(1)What's the lifetime happiness of the consumer if ONLY storage is used. Lifetime happiness=______ (2)What's the lifetime happiness of a consumer if ONLY investment is used. Lifetime happiness=_____

(1)What's the lifetime happiness of the consumer if ONLY storage is used. Lifetime happiness=__ (2)What's the lifetime happiness of a consumer if ONLY investment is used. Lifetime happiness=_

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.8P

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Your utility function is U = In(2C) where C is the amount of consumption you have in any given period. Your income is $40,000 per year and there is a 2% chance that you will be involved in a catastrophic accident that will cost you $30,000 next year. Suppose that 25% of the population is comprised of individuals like you, who have a probability of a catastrophic accident, and the other 75% of the population will not face such a shock. The insurance company knows the incidence of catastrophic accidents in the aggregate, i.e., at the population level, but not to a person. Explain the conditions under which an insurance company might offer insurance (against income loss) to individuals, even if it could not determine who might be hit with a large negative income shock and those who might be hit with a small negative income shock.
In a DD model with 3 periods t=0,1,2. Each consumer is endowed with 1 potato at t=0, has probability 1/2 of becoming hungry at t=1 and probability 1/2 of becoming hungry at t=2. Consumer utility is given by u(c)=1-1/c. Storage technology generates a gross return of 1 from period 0 to 1, and return of 1 from period 1 to 2. Investment technology generates a return of 3 from period 0 to period 2. If an investment is liquidated early in period 1, its return is reduced to 0.5. Suppose all consumers in town pool their potatos together. Of the 100 potatos, they store 70 and invest 30. When t=1 comes, early types are fed with the stored potatoes. When t=2 comes, late types are fed with the invested potatos. The expected lifetime happiness of a consumer = (keep 3 digits after decimal points, eg, 0.456)
In a DD model with 3 periods t=0,1,2. Each consumer is endowed with 1 potato at t=0, has probability 1/2 of becoming hungry at t=1 and probability 1/2 of becoming hungry at t=2. Consumer utility is given by u(c)=1-1/c. Storage technology generates a gross return of 1 from period 0 to 1, and return of 1 from period 1 to 2. Investment technology generates a return of 3 from period 0 to period 2. If an investment is liquidated early in period 1, its return is reduced to 0.5. Suppose all consumers in town pool their potatos together. Of the 100 potatos, they store 50 and invest 50. When t=1 comes, early types are fed with the stored potatoes. When t=2 comes, late types are fed with the invested potatos. The expected lifetime happiness of a consumer =
In a DD model with 3 periods t=0,1,2. Each consumer is endowed with 1 potato at t=0, has probability 1/2 of becoming hungry at t=1 and probability 1/2 of becoming hungry at t=2. Consumer utility is given by u(c)=1-1/c. Storage technology generates a gross return of 1 from period 0 to 1, and return of 1 from period 1 to 2. Investment technology generates a return of 3 from period 0 to period 2. If an investment is liquidated early in period 1, its return is reduced to 0.5. Suppose all consumers in town pool their potatos together. Of the 100 potatos, they store 20 and invest 80. When t=1 comes, early types are fed with the stored potatoes. When t=2 comes, late types are fed with the invested potatos. The expected lifetime happiness of a consumer = (keep 3 digits after decimal points)
Q2: Consider a person who is thinking about whether to engage in a life of crime. He knows that, if he gets caught, he will be in jail and his consumption will be low, xº, but if he does not get caught, he will be able to consume an amount x₁ that is considerably above Χρ· (a) Suppose that x₁ = 20; x₁ = 80 (where both are expressed in thousands of pounds) and suppose the probability of getting caught is 8 = 0.5. What is the expected consumption level if the life of crime is chosen? (b) Suppose the potential criminal's tastes over gambles can be expressed using the following utility function u(x) = In (x). Calculate the person's expected utility from a life of crime. How does it compare with the utility of the expected value of consumption? Based on your answer, explain this individual's attitude towards risk and draw the consumption/utility relationship. (c) Consider the level of consumption this person could attain by not engaging in a life of crime. What level of consumption from an…
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V*(p1, p2, 1) = True False P₁ P₂ 1² is a valid indirect utility function.
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
A consumer has the following utility function: U(x.y)=x(y+1), where x and y are quantities of two consumption goods whose prices are Px and Py, respectively. The consumer also has a budget of B. Therefore, the Lagrangian for this consumer is x(y + 1) + X(B – Prx – Py) (a) Verify that this is a maximum by checking the second-order conditions. By substituting x* and y* into the utility function, find an expression for the indirect utility function U* = U(Pr, Py, B) and derive an expression for the expenditure function E = E(Pr, Py, U*) (b) This problem could be recast as the following dual problem Min Prx + Pyy Subject to æ(y + 1) = U* Find the values of x and y that solve this minimization problem and show that the values of x and y are equal to the partial derivatives of the expenditure function, ðE/ðP, and ðE/ðP, respectively.
Analysing Utility Function and Household Optimization Consider a household with the following utility function representing their preferences over consumption: with U = u(C) + Bu(C++1) u(C) = exp(-aC), BE (0,1), a>0 where Ct and Ct+1 represent consumption in the current and future periods, respectively. The household faces a two-period decision problem. They receive endowments of Yt and Yt+1 in the current and future periods, respectively. The real interest rate is denoted by rt. Notice: The utility function u(C) takes on negative values for all positive consumption levels. However, in economic models, the absolute value of utility is less important than how utility changes with consumption. A higher level of utility represents a more preferred outcome for the household. Solving for Current Consumption Demand Function Solve for the household's demand function for current consumption (Ct). Express Ct as a function of Yt, Yt+1, rt, and the parameters ẞ and a. Discuss what happens to Ct…
Consider the Consumption and Savings model with random future income. The utility function of the individual is: u(C0, C1) = (C0) + (C1)1/2, where C0 is present consumption expenditure and C1 is future consumption. Let the present income be $5, the interest rate in the financial market r = 5%, and the probability distribution of future income Y1 = (1, 2; 1/2 , 1/2). Calculate the expected utility of saving $0 (consume $5 in the present) (use two decimals)