Answer to Question #221102 in Macroeconomics for Isaac mensah

Question

Suppose that the net investment flow is described by the equation I(t)=3t1/2 and that the initial capital stock, at time t = 0, is K(0). What is the time path of capital K?

If net investment is a constant flow at I(t)=1000 (Ghana Cedis per year), what will be the total net investment (capital formation) during a year, from t = 0 to t = 1?

If I(t)=3t1/2 (thousands of Ghana Cedis per year) – a nonconstant flow – what will be the capital formation during the time interval [1, 4], that is, during the second, third, and fourth years?

i)  Show that the Cobb-Douglas production

Q=AKαL1-α

       where Q is total output, K is capital stock, L is labour stock and A and are positive   constants, exhibit constant returns to scale.

    (ii) What returns to scale does Q=5K0.25L0.6 exhibit? 

Answer 1

Given: 

Rate of investment I(t)=3 t^1/2 

It is known that the net investment is the amount of money spent on capital by the company minus the rate of depreciation.

Let the capital asset be: K(t)

The rate of depreciation be 'd'.

Thus, the formula will be:

I(t) = K(t) - d

If t=0

I(0) = K(0) - d

3 (0)^1/2 = K(0) - d

0 = K (0) - d 

Thus, d = K(0)

Hence, for the time path of capital K is:

K(t) = I(t) + d

We know, I(t)= 3 t^1/2 and d = K(0)

K(t) = 3 t^1/2 + K(0)