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- Suppose an individual in the Grossman model is trying to decide what to have for dinner. His options are as below. Each dish has an effect on the level of home good Z and health H. Мeal Home good Z Нeath H Steak and eggs (A) Kale salad with broccoli (B) Entire box of cookies (C) +7 -2 -2 +5 +10 -20 Suppose the dinner's single-period utility function is U=3Z+H • If the individual is trying to maximize his single-period utility, and he can only select one item from the table (assuming he can afford any item in the table). Which meal would he choose? Please type in A, B, or C (do not enter space, punctuation, or any other symbols or words) • A miracle pill is discovered that halves the negative health impact of cookies. How does this impact the individual's choice? What meal would be chosen now? Please type in A, B, or C (do not enter space, punctuation, or any other symbols or words) • If the individual lives in multi-period rather than single-period, would he value Z or H more in…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 goodNutritional economics. Suppose we are considering a hungry individual in the Gross-man 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. A miracle pill is discovered that halves the negative health impact of cookies. How does this impact the diner’s choice?c. What effect does the miracle pill have on the diner’s health H? Interpret this result.Does this mean the diner would be better off without the miracle pill?d. 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…
- Suppose an individual in the Grossman model is trying to decide what to have for dinner. His options are as below. Each dish has an effect on the level of home good Z and health H. Мeal Home good Z Health H Steak and eggs +7 -2 Kale salad with broccoli -2 +5 Entire box of cookies +10 -20 Suppose the dinner's single-period utility function is U=3Z+H 1. If the individual is trying to maximize his single-period utility, and he can only select one item from the table (assuming he can afford any item in the table). Which meal would he choose? Explain your answer. 2. A miracle pill is discovered that halves the negative health impact of cookies. How does this impact the individual's choice? Explain your answer. 3. If the individual lives in multi-period rather than single-period, would he value Z or H more in multi-period? Explain your answer. Paragraph I U v A •.. > lili BWhich axiom of the exponential discounted utility model is violated by the quasi-hyperbolic ( β,δ) model? Explain.In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w, b) = w¹/4b³/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is T. Question 3 Part a Express Ben's expected utility function. (Hint: find Ben's optimal consumption in each state of nature first) Question 3 Part b Let's assume = 0.5. Knowing that bad weather…
- In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w, b) = w¹/46³/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is π. Question 3 Part a Express Ben's expected utility function. (Hint: find Ben's optimal consumption in each state of nature first) Question 3 Part b Let's assume π = 0.5. Knowing that bad weather…The Foundations of Behavioral Economic Analysis Consider the following property of choice correspondence : Show that maximization of complete and transitive preference satisfies β-axiom. I need this ASAPState the implications of the weak axiom of revealed preference (WARP) for consumer choice. The following table indicates a consumer's observed choices for two goods, a1 and *2, under three sets of prices: period Pi P2 1 1 3 3 2 1 3 3 4 3 1 Do these choices satisfy WARP? Explain why or why not.
- 1. A standard model of choice under risk is Expected Utility Theory (EUT) in which preferences over lotteries that pay monetary prizes (x₁, x2, ..., xs) with probabilities (P1, P2, ..., Ps) with Eps = 1 are represented by the function L S (a) What does it mean to say that a function represents the consumer's prefer- ences? Σpsu(xs) Choice 1 8=1 (b) State and briefly comment on the axioms required for the EUT representation. (c) Consider the following experiment of decision making under risk in which sub- jects are asked which lottery they prefer in each of the following two choices: Lottery B 0 with prob. 0.01 10 with prob. 0.89 50 with prob. 0.10 Lottery D Choice 2 Lottery A 0 with prob. 0 10 with prob. 1 50 with prob. 0 Lottery C 0 with prob. 0.90 10 with prob. 0 50 with prob. 0.10 Suppose that the modal responses are Lottery A in Choice 1 and Lottery D in Choice 2. Assume that utility of zero is equal to zero and illustrate why it is not possible to reconcile these experimental…1. For each of the following scaling functions for a von Neumann-Morgenstern utility func- tion, determine the Marginal Rate of Substitution between X1 and X2 and the equation for an indifference curve through the consumption bundle (100,100) (solve for X2 on the left hand side of the equation). State 1 is the bad outcome that occurs with probability 0.2 and State 2 the good outcome that occurs with probability 0.8. Graph these indif- ference curves and comment on what you see. Is a consumer with these preferences risk averse, risk neutral, or risk loving? (a) V(X) = InX (b) V(X)= VX (c) V(X)= X (d) V(X)= X²A utility function is called separable if it can be written as U(x, y) = U (x) + U,(y), where U > 0, U" < 0, and U1, U, need not be the same function. a. What does separability assume about the cross-partial derivative U„? Give an intuitive discussion of what word this condition means and in what situations it might be plausible. b. Show that if utility is separable then neither good can be inferior. c. Does the assumption of separability allow you to con- clude definitively whether x and y are gross substitutes or gross complements? Explain. d. Use the Cobb-Douglas utility function to show that separability is not invariant with respect to monotonic transformations. Note: Separable functions are examined in more detail in the Extensions to this chapter.
