Consider an individual firm making decisions with respect to current employment of labor for the period (t,t+h), n(t,t+h), and the employment of labor and capital for the periods (t+zh, t + (z+i)(R), z=1,2,3--------- denoted by n(t +zh)t) and k(t+(z=1)h,t), respectively. assume no costs of adjusting capital (4=0). let output in period (t+zh), l=1,2.........., be denoted by y(t+zh,t) where y(t+zh,t) = f(n (t+zh,t), k(t+(z-1)h,t) the current capital stock is then k(t,t) = k(t). the total (normal) expected dividends time t+zh, D(t+zh,t), z=1,2.....) depends upon the choice of the employment of inputs and the expected nominal prices of output, labor, stocks and bonds, these prices are denoted respectively by p(t + zh, t), w(t + zh,t), pe(t+zh,t) and pb(t+zh,t), z=1,2....... the number of stocks and bonds issued in period (t+zh,t), z=0,1,2....., where s(t,t) = s(t) and Bf(t,t) = Bf(t)
a. Define the price of bonds and equity shares expected at time (t+h). indicate how successively assuming static expectations on the interest rate, then on the expected rate of change in the aggregate price level, then on the number of equity shares and then on the real payments by firms to bonds and equity share holders alters the form of Pe(t+h,t) and Pb(t+h,t).
b. Define the necessary condition w.r.t n(t+h,t), n(t+zh,t) and k(t+h,t) for the maximization of the expected value of the s(t) shares at time t+h. assuming any changes in capital are financed by bonds.
C. From part b, obtain the comparative static results for a change in the interest rate, r(t+zh,t) and the expected rate of change in the aggregate price level, II (t+zh,t).
d. Concerning your result in part C, do changes in future interest rates, future expected rates of change in the aggregate price level of the existing capital stock effect the demand for capital at time t+h? would 4=0 alter these conclusions? do an of these valuables affect the real net investment at time t,th?
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