Question

Problem 2. The firm expects that its production function in the next period will be given by Fe(K, L)-10 v KL. The firm employs 25 workers. The real interest rate equals 5% and the depreciation rate equals 20%. The price for the firm's products is 1 EUR while the price of capital goods is 10 EUR a) Find the user cost of capital. Find net investments, assuming that initially the firm has a capital stock of 88. Modify your answer to part (a), assuming there is a 10% tax on the firm's profits. b) The firm considers hiring additional workers. How would this decision affect your answer to part (a)?

Answer 1

A)

Real(user) cost of capital = (Pk/P) (r + δ )

Pk = price of capital = 10

P = general price level = 1

r = real interest rate = 5% = 0.05

δ = depreciation raten = 20% = 0.20

Hence, $R_{c} = (10/1)(0.05+0.20) = 2.5$

At this user cost of capital, ideal level of capital will be;

MPK (Marginal Product of Capital) = rental cost of capital

$MPK = 5K^{-1/2}L^{1/2}$ = 2.5

= $MPK = 5K^{-1/2}25^{1/2}$ = 2.5

= $K = 100$

Net Investment = Change in capital * price of capital good

Net Investment = (100 - 88 )* 10= 120 EUR.

B)The rental cost of capital is affected by taxes. A tax on corporate profit would discourage business investment. Cost of capital tends to rise with the tax rate.

As we can see in the equation of MPK; The greater the amount of labor employed the higher is the rental cost of capital.