Question

In the long run in a perfectly competitive industry, price equals marginal cost and firms earn no economic profits. The following two equations describe this long-run situation for prices and costs, where the numbers indicate the amounts of each input (labor and land) needed to produce a unit of each product (wheat and cloth): P wheat = 60w + 40r P cloth = 75w + 25r If the price of wheat is initially 100 and the price of cloth is initially 100, what are the values for the wage rate, w, and the rental rate, r? What is the labor cost per unit of wheat output? Per unit of cloth? What s rental cost per unit of wheat? Per unit of cloth? The price of cloth now increases to 120. What are the new values for w and r (after adjustment to the new long-run situation)? What is the change in the real wage (purchasing power of labor income) with respect to each good? Is the real wage higher or lower “on average”? What is the change in the real rental rate (purchasing power of land income) with respect to each good? Is the real rental rate higher or lower “on average”? Relate your conclusions in part c to the Stolper-Samuelson theorem.

Answer 1

Given two price - cost equations for wheat and cloth in the long run

100 = 60w + 40r

100 = 75w + 25r

Since the prices for wheat and cloth are equal we can arrive at the following equation by equating the long run price -cost functions :

60w + 40r = 75w + 25r

=> 40r - 25r = 75w - 60w

=> 15r = 15 w

Therefore, r = w (Eq: 1)

[Substituting (Eq: 1) in any of the long run price cost equations, we get :]

100 = 60w + 40w   (r=w)

100= 100w

w = 100/100 = 1

Hence, r = 1   (r = w)

Labour cost per unit of wheat output = 60w = 60*1 = 60

Labour cost per unit of cloth output = 75w = 75 * 1 = 75

Rental cost per unit of wheat output = 40r = 40 * 1 = 40

Rental cost per unit of cloth output = 25r = 25 * 1 = 25

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Price of Cloth rises to 120

Therefore the new price - cost equation for cloth becomes : 120 = 75w + 25r

By subtracting cloth price-cost equation from wheat price-cost equation we get :

120-100 = 75w-60w -40r+25r

=> 20 = 15w -15r

Therefore, w = (20 + 15r)/15

Substituting for 'w' in the new price - cost equation for cloth :

120 = 75 (20 + 15r)/15 + 25r

120 = 100 + 75r + 25r

20 = 100r

r = 20/100 = 0.2

Substituting this value of r in the cloth's equation, we get :

120 = 75w + 25*0.2

120 = 75w + 5

115 = 75w

Therefore, w = 115/75 = 1.53333

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Change in real wage rate with respect to wheat = 60*1.53333 - 60*1 = 31.9998

Change in real wage with respect to cloth = 75*1.53333 - 75*1 = 39.999

Real wage is higher on an average in the new scenario due to price rise for cloth

Change in real rental rate with respect to wheat = 40*0.2 - 40*1 = -32

Change in real rental rate with respect to cloth = 25*0.2 - 25*1 = -20

Real rent is lower on an average in the new scenario due to price rise for cloth