Question

Macroeconomics:

Equate the marginal cost and marginal benefit of additional investment to find the optimal level of capital for the second period as a function of productivity, the de- preciation rate and the interest rate. Use the numbers for R, d and productivity to calculate the second period level of output and profits.

I'm a little confused because I thought when we equate MC(I) AND MB(I) we get the optimal level of investment??

Answer 1

Mathematically, choosing I(optimal level of investment) is equivalent to choosing K' as I= K'− (1 − d)K - from the capital accumulation equation

Like you said, current investment (I): MB(I) = MC(I)

MB(I) = MPK'+1−d / 1+r and MC(I) = 1 since one unit of output costs 1 (numeraire) and can be used for investment I

⇒ optimal investment is such that

MPK'+1−d / 1+r = 1

MPK' =d+r

additional output = user cost of capital

Please remember that,

K'= −1 + ∂Y'/∂K' +1−d /1+r = 0 ⇒ MPK' − d = r which is the same expression we got before.