Start with the initial free trade equilibrium from Maple Trade Model #2, Problem 3, as modified below.  Note that there are four new exogenous variables (XSij - an export subsidy by country i for sector j, and ITij - an import tariff), all of which are multiplicative (e.g., 1+tariff rate).  Note also that utility is now total utility (TUi), not average.

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; XS11:=1.00; XS22:=1.00;
freetrade:= {
Q11=A11*(T11^0.5)*(L11^0.5),
Q12=A12*(T12^0.5)*(L12^0.5),
L11+L12=L1,
(P11*XS11)*0.5*Q11/L11=P12*0.5*Q12/L12,
C11/C12=P12/P11,
P11*C11+P12*C12=1000000,
TU1=(C11*C12)^0.5,
Q1=(P11*Q11 + P12*Q12)/((P11*P12)^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*XS22)*0.5*Q22/L22,
C21/C22=P22/P21,
P21*C21+P22*C22=2000000,
TU2=(C21*C22)^0.5,
Q2=(P21*Q21 + P22*Q22)/((P21*P22)^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, Q1,
 L21, L22, Q21, Q22, C21, C22, P21, P22, TU2, Q2, E });

1)  Draw a table, in Excel or by hand, with five columns labeled with numbers.  For the rows, list the following variables, in order:  Q11, C11, Q11-C11, C12, Q12, C12-Q12, C21, Q21, C21-Q21, Q22, C22, Q22-C22, P11, P12, P21, P22, E, Q1, Q2, TU1, and TU2.  Run the initial free trade equilibrium, calculate export and import quantities, and report your results in column (1).  Round off production and consumption variables to zero digits, prices and average utilities to two digits, and the exchange rate to three digits.

2)  Suppose that Country 1 decides to put a 25% ad-valorem tariff on its imports from Country 2, so that:

IT12:=1.25;

Report your results in column (2).  What are the marginal effects of the import tariff on both Country 1 and Country 2?

IT12:=1.25; IT21:=1.25;

Report your results in column (3).  What are the marginal effects of the import tariff on both Country 1 and Country 2?

IT12:=1.25; IT21:=1.25; XS11:=1.25;

Report your results in column (4).  What are the marginal effects of the import tariff on both Country 1 and Country 2?

IT12:=1.25; IT21:=1.25; XS11:=1.25; XS22:=1.25;

Report your results in column (5).  What are the marginal effects of the import tariff on both Country 1 and Country 2?

TU = TU1 + TU2

Then rank the total utility of the five cases.  Which is the first-best outcome, and which is second-best?  What is the worst outcome?