports with the announcement of a future tariff increase and a magnified decline in imports after the tariff increase occurs. This version of the model has THREE sources of supply: domestic production, imports subject to the tariff policy change, and imports not subject to the tariff policy change. There are three periods in the model: an initial period prior to the announcement of the future tariff change (period 0), a second period when the future tariff change is announced (period 1), and a final period when the new tariff rate is imposed permanently (period 2). The model only addresses the possibility of stockpiling the subject imports, not non-subject imports or the domestic good. Consumers have CES preferences for foreign and domestic products, and there is perfect competition in the product market within each period.  There is also a user-specified period 2 demand shift shock in the model.

The user inputs initial expenditures on the foreign and domestic products in the initial period, the initial and new tariff rate, elasticity parameters, time cost of money, and ad valorem storage costs. The user can modify data inputs in the simulation by changing the values in the ORANGE - shaded lines in the notebook below. 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[1]:= ClearAll[f];
Inputs
Elasticity of Substitution 
In[2]:= sigma=4;
Total Price Elasticity of Demand for the Sector
In[3]:= eta=-1;
Supply Elasticity of Domestic Shipments
In[4]:= ed=2;
Supply Elasticity of Subject Imports
In[5]:= es=5;
Supply Elasticity of Non-Subject Imports
In[6]:= en=5;
Initial Ad Valorem Tariff on Subject Imports in Periods 0 and 1
In[7]:= ts0=0;
New Ad Valorem Tariff in Period 2
In[8]:= ts2=0.25;
Expenditures
In[9]:= vdomestic=50;
In[10]:= vsubject=25;
In[11]:= vnonsubject=25;
Ad Valorem Carrying (or Storage) Costs
In[12]:= cc=0.05;
Interest Rate
In[13]:= r=0.05;
Anticipated Exogenous Rate of Growth  in Market Demand between Period 1 and Period 2 (could be positive or negative)
In[14]:= gr=-0.10;
Hidden Sections
Calibration Based on Data for the Initial Period
In[15]:= vd0 = vdomestic/vdomestic;
In[16]:= vs0 = vsubject/vdomestic;
In[17]:= vn0 = vnonsubject/vdomestic;
Prices
In[18]:= pd0=1;
In[19]:= ps0=1;
In[20]:= pn0=1;
Quantities
In[21]:= qd0=vd0/pd0;
In[22]:= qs0=vs0/(ps0 (1+ts0));
In[23]:= qn0=vn0/pn0 ;
In[24]:= ad=qd0 pd0^-ed;
In[25]:= as=qs0 ps0^-es;
In[26]:= an=qn0 pn0^-en;
In[27]:= bs = (vs0 (ps0/pd0)^(1-sigma))/vd0;
In[28]:= bn = (vn0 (pn0/pd0)^(1-sigma))/vd0;
In[29]:= P0=(pd0^(1-sigma)+bs (ps0(1+ts0))^(1-sigma)+bn pn0^(1-sigma))^(1/(1-sigma));
In[30]:= k = qd0 P0^(-sigma-eta) pd0^sigma;
In[31]:= k2=k (1+gr);
Scenario NNY (stockpiling S only)
Period 2 with new tariff
In[32]:= P2=(pd2^(1-sigma)+bs (ps2 (1+ts2))^(1-sigma)+bn (pn2 )^(1-sigma))^(1/(1-sigma));
In[33]:= EqnD2=ad pd2^ed==(k2 P2^(sigma+eta))/pd2^sigma;
In[34]:= EqnS2=as ps2^es+zs==(bs k2 P2^(sigma+eta))/(ps2 (1+ts2))^sigma;
In[35]:= EqnN2=an pn2^en==(bn k2 P2^(sigma+eta))/(pn2 )^sigma;
Period 1
In[36]:= P1=(pd1^(1-sigma)+bs (ps1 (1+ts0))^(1-sigma)+bn pn1^(1-sigma))^(1/(1-sigma));
In[37]:= EqnD1=ad pd1^ed==(k P1^(sigma+eta))/pd1^sigma;
In[38]:= EqnS1=as ps1^es-zs==(bs k P1^(sigma+eta))/(ps1 (1+ts0))^sigma;
In[39]:= EqnN1=an pn1^en==(bn k P1^(sigma+eta))/pn1^sigma;
Arbitrage condition that the expected return to period 1 production is the same with immediate sale or stockpiled until period 2
In[40]:= EqnArbS=ps1==(ps2 (1+ts2) (1-cc))/(1+r);
Solve
In[41]:= FindRoot[{EqnD1,EqnS1,EqnN1,EqnD2,EqnS2,EqnN2,EqnArbS},{pd1,pd0},{ps1,ps0},{pn1,pn0},{pd2,pd0},{ps2,ps0},{pn2,pn0},{zs,0}]
Out[41]= {pd1->1.00134,ps1->1.00722,pn1->1.00089,pd2->0.991178,ps2->0.890592,pn2->0.99411,zs->0.0285583}
Assign
In[42]:= pd1nny=pd1/.%;
In[43]:= ps1nny=ps1/.%%;
In[44]:= pn1nny=pn1/.%%%;
In[45]:= pd2nny=pd2/.%%%%;
In[46]:= ps2nny=ps2/.%%%%%;
In[47]:= pn2nny=pn2/.%%%%%%;
In[48]:= zsnny=zs/.%%%%%%%
Out[48]= 0.0285583
In[49]:= qd1nny=ad pd1nny^ed
Out[49]= 1.00269
In[50]:= qs1nny=as ps1nny^es
Out[50]= 0.518305
In[51]:= qn1nny=an pn1nny^en
Out[51]= 0.50224
In[52]:= qd2nny=ad pd2nny^ed
Out[52]= 0.982433
In[53]:= qs2nny=as ps2nny^es
Out[53]= 0.280133
In[54]:= qn2nny=an pn2nny^en
Out[54]= 0.485447
Indicator for whether this scenario applies
In[55]:= ScenarioNNY=If[zsnny>0 ,1,0]
Out[55]= 1
Scenario NNN (no stockpiling from any source)
Period 2 with new tariff
In[56]:= P2=(pd2^(1-sigma)+bs (ps2 (1+ts2))^(1-sigma)+bn (pn2 )^(1-sigma))^(1/(1-sigma));
In[57]:= EqnD2=ad pd2^ed==(k2 P2^(sigma+eta))/pd2^sigma;
In[58]:= EqnS2=as ps2^es==(bs k2 P2^(sigma+eta))/(ps2 (1+ts2))^sigma;
In[59]:= EqnN2=an pn2^en==(bn k2 P2^(sigma+eta))/(pn2 )^sigma;
Period 1
In[60]:= P1=(pd1^(1-sigma)+bs (ps1 (1+ts0))^(1-sigma)+bn pn1^(1-sigma))^(1/(1-sigma));
In[61]:= EqnD1=ad pd1^ed==(k P1^(sigma+eta))/pd1^sigma;
In[62]:= EqnS1=as ps1^es==(bs k P1^(sigma+eta))/(ps1 (1+ts0))^sigma;
In[63]:= EqnN1=an pn1^en==(bn k P1^(sigma+eta))/pn1^sigma;
Solve
In[64]:= FindRoot[{EqnD1,EqnS1,EqnN1,EqnD2,EqnS2,EqnN2},{pd1,pd0},{ps1,ps0},{pn1,pn0},{pd2,pd0},{ps2,ps0},{pn2,pn0}]
Out[64]= {pd1->1.,ps1->1.,pn1->1.,pd2->0.992928,ps2->0.90131,pn2->0.99528}
Assign
In[65]:= pd1nnn=pd1/.%;
In[66]:= ps1nnn=ps1/.%%;
In[67]:= pn1nnn=pn1/.%%%;
In[68]:= pd2nnn=pd2/.%%%%;
In[69]:= ps2nnn=ps2/.%%%%%;
In[70]:= pn2nnn=pn2/.%%%%%%;
In[71]:= qd1nnn=ad pd1nnn^ed
Out[71]= 1.
In[72]:= qs1nnn=as ps1nnn^es
Out[72]= 0.5
In[73]:= qn1nnn=an pn1nnn^en
Out[73]= 0.5
In[74]:= qd2nnn=ad pd2nnn^ed
Out[74]= 0.985906
In[75]:= qs2nnn=as ps2nnn^es
Out[75]= 0.297399
In[76]:= qn2nnn=an pn2nnn^en
Out[76]= 0.48831
Assign the Relevant Scenario
In[77]:= Fraction=ScenarioNNY *( zsnny*100)/qs1nny+(1-ScenarioNNY )*0;
In[78]:= pd1hat=ScenarioNNY*((pd1nny-pd0) 100)/pd0+(1-ScenarioNNY )*((pd1nnn-pd0) 100)/pd0;
In[79]:= ps1hat=ScenarioNNY*((ps1nny-ps0) 100)/ps0+(1-ScenarioNNY )*((ps1nnn-ps0) 100)/ps0;
In[80]:= pn1hat=ScenarioNNY*((pn1nny-pn0) 100)/pn0+(1-ScenarioNNY )*((pn1nnn-pn0) 100)/pn0;
In[81]:= qd1hat=ScenarioNNY*((qd1nny-qd0) 100)/qd0+(1-ScenarioNNY )*((qd1nnn-qd0) 100)/qd0;
In[82]:= qs1hat=ScenarioNNY*((qs1nny-qs0) 100)/qs0+(1-ScenarioNNY )*((qs1nnn-qs0) 100)/qs0;
In[83]:= qn1hat=ScenarioNNY*((qn1nny-qn0) 100)/qn0+(1-ScenarioNNY )*((qn1nnn-qn0) 100)/qn0;
In[84]:= pd2hat=ScenarioNNY*((pd2nny-pd1nny) 100)/pd1nny+(1-ScenarioNNY )*((pd2nnn-pd1nnn) 100)/pd1nnn;
In[85]:= ps2hat=ScenarioNNY*((ps2nny-ps1nny) 100)/ps1nny+(1-ScenarioNNY )*((ps2nnn-ps1nnn) 100)/ps1nnn;
In[86]:= pn2hat=ScenarioNNY*((pn2nny-pn1nny) 100)/pn1nny+(1-ScenarioNNY )*((pn2nnn-pn1nnn) 100)/pn1nnn;
In[87]:= cps2hat=ScenarioNNY*((ps2nny*(1+ts2)-ps1nny*(1+ts0)) 100)/(ps1nny*(1+ts0))+(1-ScenarioNNY )*((ps2nnn*(1+ts2)-ps1nnn*(1+ts0)) 100)/(ps1nnn*(1+ts0));
In[88]:= qd2hat=ScenarioNNY*((qd2nny-qd1nny) 100)/qd1nny+(1-ScenarioNNY )*((qd2nnn-qd1nnn) 100)/qd1nnn;
In[89]:= qs2hat=ScenarioNNY*((qs2nny-qs1nny) 100)/qs1nny+(1-ScenarioNNY )*((qs2nnn-qs1nnn) 100)/qs1nnn;
In[90]:= qn2hat=ScenarioNNY*((qn2nny-qn1nny) 100)/qn1nny+(1-ScenarioNNY )*((qn2nnn-qn1nnn) 100)/qn1nnn;
Summary of Economic Effects
Fraction of  subject imports produced in period 1 that are stockpiled until period 2 (%)
In[91]:= Fraction
Out[91]= 5.50994
price of domestic shipments (% Change)
In[92]:= pd1hat
Out[92]= 0.134162
producer price of subject imports (% Change)
In[93]:= ps1hat
Out[93]= 0.721702
producer price of non-subject imports (% Change)
In[94]:= pn1hat
Out[94]= 0.0894216
quantity of domestic shipments (% Change)
In[95]:= qd1hat
Out[95]= 0.268505
quantity of subject imports (% Change)
In[96]:= qs1hat
Out[96]= 3.66097
quantity of non-subject imports (% Change)
In[97]:= qn1hat
Out[97]= 0.447908
Effects in period 2 with stockpiling
price of domestic shipments (% Change)
In[98]:= pd2hat
Out[98]= -1.01504
producer price of subject imports (% Change)
In[99]:= ps2hat
Out[99]= -11.5789
consumer price of subject imports (% Change)
In[100]:= cps2hat
Out[100]= 10.5263
producer price of non-subject imports (% Change)
In[101]:= pn2hat
Out[101]= -0.677844
quantity of domestic shipments (% Change)
In[102]:= qd2hat
Out[102]= -2.01978
quantity of subject imports
In[103]:= qs2hat
Out[103]= -45.9522
quantity of non-subject imports
In[104]:= qn2hat
Out[104]= -3.34358