2. An economy produces with the production function Y = F(K, L) = AK /$12/3. Population grows at 2% per year and A grows at 2% per year. The depreciation rate is 5% and the saving rate is 40%. The economy is in steady state.a. Dene ii. = A352. Show that the production function can be written as = 133 where ..Y_ "=3; ' ' AL and ii: AL' What Is the growth rate of A? h. 1lll'ilhat is the growth rate of each of the following in steady state: i, i 15L, Y, {- {fr U (hint: use the approximation that if X grows at yr: and Y grows at 9%,. then KY grows at life: + 9y] c. At what rate do wages and the capital rental rate grow? (hint: wage=MPL and rental rate=MPK] d. Find the steady state value of capital per effective worker