A company has the following production function: Q = 2(KL)0.5 (please note this is to the...
A company has the following production function:
Q = 2(KL)0.5 (please note this is to the power 0.5)
Where L = Labour and K = Capital. The cost of labour per hour is K3 and the cost of capital is K42 per unit. The company has a budget of K588 available to spend on the two factors of production
a) Formulate the company’s optimization problem
b) Calculate the optimal input combination
c) Compute the output level associated with the optimal input combination
Homework Answers
A) optimization problem of firm,
Max Q=2(KL)^0.5 , given C(Q)=588
B) The optimal combination of inputs condition,
MPk/Pk=MPL/pL
√L/42√K=√K/3√L
L=14K{ optimal input combination given input prices}
Total cost=Pk*K+PL*L
588=42K+3*14K=42k+42K=84K
K=588/84=7
L=14*7=98
Option input combination:(K,L)=(7,98)
C) output associated with optimal input choice,
Q=2*√7*98=2√=2*7√14=14√14
Q=14√14=14*3.7=51.8
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