(35 points) Consider the one-period model studied in lectures 5-7. The aggregate production function is given by Y = zN where N denotes the work force, and z denotes total factor productivity. The consumer's preferences over consumption, c, and leisure, l, is given by U(c; l) = C^0.5 + L^0.5

The household has h units of time to devote to either labour supply Ns or leisure l. There is not government so T = 0 = G.

a) Write down and solve the rms maximization problem for the labour demand curve.

b) Show that prots are equal to zero.

c) Write down the households optimization problem. What is the solution to the households problem using the tangency condition?

d) Derive the labour supply curve. What is the sign of the slope of the labor supply curve?

e) Define the competitive equilibrium.

f) Impose the competitive equilibrium and solve for optimal labor demand.

g) What is the solution for output, consumption and leisure at the optimum?

h) How much does Y change if there is an increase in h by one unit?