Consider a trader i has following utility function: u;(X1, x2) = xf x¯", where Xi refers to the quantity of asset with price pi, and i = 1,2 in this case. Suppose the total money of this trader to be completely used for trading is M, and during the whole trading process the price of asset remains constant. (a) buy when she wants to maximize her utility function. Determine the optimal quantity x; for each asset that this trader can Describe in words about her preferences correponding to a = 0, a = 1, (b) and a = 0.5.
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- Let vij be bidder i's valuation for object j, where i in {1,2,3} and j in {1,2}. Bidder i knows its valuation vi; but other bidders only know that vi; is drawn uniformly from [0, 100]. If bidder i wins object 1 at price p1 and object 2 at price p2, bidder i's payoff is v;1 If bidder i wins only object j at price p;, his payoff is vij – Pj. If bidder i does not win any object, his payoff is 0. The auction proceeds as follows. The initial prices are zero for both objects. All bidders sit in front of their computers and observe the prices for both items in real-time. Initially, all bidders are invited to enter the bidding race for both items. At any moment in time, each bidder has the option to withdraw from the bidding race for either object or both. If a bidder withdraws from the bidding for one object, he can no longer get back to the bidding for that object, but he can stay in the bidding race for the other object if he hasn't withdrawn from it previously. The price for an object…PLS ANS 7 URGENT H = ($100, 0.4; $200, 0.6) K = ($120,p, $300, 1- p) 6. EV(H) =EV(K) What value of p makes this statement true? 7. Carol owns prospect H and is interested in selling it. Her utility of wealth function is given by u(x) = x^0.5 . What is the lowest price for which Carol would be willing to sell prospect H?Given a QD = 100 – 2P and QS = 6P – 20 If P1 = 10, compute the QD , and QS. Identify the economic effect at this price.
- 3. A firm that is located in country H, where price levels are p = (1,1), needs to send one of its two employees to its branch in country F. However, in country F price levels are p′ ≫ p, so the firm will have to pay additional salary to ensure that its employee is equally well-off in country F as she was in country H. Suppose the utility functions of the two employees are u1(x1, x2) = x1 + x2 and u2(x1, x2) = min {x1, x2}. The two employees are otherwise identical, including current salary. If the firm wants to minimize the additional salary it needs to pay, which employee should it send? Explain.A4 The Suboptimality of Lower-Than-Cost Reserve Prices: A seller chooses to sell an object by means of a Vickrey auction. If trade occurs, the seller incurs a positive opportunity cost (i.e. c > 0). There are n > 1 bidders participating in the auction. Suppose that the all of the bidders play according to a symmetric and increasing BNE strategy. Show that the seller is always better off by setting the reserve price equal to her cost (i.e. r = c) than by setting the reserve price below her cost (i.e. r < c).Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. Suppose that Shelly's preferences for consumption and leisure can be expressed as u(c ,l)=(c-300) (l-60). a) Calculate her utility, u0 , if she consumes c = $1000 and enjoys l = 110 hours of leisure per week. b) Evaluate her marginal utilities of consumption and leisure at this point and use them to determine the slope of her indifference curve at this point. [Hint:Using calculus, it can be shown that for any given level of utility u, MUc = l - 60 and that MUl = c - 300.] c) Marginal utilities are important because they can be used to calculate the change in utility, ∆u, that results from changing c and l by the small amounts ∆c and ∆l. The induced change in utility is approximately (≈): ∆u ≈ MUl ∆l + MUc ∆c. Based on your answers for (b), what happens to her utility if her consumption increases by ∆c = $2 and her leisure declines by ∆l = 1 hour? d)…
- It is October and Sam has won a price of $9000. She has the following two options:• Option A: receiving the entire amount in October;• Option B: receiving the price in three equal installment, that is, receiving $3000 in eachof the following months (October, November, December).Sam decides to distribute her price over time by choosing Option B. Assume that Sam hasconstant marginal utility of money. Prove mathematically that Sam’s preference for Option B cannot be explained by hy-perbolic discounting (the β − δ model). Assume 0 < δ < 1 and 0 < β ≤ 1.Suppose Martha earns an of income 400 Birr currently, and her utility function is given by: U(m) = 4m, where m represents income. She has two options: Option 1: to buy a share. If she is successful her income will be 700 Birr and if she is not successful her income will be 100 Birr. Option 2: to do nothing and keep on earning 400 Birr. Assuming that success and failure are equally likely, a) What would be her expected income if she buys the share? b) What would be her expected utility of buying the share? c) Would Martha buy the share? Why? and Is Martha risk averse, risk lover or risk neutral?The economy is populated by 100 agents. Each agent has to divide 1 unit of timebetween work and leisure given the wage rate w paid on the labor market. In additionto the salary, he or she also receives dividend a income of π = Π/100 (the total profitof the firms Π is distributed equally among all the consumers in form of dividends)Suppose that the government does not incur expenditures, so G=0.The agent’s utility function depends on consumption (c) and leisure (l), and it is assumedto satisfy u(c, l) = 0.5 ln(c) + 0.5 ln(l). On the other side of the market, there arefirms who hire workers and produce output. The representative firm operates witha Cobb-Douglas production technology Y = zK^0.5N^0.5, where z denotes the totalfactor productivity, and K = 100 is a fixed amount of capital. Each of the firm’semployees receives wage w, i.e. the total labor cost of the firm is equal to wN^dSuppose that initially z = 1 (so the competitive equilibrium is the one we calculatedin class), but the…
- Now,suppose N=3 with a market clearing interest rate. The first two agents are the same as earlier. The third agent has an endowment of 20 in the first period and consumes 15 in the second period. If the first two agents each consumed 21 units in the first period, how much did the third agent consume in the first period? Plz do fastSuppose the consumer's utility function is given by U(x,y) = X3/5y2/5, and the exogenous variables are given by M = 500, Px = 5, and Py = 4. Price of y changes to Py = 2. What is the income effect ony?O A.-14.53O B. +14.53O C. +24.21O D. +25.79O E. None of the above Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.V7 Consider a owner-manager problem in which πgross = 2e + ε [manager has control over e, ε are factors outside of manager’s control, ε~N(0,σ2 )] The owner pays the manager a salary of s out of the gross profits. Manager’s cost of effort = e2 /2. Manager has constant risk aversion utility function. σ 2 = 4 A = 1 a) What is the first-best outcome for manager utility, manager effort, and net profits of the owner? b) Now consider that the owner cannot observe manager effort and offers a salary tied to gross profits: s(πgross) = a + b πgross What is the second-best outcome for manager utility, manager effort, and net profits of the owner?