assume that the production function for a certain production process is given by

Question

assume that the production function for a certain production process is given by the cobb douglas production function Q=L^1.5 K^0.5

A) if the wage rate is 10 and the cost of capital is 20 what is the cost minimising input bundle to produce 200 units of output? illustrate this position on a n isocost isoquants diagram?

B) if K is fixed in the short run what are the minimum costs in the short run and long run of increasing output to 300 units? illustrate this position on a diagram showing the short run and long run expantion path > Explain the cost differences

Explanation / Answer

A) At cost minimizing output the following condition is met:

MRL/MRK = w/r

L^0.5 K^0.5 / L^1.5 K^-0.5 = 10/20

K/L = 10/20

or K = L/2

Put this value into production function:

Q = L^1.5 K^0.5

200 = L^1.5 (L/2)^0.5

L = 16 approximately

Hence K = L/2 = 8

Thus cost minimizing input combiination is 16L and 8K.

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