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Question: 1 the ak model consider an economy with an aggregate...

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1. (The AK Model) Consider an economy with an aggregate production function given by y = F(K) = AK Capital is the only relevant factor of production. A is fixed and represents the productivity of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com- pute the marginal product of capital. Does this function satisfy the neoclassical assumptions? b) Compute the growth rate (gK) of capital K in this economy. What happens to gk if the savings rate is higher? c) Compute the growth rate (gy) of output. Compute the capital share of output. d) Make a graph of the curve In(Kt) with time on the x-axis. Carefully show the shape and label the slope of this curve.

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