Suppose Tobin'sq model is given by the following two equations.

(1) qt=rqt+1MPKt

(2)qt=1+2kt

In the above equations,q,r,k,MPK represents Tobin's q, interest rate, capital stock, and marginal product of capital, respectively, and the interest rate is an exogenous variable. Also, the production function of this company is given as y=k0.5.

(a) Under the given interest rate and production technology, all adjustments have been made and no more adjustments are needed (q=k=0). Find the value ofq,k,MPK in the steady state when the value of the interest rater is 5.

(b) Suppose that the firm stays in a steady state in the same condition as in (a), and then the interest rate suddenly drops from 5 to 4.5 at t = 1 and continues. Using Tobin'sq theory above, find the value ofq,k in the period t=1 immediately after interest rate decline and the period t=2 after it.

(c) If there is no adjustment cost for investment, indicate how the two equations representing Tobin'sq model above differ and explain the intuitive meaning of the changed equations.