Please show your reasoning and related calculation clearly
1. Suppose in a market of good G, the demand curve and supply curve are given re spectively by P=(10QD)2 P=Q where P denotes price; Q5 denotes quantity supplied; and (2;. denotes quantity de~ manded. However, each unit of good G produced generates a positive of externality valued at $40. (Hint: you could assume that Q9 5 10.) (a) What is the total dollar value of externalities at the free market equilibrium? (10 marks) (b) What is the socially optimal quantity of good G produced and consumed? (10 marks) (c) What tax or subsidy policy could may lead to an socially optimal level of pro- duction and consumption? (10 marks) 2. Suppose a society has two individuals, Ana and Bill. In the first period, Ana and Bill decide whether to study for an university degree at the same time. If one decides to attend university, his/her payoff in the first period is -10. If one decides not to attend university, his payoff in the first period is zero. In the second period, Ana and Bill's earnings are not only determined by their own education level, but also by the education level of the other as well. Let (A, B) denotes the earnings of Ana and Bill respectively in the second period. The following table lists the second period earnings (excluding first period payoffs) in four different scenarios: Bill attended univ. Bill did not attend univ. Ana attended univ. (30, 30) (10, 8) Ana did not attend univ. (8, 10) (5,5) Assume that neither Ana nor Bill discounts second period payoffs, namely their dis- count factors are both 1. Their education decisions in the first period are only deter- mined by the sum of their own payoffs from the two periods. Moreover, they decide whether to go to university in the first period simultaneously. 4 (a) Does education have externality in the example above? If so, is it positive or negative externality? (10 marks) (b) If Ana knows that Bill would not attend university, would Ana attend univer- sity? Is the case that neither Ana nor Bill attends university a Nash equilibrium? (10 marks. Hint: in a Nash equilibrium, no one finds it profitable to deviate from their choice unilaterally.) (c) If Ana knows that Bill would attend university, would Ana attend university? Is the case that both Ana and Bill attend university a Nash equilibrium? (10 marks)3. Suppose that education does not increase an individual's marginal productivity and that there are two types of people in the world: over-aduevers and slackers. Over- achievers don't really mind going to school and for them the cost of y years of school is 1%. Slackers, on the other hand, find school more burdensome, and for them the cost of 3; years of school is y. Consider two different rms. Firm 1 offers to pay workers such that the present discounted 1.ralue of their lifetime earnings is $12 if workers have at least 6 years of schooling, and $3 to all other workers. Firm 2 offers to pay workers such that the present discounted value of their lifetime earnings is $12 if workers have at least 2 years of schooling, and $3 to all other workers. (a) For each firm separately, analyze whether its educational requirements will en- able them to distinguish between over-achievers and slackers. (It) marks) {b} What is the minimum educational requirement a rm can offer and still expect to be able to distinguish between over-achievers and slackers? (10 marks)
