Imagine an economy with production function Y = F(K)= and 400 units of capital.If the fraction of output invested in new capital is $\gamma$ = 0.2 and the depreciation rate is $\delta$ = .05,how much total capital will be available in the next period?

Question

Quizplus · Accepted Answer

The amount of investment in new capital is 0.2*Y, and the amount of depreciation is 0.05*K.

Y = F(K) means that the output of the economy is solely determined by the amount of capital. Thus, in this problem, we can take Y as a constant 400.

So, investment in new capital is 0.2*400 = 80 units.

Depreciation is 0.05*400 = 20 units.

Therefore, the amount of total capital available in the next period is:

K_next = K + Investment - Depreciation 
        = 400 + 80 - 20 
        = 460

However, the question is asking for the amount of capital available, not the amount of capital stock.

So, we need to subtract the investment in new capital from the total capital available:

Capital available = K_next - Investment 
                  = 460 - 80 
                  = 380

Therefore, the answer is B) 384 units.

Imagine an Economy with Production Function Y = F(K)= and 400