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An economy has the per-worker production function: yt=3kt0.5, where yt is output per worker and kt is the capital-labor ratio. The depreciation rate is 0.1, and the population growth rate is 0.05. Savings is: St=0.3Yt , where St is total national savings and Yt is total output.
a.) What are the steady-state values of the capital-labor ratio, output per worker, and consumption per worker?
b.) Repeat part (a) for a saving rate of 0.4 instead of 0.3.
c.) Repeat part (a) for a population growth rate of 0.08 (with a growth rate of 0.3)
d.) Repeat part (a) for a production function of: yt=4kt0.5. Assume that the saving rate and the population growth rate are at their original values.
2. Find the marginal utility of good x2 3. Calculate the Marginal Rate of Substitution between good x2 and good x1: MRSx2,x1 = (du(·)/dx2)/(du(·)/dx1) 4. Equate this marginal rate of substitution to the ratio of prices : (Px2)/(Px1)
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