Fare F ($/trip) and travel time T (hr/trip) for Bus and Rails are given Bus: F= 40, T = 3 Rail: F = 56, T=2.5 We have a utility function u = -0.005 F -0.1 t * Use the logit model to find the probability of choosing bus * What change in rain rare would achieve the probability of choosing rail to be 55%? * What value use time is implied by the utility function? Start to think about the utility of one-hour a. it will be #% b. #$ c. $20$/hr
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Fare F ($/trip) and travel time T (hr/trip) for Bus and Rails are given
Bus: F= 40, T = 3
Rail: F = 56, T=2.5
We have a utility function u = -0.005 F -0.1 t
* Use the logit model to find the probability of choosing bus
* What change in rain rare would achieve the probability of choosing rail to be 55%?
* What value use time is implied by the utility function?
Start to think about the utility of one-hour
a. it will be #%
b. #$
c. $20$/hr
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- Nutritional economics. Suppose we are considering a hungry individual in the Grossman model deciding what to have for dinner. His options are listed in Table 3.2. Each dish has an effect on the level of the home good Z and health H. a. Suppose the diner’s single-period utility function is as follows:U =3Z +HIf the diner is trying to maximize his single-period utility, and he can only select one item from Table 3.2, which meal would he choose? b. If the diner is instead trying to maximize his lifetime utility and not just his single period utility, how might your answer to Exercise 16(a) change? Is he likely to value Z or H more in the lifetime context than the single-period context? Explain your answer, and be sure to invoke the concept of a capital goodAn individual’s utility function is given as U (X) = X 0.5 where X represents the money, he has available for spending in a given time period. This individual has income of $225 in each time period and he discounts the future at the rate of 0.7. If he invests his up-front cost is 25 and his return in in the next time period is 35. a. Would this individual consider investing if his investment is financed by borrowing and cost of borrowing is 30%? (Consider two period model to justify your answer) b. Would this individual consider investing if his investment is financed by current savings? (Use two period model to justify your answer). c. Would this individual consider investing if his investment is financed by: $10 from current savings and rest of it from borrowing and the cost of borrowing is 30%? (Use two period model to justify your answer).Suppose that consumers have utility function U(C) = log(C) where C is the consumption level and log is the natural logarithm. Consumers have initial consumptionlevels of 100 and are exposed to the following risk of loss: lose 10 with probability0.4 and lose 5 with probability 0.6. They are considering buying insurance to coverthese losses. What is the fair price for the insurance?
- Suppose the large number of bike accidents in a small town results in new legislation that requires all citizens of the town to wear specialized bike helmets when riding. These new helmets reduce the probability of head trauma by 25% during a bike accident. While the new helmets the probability of a serious head injury resulting from a bike accident, they also incentivize cyclists to ride safely, which could the number of bike accidents and thus head injuries to cyclists.Present the classical model of choice under uncertainty. What are the five assump- tions which characterize the Von-Neumann-Morgenstern expected utility repre- sentation?Donna just paid $800 for a new iPhone. Apple offers a two year extended warranty for $200 and Donna is considering purchasing it. She has utility given by U(X)=√X. Without the extended warranty, the iPhone becomes worthless if it breaks. What is the minimum probability, p, that the iPhone breaks in the next two years that will cause Donna to prefer to purchase the extended warranty? p=_____________ If the probability that her phone breaks is p=0.25, will Donna will prefer to buy or not buy the warranty?
- In the CRRA utility family u(x) = x^(1−γ). If this individual has autility where γ = 0.01, would he prefer the payment of $320 or the gamble?how then can we find the total utility given q1=24, q2=30 and q3=15Arielle is a risk-averse traveler who is planning a trip to Canada. She is planning on carrying $400 in her backpack. Walking the streets of Canada, however, can be dangerous and there is some chance that she will have her backpack stolen. If she is only carrying cash and her backpack is stolen, she will have no money ($0). The probability that her backpack is stolen is 1/5. Finally assume that her preferences over money can be represented by the utility function U(x)=(x)^0.5 Suppose that she has the option to buy traveler’s checks. If her backpack is stolen and she is carrying traveler’s checks then she can have those checks replaced at no cost. National Express charges a fee of $p per $1 traveler’s check. In other words, the price of a $1 traveler’s check is $(1+p). If the purchase of traveler’s checks is a fair bet, then we know that the purchase of traveler checks will not change her expected income. Show that if the purchase is a fair bet, then the price (1+p) = $1.25.