Question

Problem 2. The firm expects that its production function in the next period will be given by Fe (KL) 10VKL. 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 1O EUR 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. a) 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.