Emissions of nitrogen oxides, which are major constituents of smog, can be modeledusing a normal distribution. Let x denote the amount of this pollutant emitted (inparts per billion) by a randomly selected vehicle. Suppose the distribution of x can bedescribed by a normal distribution with μ = 1.6 and σ = 0.4. A city wants to offer somesort of incentive to get the worst polluters off the road. What emission levelsconstitute the worst 10% of the vehicles?
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Emissions of nitrogen oxides, which are major constituents of smog, can be modeled
using a
parts per billion) by a randomly selected vehicle. Suppose the distribution of x can be
described by a normal distribution with μ = 1.6 and σ = 0.4. A city wants to offer some
sort of incentive to get the worst polluters off the road. What emission levels
constitute the worst 10% of the vehicles?
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- Assume that there are two parties, I and V. I engages in an activity that tends to injure V. V and I both can take care to reduce the expected harm from accidents. Specifically, suppose that if I takes no care (i.e., spends $0 on accident precautions), expected injury to V is $250. If I spends $40 on accident precautions, however, the expected injury to V is reduced to $175. Further suppose that V has a choice between taking no care or spending $50 in care to avoid accidents. If V spends $50 in care, V’s expected harm falls by $20 regardless of the level of care that I takes. Assume that courts adopt the socially‐optimal level of injurer care as the negligence standard. That is, if I takes less than the socially‐optimal level of care, she will be found negligent and must pay for all damages to V. If I takes at least the socially optimal level of care, she will not have to compensate V for his damages. 1. Under a negligence standard, what is I’s dominant strategy? a) I does not have a…An individual has the utility function U(I) = I^(1/2), where I is their net income. (Note that I to the exponent/power of 1/2 is the same as the square root of I.) The individual starts with $1600 in income. The individual has a 20% probability of being very sick, 30% probability of being slightly sick, and 50% probability of being healthy. If the individual is sick, they lose net income because they need to pay healthcare costs. The healthcare costs are $1600 if they are very sick, $700 if they are slightly sick, and $0 if they are healthy. Please use this information for the following parts of this question unless otherwise specified. What is the individual's expected utility? Suppose a health insurance company offers the individual a full insurance contract. What is the actuarially fair, full insurance premium for this individual? What is the individual's expected utility if they purchase a full insurance contract at the actuarially fair, full insurance premium?Assume that there are two parties, I and V. I engages in an activity that tends to injure V. V and I both can take care to reduce the expected harm from accidents. Specifically, suppose that if I takes no care (i.e., spends $0 on accident precautions), expected injury to V is $25. If I spends $5 on accident precautions, however, the expected injury to V is reduced to $18. Further suppose that V has a choice between taking no care or spending $4 in care to avoid accidents. If V spends $4 in care, V’s expected harm falls by $2 regardless of the level of care that I takes. Assume that courts adopt the socially-optimal level of injurer care as the negligence standard. That is, if I takes less than the socially-optimal level of care, she will be found negligent and must pay for all damages to V. If I takes at least the socially optimal level of care, she will not have to compensate V for his damages. What is the Nash equilibrium of this game under a rule of no liability? Question…
- Exlplain Linear Conditionally Unbiased Estimators and the Gauss–Markov Theorem with its limitations?Suppose that Winnie the Pooh and Eeyore have the same value function: v(x) = x1/2 for gains and v(x) = -2(|x|)1/2 for losses. The two are also facing the same choice, between (S) $1 for sure and (G) a gamble with a 25% chance of winning $4 and a 75% chance of winning nothing. Winnie the Pooh and Eeyore both subjectively weight probabilities correctly. Winnie the Pooh codes all outcomes as gains; that is, he takes as his reference point winning nothing. For Pooh: What is the value of S? What is the value of G? Which would he choose? Eeyore codes all outcomes as losses; that is, he takes as his reference point winning $4. For Eeyore: What is the value of S? What is the value of G? Which would he choose?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.
- Explain the variance version the Theorem of Coase9 Use the filtering model to determine the number of high quality (H) and low quality (L) homes at time t. Assume that there are a total of 2,000 homes in the community in time (t-1), of which 40% are high quality and the rest are low quality, the filtering rate is 0.03, and the retirement rate is 0.02In this plot we model some of the Australian markets targeted by the Safeguard Mechanism (e.g. fossil fuels). On the horizontal axis we have the quantity, and on the vertical axis its price. If there were no externalities the welfare maximizing quantity would be [Select (1)], while [Select (2)] would reflect the true benefit and cost to society. However, this model describes the presence of a [Select (3)] externality in [Select (4)]. Therefore, the welfare-maximizing quantity is [Select (5)] and the deadweight loss is [Select (6)]. If the externality was fully internalized through a corrective tax equal to [Select (7)], then the new market price would be [Select (8)], the new market quantity would be [Select (9)] and society's welfare would be [Select (10)] without the corrective tax. (1) a) Qa b) Qb c) Qc d) none of the above (2) a) Pa b) Pb c) Pc d) none of the above (3) a) positive b) negative c) Neither a positive nor negative (4) a)consumption b) production (5) a) Qa b) Qb c)…
- In order to encourage energy conservation, many public utility companiescharge consumers a higher rate on units of electricity consumed in excess of some threshold amount. In contrast, a common practice by other firms is to offer “quantity discounts” to consumers who purchase large quantities of a good. Suppose income is $100, PX = $2 if the consumer buys less than 40 units of X, and PY = $5.A. For the energy case, assume PX = $3 if the consumer buys more than 40 units of XB. For the “quantity discounts” case, assume PX = $1 after 40 units of X were consumed Draw the budget constraints in each of the cases above. What are the implications of the opportunity sets in terms of consumer behavior to consume each of the products?Question 3 Consider the following airline capacity allocation problem with buy-up. The total capacity is 100.There are three classes. All class demands follow normal distribution. The fare prices and demand statistics are given as follows: Class Fare Mean Std. Dev. 1 1000 17 6 2 900 45 15 3 500 90 20 Suppose that if a class 3 demand is rejected booking, each individual has a probability of 0.3 to become a class 2 demand; and if a class 2 demand is rejected booking, each individual has a probability of 0.2 to become a class 1 demand. The airline company needs to determine the nested protection levels. Use @risk simulation optimization tofind the optimal decisions. (Please round all the simulated numbers and solutions to the nearest integer.)Fare F ($/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