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- 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…Sarah is considering two investment proposals. Proposal A is to purchase a new computer. Proposal B is to purchase a new printer. She will not buy the printer unless she buys the computer. The relationship between Proposals A and B is best described by which of the following? a. B and A are mutually exclusive b. B is contingent on A c. A is contingent on B d. Not enough information is given to determine a relationshipSuppose that we have an economy with many identical households. There is a government that exogenously consumes some output and pays for it with lump sum taxes. Lifetime utility for a household is: U =InCt +ßlnCt+1 The household faces two within period budget constraints given by: Ct + St = Yt – Tt Ct+1 =Yt+1 -Tt+1 +(1+rt)St Use the Euler equation and intertemporal budget constraint to derive an expression for the consumption function. The government faces two within period budget constraints: (1) G_t + SG_t = T_t (2) G_(t+1) = T_(t+1) + (1 + r_t)SG_t In equilibrium, what must be true about S_t and SG_t?
- The diagram below depicts Marco’s choice of consumptions in periods 1 and 2. He has $100 worth of grain in period 1 and no income in period 2. Marco has two choices. In scheme 1, he can sell the grain that he does not consume and lend the money at 10%. In scheme 2, he can invest the grain that he does not consume (e.g., planting as seed) for a return of 50%. Which of the following statement is correct? [ Only One Option correct ] GIVE EXPLANATION FOR EACH OPTION. A. Going from scheme 1 to scheme 2, the substitution and income effects have opposite effects on period 2 consumption.B.Marco can do better than consumption choice B by investing all of his grain and consuming the output in period 2.C. Marco is less impatient at B than at AD. Marco can do better than consumption choice B by investing all of his grain and borrowing against his period 2 output.Clare is contemplating her possible consumption patter for this year and next. She know that she will have income of $50,000 this year and $55,000 next yea. Her plan is to consume $40,000 this year (t=0). She is also going to invest 30,000. This investment has a positive NPV of $450. She decides to take the investment; in addition, the return on the investment is 9.62%. What consumption she can expect at t=1? (show a detailed procedure)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…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 BAnna has endowment 1500 now and 500 later. Internet rate is 2.0%. She prefers smooth consumption to time (i.e., u0=u1=u). a. Assume utility function, u(c)= log c. What are the optimal consumption c0and c1if Anna's beta=1, and she wants to maximize her utility? b. Now assume that the utility function, u(c)=c0.5. If everything else remains the same as Problem 1(a), what are the optimal consumption c0and c1if Anna wants to maximize her utility?
- 5.19 explain.With the help of a diagram explain the main principles of the first-order Markov Model.In your answer explain any notation that you use. Explain what is meant by the term‘’first-order”.3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up = log(co) +a log(ci) where c is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h /() and human capital is paid at rate w. The parent has a total income of (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.