Problem 2 In a competitive market there are m consumers and n firms. Consumers and firms take prices as given. Each of the m consumers has income y and utility function u(q, =) = = + 20q - where q (with price p) is the quantity consumed of the firm's output and z (with price 1) is dollars spent on all other goods. All n firms are identical with cost function c(q) = $ + 10q+40. (a) Find the demand function of each consumer for the firms' output q. What is the market demand function, Q"(p)? (b) Find the supply function of each firm. What is the market supply function, Q5(p)? (c) Suppose m = 1000 and n = 10. Draw a graph of the market supply and demand curves and find the equilibrium price and quantity on this market. How much does each consumer consume? How much does each firm produce? Do firms make a profit or loss in equilibrium? (d) Given your answers in (c), what will happen in the long run in this market if firms can freely enter and exit? With free entry/exit, what would be the long-run industry equilibrium price? Quantity produced per firm? Number of firms? What would happen if m = 100 instead