Question

Suppose a country produces two goods: wine and cloth. Suppose that each cask of wine always requires 4 labor units and 1 capital unit in its production and each bolt of cloth requires 2 and 5 units respectively of labor and capital. This is regardless of the factor prices.

(a) If wage and rental rate of capital each equal 100, what are the unit costs of wine and cloth?

(b) Suppose wage and rental rate of capital are both 110, what are the new unit costs of wine and cloth?

(c) Suppose wage is 120 and rental rate of capital is 105, what are the new unit costs of wine and cloth?

(d) Suppose wage is 90 and rental rate of capital is 120, what are the new unit costs of wine and cloth?

(e) Under perfect competition the unit cost of production must be equal to price. Therefore, each cost in parts (a) to (d) must be the same as the price of the good. (i) Plot Pw/ Pc (on the vertical axis) against w/r (on the horizontal axis), using the numbers you get from (a)-(d) above. How does the curve look like? (ii) Plot w/r (on the vertical axis) against L/K ratio (on the horizontal axis) of cloth and wine respectively. Please indicate the coordinates of all relevant points and intercepts so as to fully define the curve. How does the curve look like? (Hint: Note that the two factors are not substitutable here.)

(f) The Stolper-Samuelson Theorem states that “if the relative price of a good increases, then the real return to the factor used intensively in the production of that good increases, while the real return to the other factor decreases.” Using the results in parts (c) and (d), can you verify the Stolper-Samuelson Theorem? (Hint: You need to calculate how the values of r/Pc , r/Pw , w/Pc and w/Pw

Answer 1

Cost of a good = wL+rK

Where w = wage rate and r = rental rate

L = labor units used and K = units of capital used

One cask of wine requires 4 labor units and 1 capital unit.

That is, L=4 and K=1

So, cost of producing one cask of wine = 4w+r

One bolt of cloth requires 2 labor units and 5 capital units.

That is, L=2 and K=5

So, cost of producing one bolt of cloth = 2w+5r

1. w=r=100

cost of producing one cask of wine = 4(100)+100 = 500

cost of producing one bolt of cloth = 2(100)+5(100) = 700

2. w=r=110

cost of producing one cask of wine = 4(110)+110 = 550

cost of producing one bolt of cloth = 2(110)+5(110) = 770

3. w=120 and r=105

cost of producing one cask of wine = 4(120)+105 = 585

cost of producing one bolt of cloth = 2(120)+5(105) = 765

4. w=90 and r=120

cost of producing one cask of wine = 4(90)+120 = 480

cost of producing one bolt of cloth = 2(90)+5(120) = 780