Investment and its determinants. Suppose that the firm produces using only capital: Y = zK, Y = zK' with 0 < < 1. Recall that Kt1 = (1 )Kt + It, where 0 < < 1 is the depreciation rate. Hint: See a similar problem in the handout about the real intertemporal model with investment (section 2). (a) Write down the firms value V as the present value of current and future profits. Write down the firms maximization problem including objective function, constraints (if any), and choice variable(s). (b) Obtain the FOC(s). (c) Derive the investment function for the firm (solve for I as a function of the exogenous variables and parameters). (d) Show how investment depend on the real interest rate, future TFP, and the depreciation rate (r, z, ). Put differently, show the signs of dI/dr, dI/dz, and dI/d