Question

Using the Cobb- Douglas production function and the following data:

Output (Y) = $ 6 trillion, rental cost (rc) = 0.15, the share of capital in output (γ) = 0.4

Calculate the desired capital stock (K*)

Now suppose that Y is expected to rise to $ 7 trillion. What is the corresponding K*?

Suppose the capital stock was at its desired level before the change in the income was expected.

Answer 1

Solution:

The formula for desired capital stock (K*):

K* = 0.5($\frac{W}{R^{K} }$) Y

Where: W is the wage rate

             Y is the firm’s level of output

             R^K is the rental price of capital

K* = 0.5 ($\frac{0.4}{0.15 }$) 6 = 0.5 $\times$ 2.67 $\times$ 6 = 8.01 trillion

Desired capital stock (K*) = 8.01 trillion

 

When Y = 7 trillion

K* = 0.5 ($\frac{0.4}{0.15 }$) 7 = 0.5 $\times$ 2.67 $\times$ 7 = 9.345 trillion

Corresponding desired capital stock (K*) = 9.345 trillion

Change in the desired level of capital stock = 9.345 trillion - 8.01 trillion = 1.335 trillion