Answer the following questions correctly.,,,

F. In year 5, an economist (also schooled in 14.03) from the Rothschildian Board of Social Welfare visits the Board of Health and says, "I see that you've worked out the national health plan premium so that it no longer makes/loses money every year. That's a step forward. However, I'm concerned that your break-even program is not actually maximizing average social welfare. What I'd like you to do is calculate average well-being (utility) under three different policy options: 1) No health plan; 2) Your current break-even plan; 3) A third mandatory plan for all citizens that also breaks even. Then report back to me." Please perform these calculations for the three plans. Which health plan do you recommend based upon your calculations? G. Explain substantively why your preferred policy option yields higher average social utility than the other two health insurance plans. 2. Imagine that employers in the mining industry are reluctant to hire workers of poor health due to the arduous working conditions in the mine. It takes a half-year of mining by a worker to cover her $1,000 annual salary, and unhealthy workers often quit before this time is up. Moreover, mining is so tough that after one year of work, even the healthiest person leaves mining Assume that health (h) is distributed uniformly on the [0,1] interval where a person with health 0 becomes ill immediately on entering the mine, a person with health 1 works a whole year before becoming ill, and a person with health 0.5 works for half a year before becoming ill, etc. Hence, the firm's revenue per worker is $2,000h, where h is the fraction of the year that a worker stays in mining before becoming ill. Once a person becomes ill, she leaves the mine for good (but immediately recovers and hence suffers no additional disutility). Each person knows his health before applying. The disutility of applying for the job is $3 (because everyone hates filling out applications). People who don't work in the mine earn $500 in the Saloon sector (which provides fine drink and dining to miners). A. In the early days, mining companies could not tell the health of applicants apart. While 3 the job application requested health information (on a zero-one scale), there was no way to verify this information and the Fairness in Mining Law clearly states that employers cannot refuse to pay the $1,000 salary of workers who become ill on the job. What is the mean health reported by workers on their job applications? What is the mean health of workers who are hired? What are average profits per worker? B. In 1970, a manicurist working for Consolidated Amalgamated Mining Corporation invents a screening test that can precisely determine applicants' health by shining a light on their fingernails (which, of course, are used heavily in scraping ore from mineshafts). This test is costless to the company and almost completely painless, yielding a disutility to the test taker of only $1. CAMC immediately requires it of all applicants. What is the health of the least healthy worker who applies for the job? What is the health of the least healthy worker hired? What is the average health of workers hired? What are average profits per worker? C. In 1980, after a damning story on 60 Minutes, Congress passes the Non-Discrimination in Mining Act that stipulates that companies cannot require their applicants to take fingernail health-screening tests. CAMC's stock price falls precipitously as investors anticipate a return to the "bad old days" when half of the company's employees became ill within half a year. Unfazed, CAMC's Personnel Director suggests the following policy: the company will offer a $2 bonus to any applicant who volunteers for the health-screening test. "This should solve the problem," she says. The CEO replies, "That's a strange idea. People earn $500 more per year working for us than working for the saloon up the street. Why would anyone want to reveal their health status, possibly costing them a high paying job, for a mere $2 - less than the $4 disutility of applying and taking the test?" However, after further conversation, the CEO is persuaded of the wisdom of the Personnel Director's policy and the company implements the policy. What is the health of the least healthy worker who applies for a job? What is the health of the least healthy worker hired? What is the average health of workers hired? What are average profits per worker?1. Consider a two consumers exchange economy where the two people (A and B) act as price takers. There are two goods, food F and clothing C sold at prices pp and pc respectively. A and B have endowments (FA, CA) and (FB, CB), respectively. To make things easy, A and B have the same utility function. Unfortunately, that function is (omitting subscripts): U(F, C) = 7 FCB + 44 F2 Cas + a In(F) + 8 In(C) + (Fo CA) e can where a > 0 and B > 0. (i) Identify the Walrasian Equilibrium of this economy in terms of endow- ments and the parameters of the utility function. [Hint: is there some principle of consumer theory and of general equilib rium theory that can simplify things a little?] 2. In a two-persons (Ms. A and Mr. B), two-commodities (apples and oranges), pure exchange economy, Ms. A likes only apples and does not care how many oranges she has. On the other hand, Mr. B likes only oranges and does not care how many apples he has. Both people behave as price-takers. (i) Suppose that A owns all the apples and B all the oranges. Is there a Walrasian equilibrium? If so, what is (are) the equilibrium price and allocation(s)? (ii) What are the Pareto optimal allocations in such an economy? (ili) Suppose now that the initial endowments are such that Ms. A owns some oranges and Mr. B some apples. Is there a Walrasian equilibrium? If so, describe any equilibrium price and allocation. 3. In a two-persons (MS. A and Mr. B), two-goods (good X, and good X2), pure exchange economy, Mr. A likes only good X, and does not care how many units of good X, he has. In other words, Mr. A's preferences are represented by the utility function: UA(X4, X4) = XA. On the other hand, Ms. B likes only good X2 she does not care how many units of good X, she consumes, but she suffers from a negative externality imposed on her by Mr. A's consumption of good X1. In other words, Ms. B's preferences are represented by the following utility func- tion: UB(XB, XP, XA) = X5 - X4. Finally, assume that Mr. A owns 5 units of good X, and 15 units of good X2, while Ms. B owns 15 units of good X, and 5 units of good X2. (i) Is there any Walrasian equilibrium in this economy? (ii) If so, what is (are) the Walrasian equilibrium price(s) and allocation(s)? (iii) Find the Pareto efficient allocation(s) in such an economy. (vi) Is the Walrasian equilibrium allocation Pareto efficient? Explain your answer.5. Consider a technology that produces a unique output and satisfied the fol- lowing restrictive form of additivety: f(x + ') = f(x) + f(:'). Further assume that the inputs are infinitely divisible, meaning that if r e V(y) then Ar E V()'y), for every >' and A e (0, 1). Show that this technology must be convex. 6. Does the input requirement set V(y) = {(21, 12, 13) | 21 + min ( x2, x}} 2 3y, 1, 2 0Vi = 1,2,3} corresponds to a regular (closed and non-empty) input requirement set? Does the technology satisfies free disposal? Is the technology convex