Q5<\/p>
*Show that the monotone likelihood ratio condition (f(x)\/g(x) increasing in x, where x is a real number) implies first-order stochastic dominance (F(x) G(x) for all x). 2. Let = 1 or 2 denote the state of nature in a two state world. Let p0 = Pr( = 1). Let f(p) be an arbitrary distribution on the unit interval such that pf(p)dp = p0. Show that f(p) can be construed as a distribution over posterior probabilities of p, stemming from an experiment with outcomes y, a prior probability p = p0 and two likelihood functions p(y|1) and p(y|2). [It may be easier to solve the problem if you assume that f(p) consists of two mass points so that the experiment will have only two relevant outcomes, say, yL and yH.] 3. An agent has to decide between two actions a1 and a2, uncertain of the prevailing state of nature s, which can be either s1 or s2. The agent's payoff as a function of the action and the state of nature is as follows: u(a1,s1) = 10, u(a1,s2) = 7 u(a2,s1) = 5, u(a2,s2) = 11 The prior probability of state s1 is p = Pr(s1). a. Give a graphical representation of the agent's decision problem as a function of the probability of state s1. If p = (.4), what is the agent's optimal decision? b. Let the agent have access to a signal y before taking an action. Assume y has two possible outcomes with the following likelihoods Pr(y1|s1) = 1 Pr(y1|s2) = 2 How valuable is this information system if 1 = 2 = ? How valuable is it if 1 = and 2 = 0? c. Show that, irrespectively of the prior, the information system 1 = and 2 = 0 is preferred to the information system 1 = + and 2 = , where and are any numbers between 0 and 1. (Hint: show that latter system is garbling of former). 1 4. *An agent can work hard (e = eH) or be lazy (e = eL), where eH > eL > 0. There are two profit levels, x1 and x2; x1 < x2. Hard work makes the high profit level more likely. Specifically, Prob(x = x2) is fH if the agent works hard and fL < fH, if the agent is lazy. The principal can only observe realized profits x. The principal is risk neutral and the agent is risk averse with preferences u(w) - e. The utility function u is strictly concave and increasing. a. Assume that the Principal's reservation utility is 0; that is, the Principal has to be assured a non-negative profit. Show how to solve for the Pareto Optimal action and incentive scheme s(xi) = si, i = 1,2, where si represents the payment to the agent if the outcome is xi. b. Suppose that the agent is given the opportunity to choose a third action eM with the features that Prob(x2|eM) = fH + fL and eM > eH + eL. Can the Principal implement eM? c. Suppose that the second-best solution in Part a is such that it is optimal to implement eH. Let the agent have access to the action eM described above, but assume now that eM < eH + eL. Will the solution to Part a stand once the agent is given access to eM? 5. Consider the risk-sharing problem we saw in class. Show that the Pareto frontier is concave (in expected utility space), or, equivalently, that the feasible set of utility pairs is convex.<\/p>
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1. Consider the following regulation problem. Let x be output, c be marginal cost of output and R be net return of production. The firm's net profit before regulatory payments is given by R = x cx, for 0 x 1. Note that x has to lie in the unit interval and that output has been normalized to equal revenue. Assume that the regulator does not know the firm's cost coefficient c, which can take on n values: 0 c1 ... cn 1. The regulator assesses probability pi 0 to each of the i possible marginal cost levels. The firm knows its marginal cost and chooses x. The regulator can tax the firm based on its realized revenue. a. Set up the program that solves for the regulator's optimal policy, expressed as a direct revelation mechanism. Assume that the regulator's objective is to extract as much surplus from the firm as possible, subject to the constraint that the firm can quit if profits are negative (and pay nothing). b. Draw a diagram that shows how the firm chooses its best response as a function of its cost. Prove that the firm's output choice x is a non-decreasing function of marginal cost. c. Show that the optimal policy takes the simple form: a fixed charge T for producing anything (hence, all firms with c T produce and those with c > T do not). It suffices that you give an argument for n = 3. *2.Consider a screening model of the following sort. The agent produces output q at a cost c(q,) = q, where q is output and is a cost parameter. The principal, who cannot observe either c or , offers to pay the agent the amount p(q) if the agent produces output q. Given this incentive scheme, an agent with cost parameter responds by producing the amount q(). What kind of payment scheme p(q) should the principal choose in order to implement the response function q() = 1\/2 ? 1 *3.A seller may supply a single object to a buyer. Let x be 1 if trade takes place and 0 if not. Let tS be the amount of money that the seller receives and tB the amount that the buyer pays. Let v be the buyer's valuation and s be the seller's valuation of the object and assume preferences are quasi-linear. We can then normalize utilities so that the seller's utility is tS cx and the buyer's utility is vx tB. Assume the preference parameters v and c are independently drawn from a uniform distribution on [0,1]. The buyer knows v and the seller knows c. a. What is the efficient rule for trade? b. Let mS and mB be the seller's respectively the buyer's reported preference for the object. Determine the set of direct mechanisms (expressed as a function of the reports) that admit truth telling as a dominant strategy and implement efficient trade (ie. the set of Groves mechanisms). c. Show that there is a unique Groves mechanism that has the property that whenever trade does not occur, the transfer payments are set equal to zero (tB = tS = 0). Is this mechanism feasible? d. Show that there is no Groves mechanism for which the budget breaks even for all reported preferences. 4. Suppose there are a continuum of sellers and a continuum of buyers (where each continuum is normalized to one). Each seller has one unit of the good and has valuation vs drawn (independent from those of the other sellers and buyers) from the distribution Fs on [a,b]; similarly, each buyer has unit demand and has valuation vb drawn (independently) from the distribution Fb on [c,d]. Assume that b > c (not everyone ought to trade). Let ms(vs) and mb(vb) denote a seller's probability of selling and a buyer's probability of buying, respectively. Let ts(vs) and tb(vb) denote a seller's transfer and a buyer's transfer (from the planner), respectively. Among the many possible mechanisms that might be used, consider the \"Walrasian mechanism\": ms(vs) =1 and ts(vs) =p if vs p and ms(vs) = 0 = ts(vs) if vs > p, mb(vb) =1 and tb(vb) = p if vs p and mb(vb) = 0 = tb(vb) if vb < p. a. Show that IC and IR are satisfied for any p. b. Show that there is a value of p such that the mechanism is balanced and trade is efficient. c. The Myerson-Satterthwaite Theorem states that it is impossible to achieve efficient and individually rational trading in a Bayesian NE between a buyer and a seller with private information about their valuations. How can this be reconciled with parts a and b above?<\/p>
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An excavation contractor deposited 200000 quarterly into a fund paying a nominal interest rate Of 8% per year compounded semiannually For a period of 4 years assume there is no interpolation interest accured . At the end of the fourth year they want to purchase a fleet of trucks for 5000000.The contractor intents to make an immediate cash payment equal amount accumulated and to pay for the rest by equal month end payments. Their financing agreement with the truck dealer is payment should be completed in 18 months and the nominal interest rate should be 18% per year compounded monthly. What will these monthly payments be? Use 4 digits after the decimal point in your interest rate calculation With cash flow diagram <\/p>
Illustrate and explain how a firm's short-run demand for labor curve is derived. Also, show and explain that a firm will stop producing in the short-run if the wage rate (w) exceeds the VAP at it's maximum. (hint: a firms will produce in the short-run as long as TR TVC). Another hint: You need to show that TR = VAP x E <\/p>
The stock price of Obelix and Company is $81.40. At the money call options trade at $2.53, while at the money put options trade at $2.52. You form a straddle from the two options. If the stock price fell, at what price would you start to make a profit?<\/p>
<\/p>", "transcribed_text": "", "related_book": { "title": "Accounting", "isbn": "324401841, 978-0-324-6250, 0-324-62509-X, 978-0324401844", "edition": "22nd Edition", "authors": "Carl S. Warren, James M. Reeve, Jonathan E. Duchac", "cover_image": "https:\/\/dsd5zvtm8ll6.cloudfront.net\/si.question.images\/book_images\/142.jpg", "uri": "\/textbooks\/accounting-22nd-edition-142", "see_more_uri": "" }, "free_related_book": { "isbn": "1013467450", "uri": "\/textbooks\/hydroxylamine-its-quantitative-determination-and-some-double-salts-1st-edition-978-1013467455-170846", "name": "Hydroxylamine Its Quantitative Determination And Some Double Salts", "edition": "1st Edition" }, "question_posted": "2024-06-13 16:31:17", "see_more_questions_link": "\/study-help\/questions\/business-banking-2021-September-12", "step_by_step_answer": "The Answer is in the image, click to view ...", "students_also_viewed": [ { "url": "\/let-x-be-normally-distributed-with-mean--2500", "description": "Let X be normally distributed with mean = 2500 and standard deviation = 800> a. Find x such that P(X x) = 0.9382> b. Find x such that P(X>x) = 0.025> c. 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A nickel and a dime are flipped at the same time. 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