John currently lives in Sydney where he earns $2700 a week as a high school principal. If he moves toBatemans Bay, he has to accept a position as a classroom teacher where he will earn $2100 a week. Johnonly considers two goods, cost of living (c) and health (h). In Sydney, pe = 54 and ph = 90. In Batemans11Bay, 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?

John currently lives in sydney where he earns $2700 a week In Batemans John will earn = $2100 a week…

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, Pc = 54 and ph = 90. In Batemans Bay, Ph = 36. John's utility function is u(c, h) = h + cihi. 1 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?

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, Pc = 54 and ph = 90. In Batemans Bay, Ph = 36. John's utility function is u(c, h) = h + cihi. 1 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?

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 6P

See similar textbooks

Similar questions

Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should begiven to Eren to offset his change un utility due to the price increase of an expensivemeal. Calculate the compensative variation (CV).
Eren’s two main hobbies are taking vacations overseas (V) and eating expensivemeals (M). His utility function is given as: U(V,M) = V2MLast year, the average price of taking a vacation overseas was US$200 and the averageprice of an expensive meal is $50. However, due to supply problems in Onions, theaverage price of an expensive meal rose to $75. The average price of a vacation did notchange. His income, which is $1500, did not change. Calculate the change in consumer surplus from consuming the expensivemeals considering the price change (Hint: you need to compare his optimalconsumption bundle before and after the price change to get the change in CS).
abby 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.
Styles 15. Damian Matthews is busy. He allocates his free time between watching movies and working out at the gym. The table below shows his utility from the number of times per week he watches a movie or goes to the gym. Damien has 14 hours a week to spend on movies or the gym (think of hours like $ of income here). Each movie takes 2 hours. Each gym trip takes 2 hours. Q of Gym Total Q of Movie Total Utility visits Utility from visits from Gym Visits movies 100 1 60 180 110 3 240 3 150 4 280 4 180 310 190 330 195 340 7 197 a) What bundles of gym visits and movies can Damien consume if he spends 1) all his time in the gym or 2) all his time watching movies? b) Calculate the marginal utility of each gym visit'and movie. Then calculate the Marginal Utility per hour of each activity. c) How should he allocate his time to maximize his utility? 12
Suppose you have $10, which you can wager in a game called "double or quits." In this game, you roll a fair die. If you roll a 4, 5, or 6, you win the game, getting back your $10 plus $10 more for a total of $20. If you roll a 1, 2, or 3, you lose the game and your $10. Your utility function is shown on the following graph Utility 10 20 Income According to this graph of your utility function, would you be considered risk-averse or a risk-taker? Why? Risk averse because of increasing marginal utility of income Risk taker because of increasing marginal utility of income Risk taker because of diminishing marginal utility of income O Risk averse because of diminishing marginal utility of income
Jane spends $210 per month on wine and beer. Her utility function is given by TU = 100WB, where W represents the number of bottles of wine that she buys and B represents the number of cases of beer that she buys. If wine costs $10 per bottle and beer costs $15 per case, she will maximize utility by buying: 10 bottles of wine and 13.33 cases of beer. equal amounts of wine and beer. none of the above. 10.5 bottles of wine and 7 cases of beer. 2 bottles of wine and 3 cases of beer.
EXERCISE 7 Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L, P) = 3L + P. (MU₁ = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so…
Ceja has utility function U=A2*B2 , where A equals the number of apples she eats each week, while B is the number of bananas she eats each week. Ceja has $20 to spend on fruit each week. The price of an apple is $1, while the price of a banana is $0.25. Find out the combination of Apples and Bananas that maximize Ceja’s satisfaction. If price of Banana is increased by $.25, what will be the new combination of A and B that would maximize her utility? Show graphically and drive the demand curve for Bananas
Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.
Alexi has a budget of $21 to spend on toaster and breads. He does not directly gain any utility from owining a toaster but for every slice of toasted bread he consumes he gain 2 units of utility, that is if he owns a toaster. Without the toaster, he gain 0 units of utility from consuming plain bread. Suppose the toaster has inferior quality and will break after toasting only 10 slices, then Alexi needs to buy a new one. The current market price for cheap toaster is $5 and the price for a single slice of bread is $1. Assume that Alexi aims to maximize consumer surplus. Find Alexi's income-consumption curve for slices of bread for incomes between $0 and $21, assuming a price of $1 per slice.
Alexi has a budget of $21 to spend on toaster and breads. He does not directly gain any utility from owining a toaster but for every slice of toasted bread he consumes he gain 2 units of utility, that is if he owns a toaster. Without the toaster, he gain 0 units of utility from consuming plain bread. Suppose the toaster has inferior quality and will break after toasting only 10 slices, then Alexi needs to buy a new one. The current market price for cheap toaster is $5 and the price for a single slice of bread is $1. Assume that Alexi aims to maximize consumer surplus. In a graph, draw total utility as a function of number of toasted slices, assuming that Alexi buys 1 toaster.
maddy 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. maddy utility function is U (f, d) = f 0.9d0.1,where f and d represent quantity of food and diapers, respectively.Part aFind Jennifer’s optimal consumption bundle. Make sure to draw her budgetconstraint and indifference curves and clearly demonstrate your solution.Part bmaddy uncle Sam, who is aware of her financial troubles, offers to help herout. Specifically, he offers to pay half of her weekly diaper expenses. Howmany diapers maddy would buy now? Again, demonstrate your solution bothgraphically and analytically.