(1} Recall the standard production function that we have been working with: Y = AK\" (\"11: Also recall that the marginal product of capital (MPK) and the marginal product of labor (MPL) are just the rst derivatives of the production function with respect to capital and to labor. Also recall that the steady-state level of k" is: 1 , 5;! m k _(n+5) Assume that the parameters 3, H, T: and a: do not change, but that A then rises, from, say, 2.00 to 2.02 (the actual values do not matter). (a) At the new steady state, is the MPK higher, lower, or the sarne'iI Show analytically (calculus), numerically (actual gures), or conceptually (prose). Then provide an intuition that explains the result. (b) At the new steady state, is the MPL higher, lower, or the same? Show analytically (calculus), numerically (actual gures), or conceptually (prose). Then provide an intuition that explains the result. (c) If A does not increase and none of the parameters change, explain why k and y will not increase. (Hint: Recall the concept of marginal product.) Would adding human capital (so that Y = AK\"(hL}1'\") change the result