(a) Write down the firm's optimization problem. (b) Substitute the law of motion for capital Kt+1 = (1 ) Kt + It into the optimization problem for I1 and I2 to write the firm's problem as an optimization problem for with respect to K2 and K3. (c) Write the firm's first order condition with respect to K2 and K3 in terms of Tobin's Q, q1 = 1 + I1, , r, 2,, 3 and q2. (d) Substitute in to write q1 as a function of 2, 3, , and r. (e) Assume 3 increases. Does investment in period one rise or fall today relative to the case where does not rise in a year? Explain intuitively and contrast this with a world in which there are no adjustment costs