Suppose that the production function in the Duchy of Burgundy is given by Y = representative firm hires workers N at a wage rate w, and seeks to maximize its profits. The representative household derives utility from consuming goods produced by the firm C and from leisure L. Their utility function is

U =log(C)+0.5log(L) The time endowment of the individual is equal to 24 hours, which must be divided between labor

and leisure,

(a) Derive the labor demand function that relates the quantity of labor demanded by the firm N

and the real wage w.

(b) Derive the labor supply function that relates the quantity of labor supplied by the household

N and the real wage w.

(c) Compute the equilibrium in the labor market, in terms of labor N and the real wage w.

(d) Compute: (i) full-employment output, (ii) total consumption, (iii) total labor income. Are these the same? Why?

(e) Messengers from Bavaria bring news of agricultural technology developments that allow firms

to improve their production function to Y = 1.5 N. Find the new labor market equilibrium.

(f) Draw a graph of the labor market that describes the change in equilibrium from (c) to (e).