Suppose that an economy's production function is given as Y=A·K2-L1/2, and the price of output, nominal...

Suppose that an economy's production function is given as Y=A·K2-L1/2, and the price of output, nominal wage rate, and the rental price of capital are given as P, W, and R, respectively.

i) Derive the demand for labor (Lº) as a function of real wage (W/P), using a representative firm's profit maximization. That is, solve the problem of Max [P·Y– (W-L + R:K)] for L.

(ii) If the capital stock doubles (from 'K' to '2K'), how much is the demand for labor affected?

(iii) If the productivity (or technology) parameter doubles (from 'A' to '2A'), how much is the demand for labor affected?

Solutions

Expert Solution

Solution:

(i) Labor Demand function

L° = (1/4)* [(W/P)^(2/3)] * [ R^2/(AW^2)]^ (2/3)

(ii) New labor demand is 0.3968 times of L°

(iii) New labor demand is 0.6299 times of L°

Rahul Sunny answered 1 year ago

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