In the competitve market for widgets there are 50 identical consumers and 200 identical rms. Each individual consumer has the following demand function for widgets qD(P) : 100 2P where 9'3 is the quantity an individual consumes and P is the widget's price. Each rm has the following cost function: C(q) = 100 + 2:} + 12. a) {3 points) Find the market demand function for widgets QB (P). Find the industry supply function for widgets 623(1)), make sure to nd each rm's supply function before you find the supply function for the industry as a whole. b) {4 points) What is the equilibrium price in this industry? How many widgets does each consumer consume? How many widgets does each firm produce? How much of a prot or loss does each firm make? c) (5 points) Suppose there is a per unit tax of 1' : $3 put in place on the firms. What are the prices in the market (reminder: tax wedge here)? What is the government revenue? What is the deadweight loss? What is the consumer's tax incidence (in terms of the percentage of the tax)? d) (4 points) Ignoring the tax from the previous section, suppose the firm's long-run cost function is 2 C(q) : 25 + %. What is the long run competitive equilibrium price P" and quantity Q" (Hint: find the minimum long-run average cost)? How many rms are in the market