Answer to Question #273130 in Macroeconomics for Abc

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. Further, the rate of adjustment of actual capital stock to desired level (λ) = 0.4 in the flexible accelerator model of investment. What will the rate of investment be in the first year after expected income changes?

Does your answer in ‘part c’ refer to gross or

Answer 1

(a)

The formula for desired capital stock$(k^•)$ :

$k^•=0.5(\frac{W}{R^k})Y$

where W is wage rate.

Y is 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 = 8.01 trillion.

(b)

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.

(c)

Change in the desired level of capital stock:

$=9.345-8.01=1.335$ trillion.