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- Describe the relationship between Expected Value, Expected Utility and Certain Equivalent (at least 150 words)Demand for your firm's products is related to the state of the economy. If the economy is expanding next year, the company estimates sales to be $120 million. If there is a recession next year, sales are assessed to be $40 million. Otherwise, sales are estimated at $70 million. Economists have estimated the chances that the economy will be either expanding, in a recession, or normal next year to be 20%, 30%, and 50% respectively. Calculate the expected annual sales. Enter your numerical answer: expected annual sales: $ million(a) The price of a good changes according to the recurrence equation 2p + Pt-1 = 30 where p, is the price, in pounds, on the tth day. (1) If the price on the first day is £7, how does pi behave in the long-term? (ii) After how many days will the price be within a penny of its limiting value?
- Gerry likes driving small cars and buys nearly identical ones whenever the old one needs replacing. Typically, he trades in his old car for a new one costing about $15,000. A new car warranty covers all repair costs above standard maintenance (standard maintenance costs are constant over the life of the car) for the first two years. After that, his records show an average repair expense (over standard maintenance) of $2600 in the third year (at the end of the year), increasing by 50 percent per year thereafter. If a 30 percent declining-balance depreciation rate is used to estimate salvage values and interest is 8 percent, how often should Gerry get a new car? Click the icon view the table of compound interest factors for discrete compounding periods when i = 8%. Gerry should get a new car every years, which has the V EAC of s (Round to the nearest whole number as needed)The monthly sales of Sunny Electronics' new sound system are given by q(t) = 2,000t − 50t2 units per month, t months after its introduction. The price Sunny charges is p(t) = 1,000 − t2 dollars per sound system, t months after introduction. Find the rate of change of monthly sales. HINT [See Example 4(a).] q'(t) = Find the rate of change of the price. p'(t) = Find the rate of change of monthly revenue 5 months after the introduction of the sound system. $ per month Interpret your answer. When t = , the revenue is increasing at a rate of $ per month.Gerry likes driving small cars and buys nearly identical ones whenever the old one needs replacing. Typically, he trades in his old car for a new one costing about $15 000. A new car warranty covers all repair costs above standard maintenance (standard maintenance costs are constant over the life of the car) for the first two years. After that, his records show an average repair expense (over standard maintenance) of $2500 in the third year (at the end of the year), increasing by 50% per year thereafter. If a 30% declining balance depreciation rate is used, and interest is 8%, how often should Gerry get a new car?
- R(p) = pN(p).| Bob is currently selling tires for 60 dollars each. His weekly sales are running at 130 tires per week, so N(60) = 130. His marketing department estimates that he will lose 2 sales per week for each 10 dollar increase in unit price, so N'(60) = -0.2. Estimate Bob's increase in weekly revenue for each one dollar increase in tire price. Revenue increase =1 dollarsQdb=D -5Pb+5Pm +0,05 R+ 25 Qob=10P6 Qdb3 Quantity asked for chocolate .cookies. Pb= The price of the chocolat cookie() Pm= The price ofa muffin ) R= The revenue () Qob%3DThe quantity offeced of the chocolote cootie. %3DThe Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving on a business trip to Boston and will eat dinner at three of these restaurants. Your company will reimburse you for a maximum of $50 per dinner. Business associates familiar with these restaurants have told you that the mea cost at one-third of these restaurants will exceed $50. Suppose that you randomly select three of these restaurants for dinner. a. What is the probability that none of the meals will exceed the cost covered by your company (to 4 decimals)? b. What is the probability that one of the meals will exceed the cost covered by your company (to 4 decimals)? c. What is the probability that two of the meals will exceed the cost covered by your company (to 4 decimals)? d. What is the probability that all three of the meals will…
- Consider the lottery that assigns a probability T of obtaining a level of consumption CH and a probability 1-T of obtaining a low level of consumption c, with CH > C1. Consider an individual facing such a lottery with utility function u(c) that has the properties that more is better (that is, a strictly positive marginal utility of consumption at all levels of c) and diminishing marginal utility of consumption, u"(c) < 0. As usual, we are using the shorthand u'(c) consumption and u"(c) = " = dư ( to be the second derivative of the utility function (which is also the derivative of the first derivative of the utility function). du(c) for the first derivative of the utility function with respect to dc du(c) dc2 du' (c) dcEmma has a utility functionU(x1, x2, x3) = logx1+ 0.8logx2+ 0.72logx3 incomes x1 , x2, x3 in the next three years. This is an example of (A) expected value; (B) quasi-hyperbolic utility function; (C) standard discounted utility; (D) none of the above.Orange Tech (OT) is a software company that provides a suite of programs that are essential to everyday business computing. OT has just enhanced its software and released a new version of its programs. For financial planning purposes, OT needs to forecast its revenue over the next few years. To begin this analysis, OT is considering one of its largest customers. Over the planning horizon, assume that this customer will upgrade at most once to the newest software version, but the number of years that pass before the customer purchases an upgrade varies. Up to the year that the customer actually upgrades, assume there is a 0.50 probability that the customer upgrades in any particular year and that the customer will upgrade in 25 years if they haven't already by that point. In other words, the upgrade year of the customer is a (discrete) random variable. For guidance on an appropriate way to model upgrade year, refer to Appendix 13.1. Furthermore, the revenue that OT earns from the…