5. (15 points) Consider the oneperiod model. 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, 0, and leisure, l, is given by U(c, l) = (2% + 1% The household has h units of time to devote to either labour supply N 3 which earns wage w, or leisure I. There is not government so T = 0 = G. (a) Write down the rms maximization problem (b) Solve for the rms labour demand curve (c) What is the slope of the labour supply curve? (d) Show that prots are equal to zero. (e) Write down the households budget constraint. (f) What is the solution to the households problem using the tangency condition? (g) Derive the households labour supply curve. (h) What is the sign of the slope of the labour supply curve? (i) Draw the labour market with an example of what the labour supply and demand curve look like