²(₂): 1. Consider a deterministic DGE model where time lasts for two periods. The representative consumer has the utility function U₂ = faces the budget constraint c, +a, -y,+(1+r), for t= 0,1; and has an initial assets position given by a., <0. a) Specify the maximization problem of the representative consumer and provide its economic interpretation. b) Assume (1) and (i) y, for t=0,1, with >0. Derive analytically the optimal consumption and assets holding plan and provide an economic interpretation. c) Explain how your result in part (b) changes if the initial asset position is positive.
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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…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 BNutritional 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 good
- 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…Consider the problem of an individual that has Y dollars to spend on consuming over two periods. Let c denote the amount of consumption that the individual would like to purchase in period 1 and c2 denote the amount of consumption that the individual would like to consume in period 2. The individual begins period 1 with Y dollars and can purchase cı units of the consumption good at a price P and can save any unspent wealth. Use sı to denote the amount of savings the individual chooses to hold at the end of period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the individual has at his/her disposal to purchase consumption goods in period 2 is (1+r)81. This principal and interest on savings is used to finance period 2 consumption. Again, for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumption good in period 2. 2 The individual's total happiness is measured by the sum of period utility across time, u(cı) + u(c2). Let u(c)…Q1. Consider a consumer with a lifetime utility function U(c, c') = u(c) + Bu(c) that satisfies all the standard assumptions listed in the book. The period 1 and 2 budget constraints are c+s=y c+sy+(1+r)s (a) What is the optimal value of s'? Impose this optimal value and derive the life-time budget constraint.
- Nutritional 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…An agent has income m that can be spent on frequent flier miles f or on other goods – a “composite good” g. Their respective prices are: pf = 10 per mile and pg = 1 per unit. The flier miles have a stepwise price schedule. After the first 25 miles the price is reduced by 20% and after 50 miles the price is further reduced by another 50%.1. Put g on the vertical axis and f on the horizontal axis. Assume m = 200, and draw the budget constraint with all the intercepts and appropriate slopes. 2. On a separate graph, repeat part (1) for m = 300. 3. On a separate graph, repeat part (1) for m = 600.Consider the problem of a consumer who chooses between consuming goods and enjoying leisure in the current and future periods. Denote the consumption and leisure in the current period as C and l, and the consumption and leisure in the future period as C′ and l′, respectively. The preference is summarized by the following utility function: U(C,C′,l,l′)=lnC+ψlnl+β(lnC′ +ψlnl′). This individual is endowed with h units of time in each period. Wage rate per unit of labour time is w and w′ in the current and future period. In addition, the consumer receives profit transfer π and π′ and pays lump-sum taxes T and T′ in the current and future periods. Denote the saving in the current period as Sp. Answer the following questions. Derive the life-time budget constraint of this consumer. Set up the consumer’s problem. Solve for consumption (C and C′), leisure (l and l′), and saving (Sp). How does an increase in wage rate w affect C, Sp, and l?
- 1. Use budget constraints to express consumption levels, ct and ct+1. (Hint: Use income conditions given above in the budget constraint. Notice that there are two possible states in the second period.)2. Rewrite the utility maximization problem as choosing the optimal at alone. (Hint: Replace ct and ct+1 in the utility function with your answers from point 1. Use probabilities to derive the expected value in the utility function. Remember that a random variable that takes values x1 in state one with probability p and x2 in state two with probability 1 − p has the expected value E [x] = p.x1 + (1 − p).x2)3. Derive the first order condition and find the optimal value of savings, at. (Hint: The only control (choice) variable is at)4. Does household accumulate precautionary savings to self-insure against the scenario of low income in the second period? Why or why not?Assume that there are N individuals, indexed by i=1,.,N. One of them, individual i, derives positive utility from her own consumption (denote by c), from her consumption in relation to the average consumption of everybody else (the other N-1 individuals), and from her charitable donations (denote by d). Assume an exogenous income level I. a) Write down a utility function that can represent individual i's preferences. b) Write down (without solving) the consumer's maximization problem. c) Discuss (in brief) whether you think that this utility function is preferable to the standard one and justify your answer.Zeynep is at the supermarket buying her bi-weekly groceries. As she arrived at the store right before closing, not much is left on the shelves; so her purchases are limited to beef, B, and an assortment of organic vegetables, V. Beef costs £50/kg and vegetables Ł10/kg. Her utility function is expressed as U(B,V) = B0-6v0.3. She has ±150 to spend. Please answer the following questions using this information: A) Given the vegetables cost less than beef, explain why Zeynep would not only buy vegetables. B) Write Zeynep's constrained maximization problem (objective function subject to her budget constraint). C) Using the Lagrangian technique, find how much beef and vegetables would Zeynep buy? D) Show that for the preferences represented as above, demand for beef is a function of only its own price, pg, and income, m, but not the price of vegetables, py. Note: Rather than using the given prices and income, use PB, Py and m. Find and comment on the comparative statics, i.e., how do changes…