In this problem you will compare the convergence of two economies, that we name The two economies share the same technology for the production of final output that is Y = K&N-a The also have a depreciation rate 64 and respectively. The letter have the same interpretation as the class notes and the textbook. Recall that labor and population size are equal in this version of the model. a) Write down the evolution of the stock of capital K b) Verify that the above production function has the property of being constant return to scale, and has diminishing return on capital c) Transform the production function and the law of accumulation of capital in per capita terms. Denote with a lower letter the per capita variables (for instance k = K/N) d) Determine the level of output and of capital per capita in steady state of the two economies. Denote with k and k the respective capital labor ratio and with y and y the output labor ratios. e) Suppose = B = d and that the initial level of capital at time t = 0 of economy A is ko,Ak of that of economy B is ko,B=k. In a graph plot the growth rate of capital (kt+1-kt)/kt of the two economies. = f) Which of the two economies has the larger growth rate of capital, that isin t = 0 and in t = 30? Explain intuitively with the help of the graph. g) Which of the two economies has a higher output labor ratio in t = 0 and in t = 30. Explain intuitively. h) Is it possible to have a scenario in which at time t = 0 the growth rate of capital is larger in country B than in country A. Explain it through algebra and using graphs.