Short Question 3: (30 points) This question is about the Solow growth model from Chapter 5. Consider a countries Am- brosia and Burunda. Ambrosia's GDP per worker is 1.96 times that of Burunda. The ratio of investment to output is 0.35 in Ambrosia, and in Burunda it is 0.25. Labour supply is constant over time in both countries. So is total factor productivity (TFP). Assume both countries are in their respective steady states. Suppose output in each country i = A, B is produced according to Ya = A, K L- where Ya is output for country ? at time t, A, is TFP for country i, Kit is capital stock in country i at time t, and L; is labor in country . Capital is accumulated according to AKitti = s; Yit - dKit (1) Assume that the depreciation rate and the capital share are same across two countries. (a) Derive an expression for the steady state value of output per worker (Y/L) in each country i in terms of AA, SA, d and o for country A, and in terms of AB, SB, d and a for country B. (10 points)(b) Suppose c = 1/3. What must be the ratio of TFP in country A to TFP in country B (i.e. AA/As) in order to fit the facts noted at the beginning of the question. (5 marks) [Assume that the depreciation rate and the capital share are same across two countries.(c) Assume TFP is equal across the two countries. If Burunda increases its savings rate to 0.35, what will be the ratio of output per worker (Y/L) in Ambrosia relative to Burunda in the new steady state? ( 5 points) [Assume that the depreciation rate and the capital share are same across two countries.(d) Using a Solow diagram, show the effect of an increase in savings rate in country B on capital per worker. (5 points) [Hint: you do not need to plot variables for country A in your answer]11 (e) The Consumption in economy B is given by: CBt = YBt - SBYBt, Using the Solow diagram and the equation for consumption, explain what happens to consumption over time after country B increases its savings rate. Does this policy unambiguously improve consumption? (5 points)