MACROECONOMIC THEORY IV ECO6120 prof. Francesca Rondina Winter 2019 HOMEWORK 4 – due by 4pm on Friday, February 8th, 2019. (30 points) Consider two…

Any help will be greatly appreciated. This is due on the February 8th if anyone can solve these questions before that will be great.
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MACROECONOMIC THEORY IV — ECO6120prof. Francesca RondinaWinter 2019 HOMEWORK 4 – due by 4pm on Friday, February 8th, 2019. Instructions – You can bring your assignment to Class, or slide it under the door of my office (F55 9058), or send it to me by email. (30 points) Consider two countries, Country A and Country B. You know that both countries produce output according to the following Cobb—Douglas production function:y. = K3” (MW/3 (1) where Y: is aggregate output, Kg is aggregate capital, and AtLt is aggregate effective labor. You know that inboth countries, A: is growing at the rate of 3% (g = 0.03), L is growing at the rate of 1% (n = 0.01), and thatwe can write: At = Aoegt and L, 2 L061”. You also know that the depreciation rate is zero (5 = 0) in both countries. Assume that Country A operates according to the Solow model, with a constant saving rate equal to 16%(s = 0.16). On the other hand, assume that Country B operates according to the Ramsey—Cass—Koopmansmodel. In Country B, you know that the utility function has the usual CRRA form, with coefficient of relativerisk aversion 9 = 0.75 and discount rate p = 0.9. You know that all the assumptions of the Solow model hold in Country A and that all the assumptions of the Ramsey—Cass—Koopmans model hold in Country B. a. (12 points) Use (1) to write the production function in terms of capital per effective worker: y: = f(k,g), Y Kwhere y: 2 TL and kg = fl. i. Consider Country A. Find: the steady state level of capital per effective worker kt (call this value k2), thesteady state level of output per effective worker yt (call this value 112), and the steady state level of consumptionper effective worker ct (call this value CE). Show your work. ii. Consider Country B. Find: the steady state level of capital per effective worker kt (call this value kg), thesteady state level of output per effective worker 91 (call this value 35,), and the steady state level of consumptionper effective worker ct (call this value 073). Show your work. b. (12 points) Assume that Country A and Country B are currently both operating at their respective steadystates (that you computed in part a. of the question). i. Let 3373 2 gig}; denote the steady state saving rate in country B. Compute 8g and compare it to the steady state saving rate in Country A (recall that in the Solow model the saving rate is exogenous). In which country is the saving rate higher at the steady state? Explain your answer and show your work. ii. Recall that the rate of return on capital is equal to: rt = f’ (16;). Compute the steady state rate of return oncapital in Country A, call this value r2. Compute the steady state rate of return on capital in Country B, callthis value r3}. Compare these two values, in which country is the rate of return on capital higher at the steady state? Explain your answer and show your work.