PS1_Q.docx

(a) Y = A ¯ K 1 / 3 L 2 / 3 and Y = A ¯ K 3 / 4 L 1 / 4 (plot them on the same graph). (b) Y = K . (c) Y = K (d) Y = K − A ¯ L Problem 4: If the US GDP doubles every 10 years, then the growth rate of the US GDP is: a) 0.07 b) 0.035 c) 0.2 d) 0.025 Problem 5: Consider the following variation of the aggregate production function. Now firms must use oil M to produce output (in addition to labor and capital). The price of a unit of oil is p max Π f = AK α L β M γ − wL − rK − pM (a) Find a first-order condition for the firm’s demand for oil. To find the first-order condition for the firm's demand for oil, you need to maximize the firm's profit, which is given by the difference between revenue and cost. (b) What must be true about the parameters α , β , and γ if this production function exhibits constant returns to scale? A value of denotes a steady return to scale for α + β + γ .Exit Y doubles when all inputs (K, L, and M) are doubled. There is constant proportionality in the production function. For production functions, this is a typical supposition. (c) If the price of oil p rises, what would you expect to happen to carbon

(b) Find an algebraic expression for the steady state capital per worker. (c) What happens to steady state output and consumption after a positive productivity shock? Justify your response. Steady state output increases after increase in productivity because output depends positively on K and consumption also increase because consumption depends positively on output. (d) If the real wage equals the marginal product of labor, what is the growth rate of the real wage in steady state?