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)

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)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.8P

See similar textbooks

Similar questions

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
1 -(Y– 11). V49 Suppose the random variable Y has a mean of 11 and a variance of 49. Let Z = Show that = 0. Hz =E I (Y-D] = 0 %D (Round your responses to two decimal places)
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.
A consumer is maximising her utility function: U(r. y) = (r05 +y0.5)2, subject to the budget constraint 4x + 2y = 108. (a) Set up the Lagrangian function of this utility maximisation problem and first-order conditions. (b) What are the utility maximizing amounts of x and y? Also, calculate the multiplier. (c) What are the utility maximising amounts of x and y if the budget constrain to x+ 2y = 36? How would change? Explain your reasoning. (Hint: Yc need to calculate A, rather comment on how it would change and why.)
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?
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…
Consider the lottery that assigns a probability r of obtaining a level of consumption CH and a probability 1-T of obtaining a low level of consumption cL 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) CL. Consider du(c) for the first derivative of the utility function with respect to dc d²u(c) dc2 du' (c) consumption and u"(c) which is also the derivative of the first derivative of the utility function). to be the second derivative of the utility function dc
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.(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=_____
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 =
V*(p1, p2, 1) = True False P₁ P₂ 1² is a valid indirect utility function.
Show that a decision maker who has a linear utilityfunction will rank two lotteries according to their expectedvalue.