The Consider the one-period model studied 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(cl) = c +01 The household has h units of time to devote to either labour supply N or leisure 1. There is not government so T = 0 = G. (a) Write down and solve the firms maximization problem for the labour demand curve. (b) Write down the households optimization problem. What is the solu- tion to the households problem using the tangency condition? Note that = 12-1. x z (c) Derive the labour supply curve. What is the sign of the slope of the labor supply curve? (d) Define the competitive equilibrium. (e) Impose the competitive equilibrium and solve for optimal labour. (f) What is the solution for output, consumption and leisure at the op- timum? (g) How much does Y* change if there is an increase in h by one unit? (h) How much does N change if there is an increase in 8 by one unit?