Suppose that an economy’s production function is Y = z ? K ? N. Workers consume

Question

Suppose that an economy’s production function is Y = z ? K ? N. Workers consume 70 percent of the total output in each period, and 10 percent of the country’s capital depreciates every period. Suppose that the economy is in the steady state, that the marginal product of capital equals 1/2, and that population growth is positive. (a) Find the growth rate of aggregate output in this economy. (b) Does the economy have a higher or lower output per worker relative to the goldenrule steady state? In order to transition to the golden rule steady state, would the economy have to increase or decrease its savings rate?

Explanation / Answer

Answers. This is based on the solow model of growth.

(a) Thus according to the neoclassical model,

Y = z. (K^0.3) (N^ 0.7)

Y/N = z (K/N)^0.3

(b) At the steady state,

?k = sf(k) - ?k

?k = sf(k*) - ?k* = 0 (At the steady state)

s(k*)^0.3 = ?k* => (k*)^0.7 = s/? => k* = (s/?)^1/0.7

y* = [(s/?)^1/0.7] ^0.3 = (s/?)^0.3/0.7

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