Questions d) to f) QUESTION 4Linguini and Colette consume only éclair (x,) and profiterole (x,). Linguini has utility functionUA = xfxf and Colette has utility function U® = 2xf x%. Linguini is endowed with 10 éclair (r,)and 3 profiterole (x,), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,).(a) Draw an Edgeworth boz with x, on the horizontal azis and x2 on the vertical azis. PositionLinguini on the bottom left corner and Colette on the top right corner. Indicate the total numberof units of x, and x2. Label the endowment allocation.(b) Derive the equation of the contract eurve, ie., find x (xt). In your graph in (a), draw thecontract curve.Suppose the price of éclair (x,) is $1 and the price of profiterole (x,) is $2.(c) Find each consumer's utilitymaximising basket.(d) How much of each good does each consumer wantbuy or sell? Are the markets in equilibriumat the given prices?(e) Verify that Walras' law holds at these prices.Now we will solve for the competitive equilibrium.() Use your solution to (b) to find the equilibrium price ratio, P1/P2-() Set x2 as the numeraire, i.e., assume pi = p and p2 = 1. Write each consumer's budget lineequation given the equilibrium price ratio.(h) Find the equilibrium allocation, ((xf,x±), (xf, xf)).

A utility Function is a mathematical illustration of an individual's preferences over unique…

Answered: utility function

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 9P

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QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x,). Linguini has utility function UA = xfxf and Colette has utility function U® = 2xf x%. Linguini is endowed with 10 éclair (r,) and 3 profiterole (x,), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x,). (a) Draw an Edgeworth boz with x, on the horizontal azis and x2 on the vertical azis. Position Linguini on the bottom left corner and Colette on the top right corner. Indicate the total number of units of x, and x2. Label the endowment allocation. (b) Derive the equation of the contract eurve, ie., find x (xt). In your graph in (a), draw the contract curve. Suppose the price of éclair (x,) is $1 and the price of profiterole (x,) is $2. (c) Find each consumer's utilitymaximising basket. (d) How much of each good does each consumer want buy or sell? Are the markets in equilibrium at the given prices? (e) Verify that Walras' law holds at these prices. Now we will solve for the competitive…
QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x2). Linguini has utility function UA = 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. Position Linguini on the bottom left corner and Colette on the top right comer. Indicate the total number of 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 the contract curve.
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…
Linguini and Colette consume only éclair (x,) and profiterole (x2). Linguini has utility function U4 = xfxf 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 (x,). Draw an Edgeworth box with x, 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 x, and x2. Label the endowment allocation. Derive the equation of the contract curve, i.e., find x(x). In your graph in (a), draw the contract curve. Suppose the price of éclair (x,) is $1 and the price of profiterole (x2) is $2. Find each consumer's utility-maximizing basket. How much of each good does each consumer want to buy or sell? Are the markets in equilibrium at the given prices? Verify that Walras' law holds at these prices. Now we will solve for the competitive equilibrium. Use your solution to…
10.6 For every two boxes of strawberries that she consumes, Millicent insists on having one pitcher of cream. She does not, however, insist on consuming the same amount every week. Her utility function is U = min{$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
Tom is vegetarian and always eat a salad (s) with 2 glasses of green juice (g). His utility for the two goods is therefore 1 u(s, g) = min{s, 79}
Find Indirect utility function of the following function U = max (X, Y) subject to the budget constraint P, X+ P₂ Y=M Optionis O O max (P1 P2) M² min (P1 P2) M² P1+ P2 M min (P1 P2)
Question 2 David spends his budget on chocolate and chip. His utility function is given by ?(?1,?2)= 2?1?2, where ?1 is the number of chocolates he consumers per week, and ?2 is the number of chips he buys per week. A chocolate costs 10 SEK, and a chip costs 20 SEK. David’s weekly budge for consuming on these two goods is 120 SEK. (1) What is David’s budge line? Draw the budget line on a graph with chocolate amounts on the horizontal axis and chip amounts on the vertical axis. Write explicitly at which points budget line crosses the axis. (2) What is David’s marginal utilities for the two goods, respectively? What is his marginal rate of substitution between the two goods? (3) What is David’s optimal choice? Calculate the numerical answer for the optimal bundle. Also draw an indifference curve for David on the same graph as question(1) and show the optimal bundle.
Mort consumes only beer and sausages. His income is $100. Beer costs him $0.50 per can and sausages cost $1 each, where x is the number of cans of beer and y is the number of sausages he consumes per week. Mort’s utility function is U(x,y) = -[(x-50)^2 + (y-40)^2]. What consumption bundle should he have?
[5.5CP]Natasha's utility function is U(C, F) = (3 + F)VC, where C stands for concert tickets and F stands for film tickets. Her income is $300 per month and concert tickets cost $5 each. What is the formula for Natasha's MRSCF? Does it have the declining MRS property? Solve for and graph her price-consumption curve (allowing the price of film tickets, PF, to vary) and her demand curve for film tickets. For what values of Pf is her best choice an interior solution? For what prices is it a boundary choice?
Suppose Al is currently consuming five movies and two concerts per month. If his utility function is given by U = 15MC, where Mrepresents the number of movies seen and C represents the number of concerts attended, Al's total utility is equal to: 75 15 150 10 30
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.

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