The following two equations describe this long-run situation for prices and costs in wheat and cloth production The coefficients indicate the amounts of each input (land and labor) needed to produce a bushel of wheat or a yard of cloth. r is the rental price of land and wis the wage. Puheat=2r + lw Pelech = 1r +3w There are two countries, A and B. Country A is large and Country B is small. Suppose that in Country A, Pwheat = $25, Path=$25,r=$10, and w=$5.

a. In Country B, Pwless = $30 and Peloth = $20 under autarky. What are the long-run equilibrium values of r and w?

b. Suppose that once trade opens, the prices of the two goods in Country B are Puheat $27.5 and Peth $22.5. What are the long-run equilibrium values of r and w?

c. In this example, do factor prices tend to converge with trade? Does trade fully equalize factor prices?

answers:

a. We will solve the two equations in two variables to determine the r and w in country B under autarky in part a with given autarky prices and with prices after trade in part b. Pwheat=2r+1w => 30= 2r+1w............(1)

Pcloth= 1r+3w => 20= 1r+3w.........(2)

From (1), we get w= 30-2r

Put this into (2)

20= 1r +3(30-2r) => 20= 1r + 90-6r => 20-90 = - 5r

r= - 70/-5 => r= 14

Putting value of r back in w= 30-2r

We get, w=30-2*14 => w=30-28 => w=2.

Thus, w=2 and r=14 in autarky.

b. Now the equations will be as follows -

Pwheat= 2r+1w => 27.5 =2r+w....... (1)

Pcloth=1r+3w => 22.5 = 1r + 3w........(2)

From (1) we get, w= 27.5 - 2r

Putting this into (2) we get

22.5 =1r +3(27.5 - 2r) => 22.5= 1r + 82.5 - 6r

22.5-82.5 = - 5r => - 60= - 5r => r= - 60/-5 => r = 12

Putting this back into the w = 27.5-2r

We get, w = 27.5 - 2*12=> w=27.5-24 => w= 3.5

Thus, after trade, r=12 and w =3.5

c. From the above calculations, we can see that after trade the factor prices in country B is moving towards that of country A. The factor prices, however have not fully equalised.

With trade, the factor prices across countries would tend to equalize or at least converge for sure.