1. A closed economy has the following Cobb-Douglas production function: F(K; L) = K^2/5 (E L)^3/5 , where the notation is as in class. The depreciation rate is 1.5% and the saving rate is 20%. The economy is in a steady state, where the population decreases at a rate 1% and capital K increases at a rate 1%.
(a) Find the growth rates of the following variables:
(i) labor efficiency, E (ii) the number of workers per machine, L / K
(iii) the average productivity of capital, Y / K
(iv) the price of capital relative to the price of labor, r / w
(v) the difference between labor income and capital income, wL-rK
(b) If real GDP is 100 billion this year, find the number of machines next year.
(c) By how many percentage points should the government change the saving rate so that the economy may converge to the golden rule steady state (use a “+” for an increase and a “-” for a decrease)? How would the current generation feel about the change?
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