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Using the Specific-Factors Model Suppose that the marginal product of labor in sector X is described...

Using the Specific-Factors Model

Suppose that the marginal product of labor in sector X is described by MP LX = 2000−2LX and the marginal product of labor in sector Y is described by MP LY = 1000 − LY . The price of X and the price of Y in autarky are both $1. The total supply of labor is 1000. Given this information:

3. What is the equilibrium labor allocation to industry X?

4. What is the equilibrium labor allocation to Y ?

5. What is the equilibrium wage?

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Answer #1

Given that LX + LY = 1000 and that real and nominal wage rates are same (price is $1), we have equal wage rates

at equilibrium. Use the fact that MPL = wage rate and that LY = 1000 - LX, we have

2000 - 2LX = 1000 - LY

2000 - 2LX = 1000 - 1000 + LX

2000 = 3LX

LX = 667 and LY = 333.

Wage rate = 2000 - 2*667 = $667 approximately

a) 667 units

b) 333 units

c) $667 per unit of labor

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