Question

Yt= At.[root Kt] and  Π1 = Y1 − I

Suppose the firm increases its investment by one unit. Describe in words and equations (i.e. without calculating an actual number) the change in first period output, first period profits, second period output and second period profits.

Answer 1

........................................(1)

.............................................(2)

....................................(3)

....................................(4)

A unit increase in investment from

i.e

..............................................................(5)

It results in (refer eqn 4) ....................................(6)

Y(t) would remain unchanged as K(t) remains unchanged because K(t) is dependent on the Investments made in period t-1.

Hence period 1 output would remain unchanged.

.............................................................(7)

An increase in the investment in period t by 1 unit results in a decline in profits by 1 unit as Y(t) is constant and an increase in the I(t) by 1 unit results in a decline in period 1 profits by 1 unit.(refer equation 2)

Second period output would increase due to rise in K(t+1) by one unit refer(6)

Also,

..........(8)

So,there would be change in period's 2 level of output since it is dependent on K(t+1) and a rise in it would result in an increase in Y(t+1).

.................(9)

There would be a rise in the profits of the firm in period 2 due to rise in Y(t+1)

Hence a rise in investment by a unit would result in decline in the profits in the current period and results in no change in the level of Current output produced ,but it results in both higher profits and higher outputs in period 2