Please include all relevant work for each part, showing calculations along the way.

13. Consider again the social planner problem of the neoclassical growth model: 00 630- t max g 1_0_ {Ct,kt+1}$:u subject to C: + kt+1 = Aklt + (1 (5)13; where Q, and k, are positive, ,6 E (0, 1) and A > 1. The population is constant and all households have one unit of time at their disposal in every period. a. (5 points) Does the production function y, = Aktl, exhibit constant returns to scale? Show your work. b. (10 points) Use the Euler equation to derive the growth rate of consumption along the balanced growth path. What assumptions on the parameters are required for this growth rate to be positive? c. (10 points) Along the BGP, what are the growth rates of capital and output per capita? Explain your answer. d. (5 points) Income per capita in the U.S. grows at 2% per year and in Argentina at 1% per year. Suppose people in the U.S. and in Argentina have both logutility (a = 1) and discount the future according to the same 5. Furthermore, assume full depreciation, (I = 1. In the context of the model, how can one explain the differential growth rate in the U.S. and Argentina? I am looking for a precise numerical