Question

Capital is the specific factor of sector X and land is the specific factor of sector Y . The marginal product of labor in sector X and that in sector Y are, respectively, given by MPLX = 150 − LX and MPLY = 300 − LY . This economy (Home) which is a small open economy has a comparative advantage in good Y and engages in free trade. Prices of good X and good Y under free trade are, respectively PX = 1 and PY = 1. The labor endowment, capital endowment and land endowment in Home are, respectively, 240, 100 and 60.

Suppose that an ad valorem import tariff, the rate of which is 100%, is imposed in Home (assume PX = PY = 1 under free trade).

1. How many workers does the tariff increase in the import sector?

2. Compute the wage rate with the tariff.

3. Compute the price of capital (i.e., the rental rate on capital) with the tariff.

4. Choose the correct statement(s).

a. capital owners gain from the tariff

b. land owners gain from the tariff

Answer 1

1:

under free trade the number of workers is given by

$Py × MPLy = Px × MPLx$

under free trade $Px = Py = 1$

so $MPLy = MPLx$

$300 - Ly = 150 - Lx$

total labor endowment is equal to 240 so,

$Lx + Ly = 240\\ Ly = 240 - Lx.\\ putting\space Ly = 240 - Lx\\ 300 - (240 - Lx) = 150 - Lx\\ 300 - 240 + Lx = 150 - Lx\\ 60 + Lx = 150 - Lx\\ 2Lx = 150 - 60\\ 2Lx = 90\\ Lx = 45$

before the tariff the number of workers in import sector was 45.

After tha tariff the price of imported good becomes 2Px since tariff is 100%.

So now the wage equalization equation becomes,

$2Px × MPLx = Py × MPLy\\ Px = Py = 1\\ 2 MPLx = MPLy\\ 2(150 - Lx) = 300 - Ly\\ putting\\space Ly = 240 - Lx\\ 2(150 - Lx) = 300 - (240 - Lx)\\ 300 - 2Lx = 300 - 240 + Lx\\ 300 - 2Lx = 60 + Lx\\ 300 - 60 = 2Lx + Lx\\ 240 = 3Lx\\ Lx = 80$

 after the tariff the number of workers in import sector becomes 80.

$= 80 - 45\\ = 35$

So increase in number of workers in import sector after the tariff is equal to 35

2:

The wage rate with the tariff will be

$= 2MPLx = 2 (150 - Lx)$

lx=80 after tariff

$= 2 (150 - 80)\\ = 2 × 70\\ = 140$

 the wage rate after the tariff will be 140.

3:

 In specific factor model the profit = 0, so total revenue is distributed to the factors of production.

Total output of X will be $= \int MPLx\Delta x$

$= \int(150 - Lx) \Delta x$

$= 150Lx - Lx^\frac{2}{2}\\ putting \space Lx = 80\\ X = 150×80 - (80)^\frac{2}{2}\\ X = 12000 - 3200\\ X = 8800$

price of good X = 2.

So total revenue will be $= 2 × 8,800 = 17,600$

the wage rate after the tariff is = 140 and the total labor employed in the production of X = 80.

Total wage bill will be == wage rate × labor employed

$= 140 × 80 = 11,200$

Total revenue = total wage bill + total rental cost of capital

$17,600 = 11,200 + total\space rental\space cost\space of\space capital\\ 17,600 - 11,200 =total\space rental\space cost\space of\space capital\\ = 6,400$

rental rate of capital = total rental cost of capital$\div$ capital endowment

capital endowment = 100.

Rental rate of capital$= \frac{6,400}{100}=64$

hence the rental rate of capital with the tariff is equal to 64.

4:

correct statement is a. capital owners gain from the tariff.

 The capital owners gain from the tariff because the price of good X has increased capital being the specific factor.