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[A3] Solow model (35 marks). Consider a Solow model with technological growth. Technology at time t = {0, 1, 2,...} evolves as A₁ = Ao(1+g) with parameters Ao > 0 and g 20. There is a representative household of size L that produces output according to Y₁ = K (AL), with a € (0, 1). It saves an exogenous fraction 8 € (0, 1) of income, It sy, and consumes the rest. Capital evolves as K₁+1=(1-6)K, +0I, where @> 0 is some parameter and where & € (0, 1) is the depreciation rate of capital. The initial capital stock, Ko, is exogenous. (a) (7 marks) Show that output per worker, y, can be written as y= Ak, where k=K is capital per effective worker. It can be shown (no need to do it) that on the balanced growth path, * = ()" (b) (7 marks) Provide an economic interpretation of parameter in this model. Explain why, if at all, it affects initial output (at t=0) and long-run output (as t→∞). (Continued on next page) Page 3 of 7 (c) (7 marks) Suppose that g = 0.03. You observe that yo= 1 and that y> 1.03. What does that tell you qualitatively about the initial capital per effective worker, ko, relative to k*? How does k, compare to ko? Explain your reasoning (a formal mathematical proof may be helpful but is not required). (d) (7 marks) For simplicity, suppose now that g = 0, that L = 1, and that the econ- omy is in steady state at t = 0. Suppose that in normal times A always equals 1. Our economy, however, experiences a short recession by which TFP drops at t = 1 and then permanently recovers in t = 3, as shown in the table below. Explain the Ao A1 A2 A3 A4 1 0.5 0.5 1 1 1 possible movement of capital, K, and output, Y, in the following periods: at t = 1, at t = 2, at t = 3, and after t = 3. Illustrate the result graphically with t on the x-axis. (e) (7 marks) Suppose again that g> 0. In addition, this economy is now such that 0 = 0. Find the expressions for and Y. What condition ensures that output grows at a strictly positive rate? Provide an economic intuition. Ki (Continued on next page)