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ECON30002

Problem set 1

Problem 1. Solow model diagram

Describe how, if at all, each of the follow ing developments affects the break-even and act ual invest ment lines in our basic diagram for the Solow model:

(a) The rate of depreciation falls.

(b) The rate of technological progress rises.

(c) The production function is Cobb-Douglas, f(k) = k9, and capital's share, a, rises.

(d) Workers exert more effort, so that output per unit of effective labor for a given value of capital per unit of effective labor is higher than before.

Problem 2. The balanced growth path

Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate of populat ion growth falls.

(a) What happens to the balanced-growth-path values of capital per worker, output per worker, and consumption per worker? Sketch the paths of these variables as the economy moves to its new balanced growth path

(b) Describe the effect of the fall in population growth on the path of out put (that is, total out put, not out put per worker).

noindent Problem 3. Inter-temporal elasticity of substitution (normal)

Consider an individual who lives for two periods and whose utility is given

C1-01 C1θ> 0, ρ> -1.6

Let Pi and P2 denote the prices of consumption in the two periods, and let W denote the value of the individual's lifet ime income; thus the budget constraint is

PC + P2C2 = W.

(a) What are the individual's utility-maximising choices of Ci and C2, given Pi, P2, and W?

(b) The elasticity of substitution between consumption in the two periods is

(P1/P2) მ (C1/c2) მln (C1/c2)or.(CI/ca) მ (PI/P2)' მln (P1/P2))

Show that with the above utility function, the elasticity of subst it ution between Ci and C2 is 1/e.