Suppose that consumers spend their income on either health insurance or on a “composite good”. Find the optimal bundle of health insurance (HI) and other goods (G) given the following budget constraint and utility function. How much utility does this bundle give the individual? Put HI on the x axis of any graphs. Budget constraint: 1600 = 160*HI + 20*G Utility function: U=HI*G where MRS = -G/HI
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Suppose that consumers spend their income on either health insurance or on a
“composite good”. Find the optimal bundle of health insurance (HI) and other goods (G) given the following budget constraint and utility function. How much utility does this bundle give the individual?
Put HI on the x axis of any graphs.
Budget constraint: 1600 = 160*HI + 20*G
Utility function: U=HI*G where MRS = -G/HI
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- Assume an individual's optimal bundle of health insurance (Hi) and other goods (G) is Hi=5 and G=40. Now assume Medicaid is introduced and the individual described above is eligible. Medicaid offers a fixed bundle to the eligible: They may have 3 units of health insurance at no cost. If an individual elects to be covered by Medicaid, they cannot purchase additional health insurance; they are limited to the 3 units provided by Medicaid. a. Does the individual described above choose to enroll in Medicaid? Usegraphs and thoroughly justify your answer. b. Does their consumption of health insurance go up or down with theintroduction of Medicaid?Given: Budget constraint: 1600 = 160*HI + 20*GUtility function: U=HI*G where MRS = -G/HI Consider someone who has an optimal bundle of health insurance (Hi) of 5 and other goods (G) of 40 (Hi = 5, G = 40). Assume that this individual prefers to optimally purchase no health insurance (Hi). On a graph, draw the budget constraint offered above and include the indifference curve for a person who optimally chooses to be uninsured.A person has $50/week for transport expenditures for their job. Uber ride = $10. Subway ride =$2.50. If Uber rides are on the x-axis, what is the slope of the budget constraint? If the marginal utility of a person’s last Uber ride was 30 and the marginal utility of a person’s last subway ride was 5, then how should the person adjust the consumption bundle to maximize utility? A -Increase the number of Uber rides and decrease the number of subway rides B -Decrease the number of Uber rides and increase the number of subway rides C -Remain the same – the consumption bundle is already utility- maximizing D -Change ambiguously – there is not enough information to answer
- An individual has the following utility function: U = Z!/2 H/2, where Z is a composite good and H is the level of health. The individual has income, m = $100. The price of the composite good, Z, is Pz = 1. The price of health, H, is PH = 4. What is the optimal consumption bundle of H and Z that maximizes utility? Show your steps and show the decision graphically (which includes finding the endpoints of the budget constraint).Sam's extended family spends $3,200 per month on wine and beer. Their utility function is given by U = 200WB, where W represents the number of bottles of wine that they buy, and B represents the number of cases of beer that they buy. Wine costs $25 per bottle and beer costs $32 per case. Sam's family wants to maximize their utility. Calculate how many bottles of wine and how many cases of beer they should buy. Show your calculation(s).With a high stress job that oversees the public health of a nation, Tony loves to eatpomegranate (qm) and spinach (qs), both rich in anti-oxidants, to keep him healthy.Suppose his preferences for the two goods can be captured by the utility functionU(qm, qs) = (qm)^1/3(qs)^2/33 . Explain whether each of the following statements is true orfalse.(a) Tony weakly prefers (27, 1) to (3, 3).(b) Tony likes (27, 1) at least as much as (3, 3).(c) Tony strictly prefers (27, 1) to (3, 3).(d) Tony is indifferent between (27, 1) and (3, 3).(e) Tony weakly prefers (9, 1) to (3, 3).(f) Tony weakly prefers (3, 3) to (9, 1).
- A consumer with the following utility function U = xy? faces two constraints. The first is the normal budget constraint where he has GH¢150 and the price of x and y are both GH¢1. Also, the consumer has been issued 200 ration coupons by the government which he must use whenever he buys either x or y. It takes 2 coupons to buy an x and 1 coupon to buy a y (for example: to buy 3 units of x it would require GH¢3 or 6 coupons) (i) Write down the Lagrangian for this problem. (ii) Applying the steps of Kuhn-Tucker, find the optimal x and y. Identify which constraints, if any, are binding.Barbara has an annual budget of $1000 with which to spend on the opera and golf. Tickets to the opera cost $50 each, and a round of golf costs $50. Barbara's budget line is illustrated in the figure to the right, along with her satisfaction-maximizing bundle (bundle A) and the indifference curve that represents bundle A's level of satisfaction. Now suppose the golf course becomes private, whereby it charges its members a $400 annual fee to play golf, which then costs $10.00 per round. Using the line drawing tool, graph the new budget line. Assume in your calculations that Barbara pays the annual golf fee. Label this line L2. Carefully follow the instructions above, and only draw the required object. Opera (tickets per year) 24- 22- 20- 18+ 16- 14- 12- 10- 8- 6- 4- 2- 0- 8 A 16 4₁ 24 32 40 48 Golf (rounds per year) 56 A 64abby is a single mom with a weekly budget of $100. She can spend her weeklyincome on food and diapers for her son. Price of food is $1 and price of a diaperis 50 cents. Her son needs at least 5 diapers a day, therefore she must purchaseat least 35 diapers weekly. Jennifer’s utility function is U (f, d) = f 0.9d0.1,where f and d represent quantity of food and diapers, respectively.Question 1 Part aFind abbys optimal consumption bundle. Make sure to draw her budgetconstraint and indifference curves and clearly demonstrate your solution.
- John currently lives in Sydney where he earns $2700 a week as a high school principal. If he moves to Batemans Bay, he has to accept a position as a classroom teacher where he will earn $2100 a week. John only considers two goods, cost of living (c) and health (h). In Sydney, pe = 54 and ph = 90. In Batemans 1 1 Bay, Ph = 36. John's utility function is u(c, h) = h + cihi. a) What is John's optimal consumption of h in Sydney? b) What would be John's optimal consumption of c in Batemans Bay? c) What is the maximum cost of living ph such that John will accept to move to Batemans Bay?Let the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 Tux 8 14 18 20 20 Tuy 6 10 13 15 16 Mux Muy Mux/px Muy/py D) Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? E) What is the total utility of X and Y? F) Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility? G) What are the total utility of X and Yhe Calculus of Utility Maximization and Expenditure Minimization -End of Appendix Problem uppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= X05.05 UB(X,Y)= X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X = 25 and Y* = 50 - b. The optimal bundle for consumer B is X = 120 and Y* = 60