please solve this. urgently need this question SuPPase a consumer has the utility function overgoods x and y:u (x.4)= 3x" yso(a) Setup the expenditure minimization Problem Usingū as the minimum utility Jevel.(b) solve the expenditure Problem for the ComPensatedHiksian de mand evuationx° (Pas Py ,ū ) and y (Pa sPg, ū)Then, wite out the minimum exPendituse function(c) ComPare the compensated demand calculatedwith Marshallian demand for the analogousPooblem, and show the eYuivalence resultehold.

Answered: Image /qna-images/answer/2f8a6ba9-5411-4594-a7a4-0e4610c4b888.jpg

1) SuPPase a consumer has the utility function over goods x and y: you (a) Setup the exPendit ure minimization Problem Using ū as the minimum utility Jevel. (b) Sove the expenditure Problem for the ComPensated Hick sian de mand eguation x* (Par Py ū ) and y(Pa iPg,ū) Then, write out the minimum ex Pendituse function /3 %3D (c) ComPare the compensated demand calculated with Harshallian demand for the analogous Pooblem, and show the eruivalence resulte hold.

1) SuPPase a consumer has the utility function over goods x and y: you (a) Setup the exPendit ure minimization Problem Using ū as the minimum utility Jevel. (b) Sove the expenditure Problem for the ComPensated Hick sian de mand eguation x* (Par Py ū ) and y(Pa iPg,ū) Then, write out the minimum ex Pendituse function /3 %3D (c) ComPare the compensated demand calculated with Harshallian demand for the analogous Pooblem, and show the eruivalence resulte hold.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.8P

See similar textbooks

Similar questions

I need asnwers of f,g Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?
I need asnwers of e,f,g Assume there is consumer, his utility function is u(x,y) =8 * x0.5+y , and his budget constraint is px*x +y = m, which implies py = 1. a.Please derive the Marshallian demand function of x. b.Please derive the indirect utility function. c. Please derive the expenditure function If originally m = 40, px=2. d. What is his original highest utility level? Now px has decreased to 1, m and py do not change. e. What is his new maximum utility level? f. Based on (c) (d) and (e), what is his compensating variation? g.Based on (c) (d) and (e), what is his equivalent variation?
A consumer’s preferences between goods x and y are representedby the utility function u(x, y) = 2min{x, y}+10. Suppose this consumer hasincome of $16, the price of good x is $3 and the price of good y is $1. Suppose the price of good x increases to $7 while the price of good y andthe consumer’s income stay constant. Calculate the magnitudes of the compensating and the equivalent variations. Explain what each measures.
A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY = £5, respectively, and the consumer has income M = £200 to spend on X and Y. Currently, she buys 2 units of good X and spends the rest of her income on good Y.a) Determine this consumer’s current utility level. b) Computetheconsumer’smarginalutilitiesofgoodsXandY. c) Explain why the consumer’s current consumption of goods X and Y is not optimal. Should she substitute X for Y or vice versa? The consumer’s marginal rate of substitution is MRS = Y/X.d) Determine this consumer’s optimal consumption of both goods. e) By how much does the consumer’s utility increase when she consumes the optimal bundle?
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…
Consider a consumer with M = $120 to spend (income) and faces prices PX = $15 and PY =$5 for goods X and Y. Her utility function is U(X, Y) = X1/2 + Y1/2.a Carefully. express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the other…
(a) A consumer has utility u(x,y,z) = ln(x) + 2ln(y) + 3ln(z) over the three goods, x,y and z and pz=1. Optimally she consumes 30 units of z. What is her income? How much money does she spend on x? (HINT: MUx = 1/x, MUy= 2/y, MUz = 3/z and remeber the "equivalent bang for the buck" condition). (b) Forget about (a). Suppose you have t= 29 hours in total to spend on 3 projects X,Y and Z to make some money. If you spend x hours on project X, you make 2 sqrt(x) dollars; If you spend y hours on project Y, you make 3 sqrt(y) dollars; If you spend z hours on project Z, you make 4sqrt(z) dollars; Writing down your "utility function" u(x,y,z) and the constraint, solve the utility maximization problem; what is the optimal amount of time to spend on x? on y? on z?
consumptionA consumer's budget constraint is given by 500 = 40G + 10D, where G is ice cream in liters and D is drink in liters. The consumer thinks that a liter of ice cream is a perfect substitute for 3 liters of drink. Which statements are then correct?Select one or more options: a-2 liters of ice cream and 42 liters of drink are on the budget line b-The optimal choice is to consume 3 times as much drink as ice cream c-The optimal choice is to only consume ice cream d-0 liters of ice cream and 50 liters of drink are on the budget line
Suppose a consumer has a monthly income of m = 100 which she spendson two commodities: french fries (x1) and beef jerky (x2). The price offrench fries is p1 = 2 and the price of beef jerky is p2 = 5. (e) What is the slope of the budget line? Provide an economicinterpretation of this number.(f) Because of Mad Cow Disease, the price of beef jerky increasesto $10 (lower supply of beef). On a new graph, plot the originaland new budget constraint clearly identifying how the budgetconstraint has changed. What is the new relative price of beefjerky in terms of french fries?(g) Because of severe shortages, Congress passes the Jerky ReliefAct which limits each consumer to purchase at most 5 packs ofjerky. Show on a graph how this affects the consumer’s budgetset. Answer all three.
Hella the Greek's preferences can be described by the utility function U(x, y) = (x^1/2 + 3^1//2)^2. (a) What is the indifference curve for a utility of 49? (b) By how much does utility increase when Hella increases consumption of good y by one (small) unit, when initially U = 49 and x = 1? (c) Holding utility constant at 49, if initially x = 1, how many additional (small) units of y does Hella have to consume if her consumption of x drops by 6 (small) units?
Josh has a monthly income of $1000. He spends this income on gummy bears (G) and "other goods"(X). The first 2500 gummy bears always cost $0.2per unit. When buying more than 2500 gummybears, they are offered at a discounted price of $0.1per unit for any amount above 2500. The unit price of the "other goods" is $1. 1. Draw the budget set. 2. Using optimization techniques, determine Josh’s optimal bundle given that his preferencescan be represented by the utility functionU(G, X) =GX.Make sure to also Illustrate youranswer graphically. 3. Suppose instead that Josh’s utility function isV(G, X) =√GX−25. How would that changeyour answer to subquestion 2? Explain.