## Question

###### 3) Consider a closed economy in which the population grows at the rate of 1% per...

3) Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is y = 6k 12, where y is output per worker and k is capital per worker. The depreciation rate of capital is 14% per year. a. Households consume 90% of income and save the remaining 10% of income. There is no government. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker? b. Suppose that the country wants to increase its steady-state value of output per worker. What steady-state value of the capital-labor ratio is needed to double the steady-state value of output per capita? What fraction of income would households have to save to achieve a steady-state level of output per worker that is twice as high as in Part (a)?

## Answers

3.a) - per capita production function: y = 66² Law of motion of capital per capita (1+r) kat = Syt+ (1-8) ker Steady state keti = kek :(1+n) ke sy + (1-d) k ac, (n+d) te = sy are the word © sy 36168 - 24 in c = (1-5) 6.65 : 216 I (65) = 2:4. n + 6 2015b). Current output per capital at ss . 10 L y 24 To double this: y'= 48 : :. 98 -642 L :. k = 64 Given the so capital per capita a 65 = (ned) k2 - :15' (n+d) X? Ć . 0'15*8 1 6 s! = 0:2 . The house hold need to save 20% of the income. 2015

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