3. Suppose that demand for pizza slices for Alex is given by D_Alex= 202P and for Billy is given by D_Billy= 103P where P is the price of a slice of pizza. The market supply of pizza slices is given by S(P) =1 + 2P.

a. Derive an expression for the market demand for pizza slices, assuming that Alex and Billy are the only consumers of pizza.

b. Given your market demand from part (a), what is the price elasticity demand for pizza when pizza costs $5 a slice?

4. Let u(x)= a ln x +b ln y , where a, b >0 and x and y are two goods sold in this market.Derive the demand functions for goods x and y. Show all you work.