QUESTION 4Linguini and Colette consume only éclair (x,) and profiterole (x2). Linguini has utility functionUA = x4x4 and Colette has utility function UB = 2xfx. Linguini is endowed with 10 éclair (x,)and 3 profiterole (x), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x2).(a) Draw an Edgeworth box with x, on the horizontal axis and x, on the vertical axis. PositionLinguini on the bottom left corner and Colette on the top right comer. Indicate the total numberof units of x, and x2. Label the endowment allocation.(b) Derive the equation of the contract curve, ie., find x(x). In your graph in (a), draw thecontract curve.

A want satisfying power of a commodity or service is known as its utility. Utility is a significant…

QUESTION 4 Linguini and Colette consume only éclair (x₁) and profiterole (x₂). Linguini has utility function U^ = x^x and Colette has utility function U = 2xx. Linguini is endowed with 10 éclair (x₂) and 3 profiterole (x₂), while Colette is endowed with 20 éclair (x₁) and 9 profiterole (x₂). (a) Draw an Edgeworth box with x₁ on the horizontal axis and x₂ on the vertical axis. Position Linguini on the bottom left corner and Colette on the top right corner. Indicate the total number of units of X₁ and x₂. Label the endowment allocation. (b) Derive the equation of the contract curve, i.e., find x(x). In your graph in (a), draw the contract curve.

QUESTION 4 Linguini and Colette consume only éclair (x₁) and profiterole (x₂). Linguini has utility function U^ = x^x and Colette has utility function U = 2xx. Linguini is endowed with 10 éclair (x₂) and 3 profiterole (x₂), while Colette is endowed with 20 éclair (x₁) and 9 profiterole (x₂). (a) Draw an Edgeworth box with x₁ on the horizontal axis and x₂ on the vertical axis. Position Linguini on the bottom left corner and Colette on the top right corner. Indicate the total number of units of X₁ and x₂. Label the endowment allocation. (b) Derive the equation of the contract curve, i.e., find x(x). In your graph in (a), draw the contract curve.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.2P

See similar textbooks

Similar questions

Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…
Justin Barlow, a careful maximizer of utility, consumes only two goods, Krispy Kreme Doughnuts and coffee. He has just achieved the utility-maximizing solution in his consumption of the two goods when the price of Krispy Kreme Doughnuts falls by 50%. As he adjusts to this event, he will most likely * consume more of both Krispy Kreme Doughnuts and coffee consume less of both Krispy Kreme Doughnuts and coffee consume more Krispy Kreme Doughnuts and less coffee consume less Krispy Kreme Doughnuts and more coffee O consume the same amount of Krispy Kreme and coffee
10.6 For every two boxes of strawberries that she consumes, Millicent insists on having one pitcher of cream. She does not, however, insist on consuming the same amount every week. Her utility function is U = min{$₁,2c₁}min{$2,2c2} where s₁ and s2 are the number of boxes of strawberries she consumes this week and next week and c₁ and c₂ are the number of pitchers of cream she consumes this week and next. Strawberries cost $2 a box and cream costs $1 a pitcher. She has a present value of $100 to spend on these goods in the next two weeks. The weekly interest rate is 1%. How many boxes of strawberries will she consume this week? (a) 10 (b) 20 (c) 22 (d) 14.1 (e) 6.06
Farah has $100 to spend each month on bread and chicken. Suppose the price of bread is $4 a loaf and the price of chicken is $5 per pound. Draw her budget constraint and label it BC0. Put bread on the horizontal axis and chicken on the vertical axis. Be sure to identify the intercept values. Suppose Farah is a utility maximizer and she consumes 10 loaves of bread and 12 pounds of chicken. On the same graph you drew in part (a), draw an indifference curve to identify her optimal bundle. Label this bundle "E." Is her budget exhausted? Verify your answer. Now suppose Farah's income falls so that she can now devote only $80 to the two goods. Prices however remain unchanged. In the same diagram, graph her new budget constraint and label it BC1. Be sure to identify any new intercept values. Following the change in income, can Farah consume the same bundle "E"? Explain your answer. What must happen to her total utility following the decrease in her income?
Question 3 Lucy consumes only scoops of ice-cream (x) and cones (y). Moreover, she insists on consuming these two goods in the combination of 1 scoop of ice-cream and 1 cone. If there are more scoops of ice-cream than cones, she throws the extra ice-cream away. If there are more cones than scoops of ice-cream, she throws the extra cones away. Her utility function for ice-cream and cones is given by U(x, y) = min {x,y}. (The function min {x,y} returns the smaller number between x and y. In other words, if x y, min {x,y} = y; and if x = y, min {x,y} = x = y.) (a) Draw a couple of indifference curves for Lucy. Put ice-cream on the horizontal axis. (Hint: Draw the 45° line. Choose a point on the line. If you increase the amount of x but not y from that point, how would Lucy's utility change? If you increase the amount of y but not x from that point, how would Lucy's utility change?) (b) Suppose each scoop of ice-cream costs $2, and each cone costs $1. Lucy has an income of $6. Draw her…
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.
2. Eren's two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V²M Last year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. a. b. C. Calculate the change in consumer surplus from consuming the expensive meals considering the price change (Hint: you need to compare his optimal consumption bundle before and after the price change to get the change in CS). Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV). Calculate for the equivalent variation (EV) for the price change.
Brian spends his entire monthly income of $1200 on shoes (S) and pizzas (P). The price of a pair of shoes is $60, and the price of a pizza is $20. If he consumes 10 pairs of shoes and 30 pizzas, his MRS is 2P/1S. (A quantity of shoes is measured along the x-axis, and a quantity of pizza is measured along the y-axis.) His choice is optimal. True False
I am unsure the direction the utility functions would go in , with this specific scenario
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).