Ceren's preference relation is represented by a utility function u(X1, X2) = X1^1/3 X2^1/3 for any nonnegativeconsumption bundle (x1, x2). The price of good 1 is $1 and the price of good 2 is $2 and her income is $15. If the priceof good 1 increases to $5 while the price of good 2 and her income remains constant, the Slutsky income effect (notHicksian) on Ceren's good 1 consumption reduces her consumption by what? and the total (absolute) price effect iswhat? (Slutsky decomposition not Hicksian) (a) 10/3, 5 (b) 4/3, 4 (c) 7.5/3, 2 (d) 8/3, 2.5

We can solve this problem by analyzing the Slutsky equation (without Hicksian adjustment) and…

Answered: Ceren's preference relation is…

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

Sandy receives utility from consuming berries (X) and nuts (Y) as given by utility function u(X,Y) = XY. The price of berries is $9 per box and the price of nuts is $8 per pack. She spends her entire income to buy 17 boxes of berries and 62 packs of nuts. Therefore, compared to her optimal bundle, she is currently consuming (too many/not enough/just the right amount of) berries. Please note that, as usual, we allow goods to be divisible, L.e. Sandy's optimal bundle could consist of. for example, 4.2 boxes of berries and 3.7 packs of nuts. Please subrnit: 1 for too many • 1 for not enough O for just the right amount of
Let t = 3 The consumer has a preference relation defined by the utility function u(x, y) = −(t + 1 − x)2 − (t + 1 − y)2. He has an income of w > 0 and faces prices px and py of goods X and Y respectively. He does not need to exhaust his entire income. The budget set of this consumer is thus given by B={(x,y)∈R2+ :pxx+pyy≤w } A. Is the optimal demand for good 1 everywhere differentiable with respect to w? informal argument is sufficient
Donna and Jim are two consumers purchasing strawberries and chocolate. Jim’s utility function is ?(?,?) = ?? and Donna’s utility function is ?(?,?) = ?2? where x is strawberries and y is chocolate. Jim’s marginal utility functions are MUx=y and MUy=x while Donna’s are MUx=2xy and MUy=x2. Jim’s income is $100, andDonna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4?
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…
Suppose that U(f,c) = f + 8c^(1/2)is a utility function that describes Amelia’s preferences over two goods: fish(f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis.a. Derive an expression for her marginal utility (Uf)from a small increase in f holding c fixed. Also find themarginal utility for custard (Uc).b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitivedescription of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, howmany units of custard would she be willing to give up in order to get one more unit of fish?c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goodson the indifference curve.d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5properties of indifference curves? Briefly support your answer.e. Give another utility function that represents…
Imran consumes two goods, X1 and X2. his utility function takes the form: u(X1, X2)= 4(X1)^3+3(X2)^5. The price of X1 is Rs. 2 and the price of X2 is Rs. 4. Imran has allocated Rs. 1000 for the consumption of these two goods. (a) Fine the optimal bundle of these two goods that Imran would consume if he wants to maximize his utility. Note: write bundles in integers instead of decimals. (b) What is Imran's expenditure on X1? On X2? (c) Do you find more than one bundle satisfying the first order conditions? Why?
Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice cream sundaes (z)− according to the Cobb-Douglas utility function U(x,y,z)=x0.5y0.5(1+z)0.5. Suppose also that the prices for these goods are given by px=1,py=4, and pz=8 and that this consumer's income is given by I=8.a. Show that, for z=0, maximization of utility results in the same optimal choices as in Example 4.1 . Show also that any choice that results in z>0 (even for a fractionalz ) reduces utility from this optimum.b. How do you explain the fact that z=0 is optimal here?c. How high would this individual's income have to be for any z to be purchased?
Consider a consumer who has a direct utility function given as U(x₁, x2) = (x1.5 + x2.5)² where x₁ > 0 and x₂ > 0. The consumer chooses to spend his entire income m on the consumption of two goods, where each good has a price of p₁ and p2 respectively. • Obtain the marginal utility of each good. give the domain of these quantities. • Obtain the marginal rate of substitution for goods 1 and 2 (i.e. MRS12). • Calculate the direct second-order partial derivatives for goods 1 and 2. What economic principle does this adhere to?
• Question #20: While visiting family in Mexico, your professor has a budget of $ 304 ($ = pesos) that he spends on tacos and tequila. The price of tacos is $ 14 and a shot of tequila is priced at $ 12. During his visit the price of tacos changes to $ 14 . Assume your professor has a Cobb-Douglas utility function with (tacos) parameter a = ( 29/ 100 ). What is the substitution effect on purchases of tacos ? (Assume both goods are commodities.)
A) Suppose a quasilinear utility function is given by u(x₁, x₂) = 2√√x₁ + 4x₂. 1. For this utility derive the demand functions xi (P₁, P2, 1) and x₂ (P₁, P2, 1). 2. For this utility derive the Engle function I = 1(x₂, P₁, P₂) for good 2. B) Do the same for the Cobb-Douglas utility function u(x₁, x₂) = x₁x². That is, 1. For this utility derive the demand functions x₁ (P₁, P2, 1) and x₂ (P₁, P2, 1). 2. For this utility derive the Engle functions I = 1(x₁1, P₁, P₂) and I = = 1(x₂, P1, P2).
Jennifer buys both turkey (x) and cheese (y) for her sandwiches. Her preferences over these two goods can be represented by the utility function U(x,y) = min[x, 2.5y] where x represents the number of slices of turkey and y represents the number of slices of cheese. a) Given her preferences find her demand functions for turkey (x) and cheese(y).
Problem 1 Ava has an income of $1,500 and she spends her income on two goods (1 and 2). Her utility function is u(x₁, x₂) = x1x², where x₁ is the amount of good 1 she consumes, and x₂ is the amount of good 2 she consumes. The price of good 1 is $3 per unit, and the price of good 2 is $1 per unit. Suppose the price of good 1 rises to $4 per unit. (a) Calculate the substitution effect and the income effect of the price change on Ava's consumption of good 1. (b) Is good 1 a normal good or an inferior good to Ava?

SEE MORE QUESTIONS

Recommended textbooks for you

Exploring Economics

Economics

ISBN:

9781544336329

Author:

Robert L. Sexton

Publisher:

SAGE Publications, Inc

Micro Economics For Today

Economics

ISBN:

9781337613064

Author:

Tucker, Irvin B.

Publisher:

Cengage,

Economics:

Economics

ISBN:

9781285859460

Author:

BOYES, William

Publisher:

Cengage Learning

Exploring Economics

Economics

ISBN:

9781544336329

Author:

Robert L. Sexton

Publisher:

SAGE Publications, Inc

Micro Economics For Today

Economics

ISBN:

9781337613064

Author:

Tucker, Irvin B.

Publisher:

Cengage,

Economics:

Economics

ISBN:

9781285859460

Author:

BOYES, William

Publisher:

Cengage Learning

Microeconomics A Contemporary Intro

Economics

ISBN:

9781285635101

Author:

MCEACHERN

Publisher:

Cengage

Microeconomics

Economics

ISBN:

9781337617406

Author:

Roger A. Arnold

Publisher:

Cengage Learning

Economics (MindTap Course List)

Economics

ISBN:

9781337617383

Author:

Roger A. Arnold

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS