(15 points) Consider the one-period model. The aggregate production function is given by Y = =N where IV denotes the work force, and z denotes total factor productivity. The consumer's preferences over consumption, a, and leisure, /, is given The household has h units of time to devote to either labour supply N" which earns wage w, or leisure /. There is not government so T = 0 - C. (a) Write down the firm's maximization problem (b) Solve for the firm's labour demand curve (!) What is the slope of the firm's labour demand curve? (d) Show that profits are equal to zero. (e) Write down the household's budget constraint (f) What is the solution to the household's problem using the tangency condition? g) Derive the household's labour supply curve, (h) What is the sign of the slope of the household's labour supply curve? (i) Draw the labour market with an example of what the labour supply and demand curve look like