The neoclassical growth model assumes that population is growing, at any point in time a share of the population of working age is fixed, both the population and the workforce grow at a rate n, the economy is fixed and there is no role for government.
The production function for the representative firm is given by Yt = At Kt Lt1
(a) Write down the equation that determines consumption for the representative consumer and explain the trade off that the representative consumer faces in its labour-leisure choice.
(b) Graph the production function of the representative firm and both graphically and in words show that there is diminishing marginal productivity of capital.
(c) Write down the law of motion for the capital stock and for investment.
(d) Convert aggregate variables (output, capital, consumption, investment) into per capita terms.
(e) Solve for the steady state of this model. Find the equilibrium steady state equations that determine (y*, c*, i*, k*).
(f) What are the determinants of long run living standards according to this model?
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