Question 1: The teenagers of Good Times Island love to have hon res on the beach every Sat urday night. They especially love to burn rubber tyres because of the thick black smoke the tyres produce. The parents of Good Times Island, however. hate these res. The smell of the burning tyres makes them sick. There are two companies that supply rubber tyres: Greatyear {31] and Firepebble (32). Their supply functions are given by (1} (231 = 1.7513 and {:2} (232 = 2.2513. where Q is the number of tyres sold per week. There are two neighboring villages on the Island. Their demand functions are given by {1] Q51 = TE: 3F, and (2} Q33 = 25 P. Assume that rubber tyres have no other purpose (is. they are only good for bon res and cannot be used for transportation} and that rubber tyres are neither imported nor exported so that the island's demand for tyres must be met by the two suppliers. Also assume that the tyre suppliers are located in between the two villages so islanders can easily purchase tyres from either supplier and that bon re smoke easily travels back and forth between the two villages. Using this infor mation. answer the following questions. Part (a) Are rubber tyres a private or public good? Briey explain your answer. Part (b) Given only the information above, are there any externalities in the tyre market? Ifso, are they production or consumption externalities? Are they positive or negative externalities'? Explain your answer. Part (c) Derive the market supplyr function for rubber tyres on the island. Part (d) Derive the market demand function for rubber tyres on the island. Part {a} What is the market- equilibrium prime and quantity of rubber tyres? Show this graph- ically. Your graph need not be drawn to scale, but be sure to label market supply and demand curves and numerically label all intercepts and equilibrium values. Part [f] The parents of Good Times Island lobby the government to conduct a thorough inves tigation of the damages that can ensue from burning rubber tyres. The government determines that the marginal external cost of tyre burning that parents experience by having to breathe the bladt smoke is given by MECpm-gnu : {3.49 The gm'ernment also determines that then: are costs to the envirornnent. The smoke decreases visibility, leaves residue in streams, and is threatening the island's bird population. The government estimates that the marginal external mat of tyre burning to the environment- is given by MECevironmenE = 0.350. Given this infor mation. derive the equation for marginal social benets (MSB) and the equation for marginal social costs {MSG}. Part (g) Given your answer to Part {f}, what is the socially optima] quantity of rubber tyres? Graphically illustrate this equilibrium, including MSB, Iii-[5C1 market supply. and market de- mand on the same graph. Again. while your graph need not be drawn to scale. be sure to label all canes and numerically label al] intercepts and equilibrium values. Part ([1] What is the value of Total Surplus e. Social Welfare] under the market equilibrium? What is the value of Total Surplus under the socially optimal equilibrium? Which is larger? Why is this? Part (i) The government realises that, without intervention, the island is burning too many tyres and that the community would be better o' if fewer tyres were burned. They decide to charge tyre producers or at per-unit. output tax on each tyre produced {by flat, I mean the same tax for each unit produced]. What tax will induce the market to produce the socially optimal amount of tyres? Illustrate the efeet this tax will have on Market Supply, Market Demand1 and the Market Equilibrium. Part- [j] Suppose instead that the govermnent decides to charge islanders a at per-unit eon- surnption tax on each tyre burned. What tax will induce the market to consume (burn) the socially optimal amount of tyres? Illustrate the effect this tax will have on Market Supply, Market Demand. and the Market Equilibrium. Part [k] h: the scenario in. Part {i}. what prioe must teenagers pay in order to purchase a rub ber tyre":I What must they pay in Part (j)? How do these prices compare? Explain your ndings. Part (1) Suppose during the investigation that the gem-eminent also determined that the pro duetion of rubber tyres generated pollution. In this case, would the socially optimal quantity of tyres be greater than, equal to, or less than the quantity you found in Part (3;) or do you not have enough information to anawer this question? Would the optimal production tax be greater than, equal to, or less than than the value you found in Part {i} or do you not have enough information to answer this question? Part (In) Under what conditions would the socially optimal quantity of tyres be zero