Question

Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which can be combined to produce Y units of output according to the following production function:

Answer 1

7)Y = 30 K + 10 L

The above production function represent a case of perfect substitute in production factors .

marginal product of capital = MPk = dY/ dk = 30

MPk/price of capital(r) = 30 /1000 = 0.03

marginal product of labour(w) = MPl.= dY/dl = 10

MPl/price of labour = 10/400 = 0.025

since MPk/r > MPl/w

firm will use all units of capital to produce 600 units of output

total output = 600

MPk = 30

so numbest of capital units required = 600/30 = 20

(answered one question as per policy )