Consider the q-theory model of investment described in class.
(a) Characterize the effects on q, the capital stock and investment of a one-time unexpected increase in the real interest rate.
(b) Answer the previous question if the increase in the real interest rate were announced in advance.
(c)Now consider a firm attempting to decide whether and when to invest in a particular project. If the firms invents, it has to invest a fixed, ir- recoverable amount I. The value of the project V follows the following deterministic process: V = α0 +α1t. The firm discounts at the real interest rate r.
(d) Solve for the optimal time at which the firm should invest.
(e) How would an increase in the real interest rate affect the time to invest?
(f) Now suppose there are many such firms, each of which has a potential project; these firms only differ in that they discover the existence of these projects at different times. How would the aggregate amount of investment observed over any given time interval change in response to an increase in the real interest rate r?
(g) Compare your answer to the last part with your answer to part (a). Account for any differences in the response of investment to real interest rates.