Problem 2 (30 pts) Explain your answers! The market demand function for computer games is qD (p) = BOOSp and the market supply function is qs(p) = 4}). (a) Find the equations of (express price in terms of quantity) and plot the demand and supply curves corresponding to the given market demand and supply functions. Find the market equilibrium price and quantity p* and if". (b) Find the producer's surplus and consumer's surplus at the equilibrium. (c) What is the price elasticity of demand at the equilibrium point? ((1) Derive the equation of the marginal revenue curve and compute the marginal revenue at the equilibrium point in (a). (e) Given the demand function, at what price would total revenue be maximized? (f) Suppose a quantity tax of $5 per game is imposed on the computer game suppliers. What is the new equilibrium price paid by the consumers? What is the new equilibrium price received by producers? How much is the tax revenue? How much is the deadweight loss of the tax? Use a graph to explain your answers. Problem 3 (15 pts) Explain your answers! Suppose the production function of a rm is given by f (K ,L) = SK 1/4111\(3) You and a classmate are assigned a project on which you will receive one combined grade. You each want to receive a good grade, but you also want to avoid hard work. In particular, here is the situation: If you both work hard, you get an A, which gives you each 40 units of happiness .If only one of you works hard, you both get a B, which gives you each 30 units of happiness. .If neither of you works hard, you both get a D, which gives each of you 10 units of happiness. . Working hard costs 25 units of happiness. (a) Fill in the following payoff matrix: Your decision Work Shirk Classmate's Work decision Shirk (b) What is the likely outcome? Explain your answer. T (c) If you get this classmate as your partner on a series of projects throughout the year, rather than only once, how might that change the outcome you predicted in part (b)?(b) Assume these firms behave like price takers, how much will they produce and what price will they charge? Draw the outcome on a graph. What is the individual firms producer surplus? What is the total producer surplus of the market? (3 marks) (c) Suppose the four firms join together to form a single firm monopoly. What price will the cartel charge and how much output does the cartel produce? What is producer surplus for the cartel? (Hint: the marginal cost curve for the cartel firm is the supply curve found in part (a) with MC replacing P in this equation and MR = 200 -Q). What happens to consumer surplus and total welfare? (4 marks) 4. Calculate the own price elasticity of demand in the following situations (a) A price rise from po = 2 to p1 = 5 causes quantity demand to fall from go = 30 to q1 = 15 (1 mark) (b) The demand curve is given by q = 1/p with the slope of the demand curve given by $ = -1/p2. What is the own price elasticity of demand at any point?(2 marks) (c) The demand curve is given by q = 4 - 2p with the slope of the demand curve given by dp = -2. What is the own price clasticity of demand at: (i) p = 4; and (ii) p = 10? (2 marks) 5. Suppose the cost of producing q cars and q2 trucks is 45000 +80q1 + 10092. Calculate the measure of economies of scope when (1 mark each): (a) q1 = 100 and q2 = 200 (b) q1 = 500 and q2 = 800 6. Answer the following questions True, False, or Uncertain. Give a brief explanation of your answer. 1 mark for correctly identifying T, F. or U. 4 marks for explanation. (a) If a single price monopoly is instituted in what was a competitive market, consumer surplus will decrease more than producers gain. (b) If a firm's marginal cost is less than the firm's marginal revenue then the firm should decrease output and increase price. (c) If price is less than average cost then a firm will shut down. (d) A monopolist does not make a shutdown decision in the short-run and an exit decision in the long run since only competitive firms make these decisions