Start with the initial free trade equilibrium from the previous homework.

Free Trade Equilibrium:

restart;
A11:=200; A12:=200; T11:=150; T12:=50; L1:=200;
A21:=100; A22:=100; T21:=50; T22:=150; L2:=400;
IT12:=1.00; IT21:=1.00;
freetrade:= {
Q11=A11*(T11^0.5)*(L11^0.5),
Q12=A12*(T12^0.5)*(L12^0.5),
L11+L12=L1,
P11*0.5*Q11/L11=P12*0.5*Q12/L12,
C11/C12=P12/P11,
P11*C11+P12*C12=1000000,
TU1=(C11*C12)^0.5,
Q21=A21*(T21^0.5)*(L21^0.5),
Q22=A22*(T22^0.5)*(L22^0.5),
L21+L22=L2,
P21*0.5*Q21/L21=P22*0.5*Q22/L22,
C21/C22=P22/P21,
P21*C21+P22*C22=2000000,
TU2=(C21*C22)^0.5,
C11+C21=Q11+Q21,
C12+C22=Q12+Q22,
P11*(Q11-C11)-E*P22*(C12-Q12)=0,
E*P21=P11*IT21,
P12=E*P22*IT12 };
freetraderesult:=solve(freetrade,
{L11, L12, Q11, Q12, C11, C12, P11, P12, TU1,
 L21, L22, Q21, Q22, C21, C22, P21, P22, TU2, E });

1)  What is the "optimal" tariff for Country 1?  Starting with Case 1 (IT12:=1.00, so the tariff rate is 0%) and Case 2 (IT12:=1.25, so the tariff rate is 25%), draw a graph with TU1 on the vertical axis and the tariff rate on the horizontal.  Plot the values of TU1 for tariff rates of 100% (IT12:=2.00), 200% (IT12:=3.00), and 300% (IT12:=4.00).  Then try to find the tariff rate that maximizes TU1, and show each of your trial solutions on your graph.  Getting within 10% of the true solution is fine.

2)  Draw a Prisoner's Dilemma diagram, with Country 1's choice of either no tariff or the "optimal" tariff in the rows, and Country 2's choice of either no tariff or the "optimal" tariff in the columns.  Run the above equations in Maple for each, using your optimal tariff rate from #1 above, and show the solutions for both TU1 and TU2 in each of the four cells.  Adding up total utility for both countries, which cell is the social optimum, and which is the worst outcome?  If each country is only concerned with maximizing its own utility, what is each country's dominant strategy, and what is the Nash equilibrium?
 

END