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- V*(p1, p2, 1) = True False P₁ P₂ 1² is a valid indirect utility function.subjective expected utility(SEU)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.
- Problem 1 Jane has the following utility function: u(w) w^.5 or the square root. function Which of the following prospects would she prefer? P1(.4, 3,000, 600) P2(.7, 1,200, 1,000) P3(.6, 2,000, 100)Upon graduating from UT this May, you take on a management position working at UtMax theater. You will consider the utility of seeing performance over 1 month, and suppose that at a regular price of $$$ per ticket (my assigned ticket price is 145), customers will see no performance, however with the price reduced by $5, customers will see one performance per month and when reduced by $10, customers will see two performances. As long as the number performances, x, is small, your demand function for performance can be modeled by p=D(x). Write down your demand function.Consider an agent who has to choose how many donuts to eat. He exhibits the choices C({1, 2}) = {1, 2} and C({1, 2, 3}) = {2, 3}. Can these choices be explained by : (i) maximization of a complete and transitive preference? (ii) satisficing? (iii) regret aversion? %3D
- Chris Traeger is trying to decide whether or not to purchase health insurance. Chris knows that if he is healthy, his wealth will be $2,000 this year. However, if he gets sick his wealth will only be $500. Chris knows the probability of getting sick is 40%. His utility function is written below. U = (2) What is utility if the individual purchases insurance at the actuarially fair price? 25.29 utils 26.46 utils 31.62 utils 18.97 utilsJohn is a farmer with $225 of wealth. He can either plant corn or beans. If he plants corn, John earns an income of $675 if the weather is GOOD and $0 if the weather is BAD. If he plants beans, John earns an income of $451 under both GOOD and BAD weather. The probability of GOOD weather is 0.7. The probability of BAD weather is 0.3. John's utility function is u(C) = 5VC , where C is the value of consumption. Use this information to fill out the table below. (Don't forget to include the value of wealth when you compute consumption!). The PDF will round all typed numbers to two decimals; However, you should use all decimals when computing your answers. %3D Plant Corn Plant Beans Expected value of consumption Expected value of utility Certainty Equivalent Risk Premium 9. What type of risk preferences does John have? Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and…John is a farmer with $225 of wealth. He can either plant corn or beans. If he plants corn, John earns an income of $675 if the weather is GOOD and $0 if the weather is BAD. If he plants beans, John earns an income of $451 under both GOOD and BAD weather. The probability of GOOD weather is 0.7. The probability of BAD weather is 0.3. John’s utility function is U(c) = 5√c , where c is the value of consumption. Mae owns an insurance company in a nearby town and has decided to offer conventional crop insurance to corn farmers in the area. Assume that Mae has perfect information and can write and enforce an insurance contract that requires the farmer to plant corn. Here’s how the insurance contract works. At the beginning of the year, the corn farmer pays an insurance premium of $202.5. If the weather is GOOD, Mae makes no payment to the farmer. If the weather is BAD, Mae makes an indemnity payment of $675 to the farmer. a. If a farmer buys this insurance contract,what is Mae’s expected…
- T/F Explain If preference is strongly convex, the utility function will exhibit dimin- ishing marginal utility (MU).Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8 logx2+ 0.72 logx3over her 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. Emma’s preferences can exhibit which of the following behavioral patterns?(A) preference for flexibility;(B) context effects;(C) time inconsistency;(D) intransitivity.A person with utility function U(x, y) = 5 + y + 2x has nonconvex preferences. True False