(a) Write down the rm's optimization problem. (b) Substitute the law of motion for capital Kt+1 = (1 6) Kt + It into the optimiza tion problem for I1 and I2 to write the rm's problem as an optimization problem for with respect to K2 and K3. (0) Write the rm's rst order condition with resPect to K2 and K3 in terms of Tobin's Q) '11 = 1 +I1353 T, 62,, 63 and (12. (d) Substitute in to write '11 as a function of I92, I93, 6, and r. (e) Assume 6'3 increases. Does investment in period one rise or fall today relative to the case where 6 does not rise in a year? Explain intuitively and contrast this with a world in which there are no adjustment costs. 3. (BBC Lecture 1) RBC Model With Only Capital: The economy consists of a unit mass of households and a unit mass of rms and lasts two periods. There is no uncertainty. 0 Households have no initial wealth and receive income Y1 in period 1 and Y2 in period 2, where Y1 and 1'2 are output from rms that they own. They also own shares of the rms and receive the dividends. They take the interest rate r: as given, and the price of the consumption good is 1. They maximize U(C'1)i15 U(C'2) where U" > 0 and U\"