Consider the closed economy, one period model with the
following utility and production functions:
and
where Y = output, z = total factor productivity, K = capital, N=
labor, C = consumption, and / = leisure; ; and. At the competitive equilibrium, the government must satisfy its budget constraint (where G is government spending and T= lump-sum taxes); the representative firm optimizes; the
representative consumer optimizes; and the labor market clears
( = total number of hours available for work or leisure).
(a) Compute the competitive equilibrium values of consumption
(C) and leisure (1). (6 points)
(b) What is the equilibrium real wage? (2 points) (c) Graph the equilibrium from (a) on a graph with consumption on the vertical axis and leisure on the horizontal axis. Be sure to
label the optimal C. I. Y, and N. (6 points) (d) On the graph from (c), illustrate what happens to this
competitive equilibrium when government spending decreases. Note: you don t have to compute anything: just illustrate and label the new values as C, I, N,, and Y,. Be sure to distinguish your 'new' curves from the original ones with accurate
labelling. (6 points)