Microeconomics
2nd Edition
ISBN: 9780073375854
Author: B. Douglas Bernheim, Michael Whinston
Publisher: MCGRAW-HILL HIGHER EDUCATION
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 8P
To determine
Explain Natasha’s marginal rate of substitution for MRSCF, values of PF is her best choice an inferior solution and the price of the boundary choice.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
[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?
Pele enjoys coffee (C) and tea (T) according to the function
U(C, T) = 6C + 8T
(a) What does her utility function say about her MRS of coffee and tea?
(b) Suppose the price of coffee (PC) and the price of tea (PT) are both $3. If Alana has $12 to spend
on these products,
i. How much coffee and tea should she buy to maximize her utility?
ii. Draw a carefully labeled graph of her indifference curve map and her budget constraint. Put the
quantities of coffee on the horizontal axis. Be sure to identify the utility maximizing point.
(c) Would Alana buy more coffee if she had more income? Explain.
(d) Suppose the price of coffee fell to $2. How would her consumption change?
Krissy spends all her income on holiday lights (L) and fishing bait (B). Lights are priced at $2, while a pack of bait costs $1. Assume that Krissy has $30 to spend
and her utility function can be represented as:
U(L,B) = L²B²
with: MU=2LB² and MU=2L²B
(Assume B is on the y-axis when graphing).
How much utility does Krissy obtain from the optimal bundle?
Note: enter number(s) only and convert any fraction to a decimal.
Chapter 5 Solutions
Microeconomics
Ch. 5 - Prob. 1DQCh. 5 - Prob. 2DQCh. 5 - Prob. 3DQCh. 5 - Prob. 4DQCh. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6P
Ch. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10PCh. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - Prob. 15PCh. 5 - Prob. 16PCh. 5 - Prob. 1CPCh. 5 - Prob. 2CPCh. 5 - Prob. 3CPCh. 5 - Prob. 4CPCh. 5 - Prob. 5CPCh. 5 - Prob. 6CPCh. 5 - Prob. 7CPCh. 5 - Prob. 8CP
Knowledge Booster
Similar questions
- This is part 2 of a two-part question. Romeo has typical preferences over chocolates C and flowers F, with the associated utility function U (C, F) = 3CF +10C +6F. The price of chocolates is $5 per piece, and the price of flowers is $3 per stalk. He has $90 to spend on chocolates and flowers on Valentine's Day. Suppose his utility does not include any other goods. Now suppose that the price of chocolates increases. Select the true statement. Romeo will purchase his original bundle. Romeo's budget line rotates inwards about the chocolates intercept. Romeo will purchase fewer chocolates than before the change.arrow_forwardA consumer has the following utility function: U(X,Y)= 400X2/5Y3/5 Suppose that the price of a spa day (x) is £200 and the price of a city break (y) is £300 Find the number of spa days and city breaks that minimise expenditure if 12,800 units of utility are obtained. Also calculate the consumer's minimised expenditurearrow_forwardEvery month, a family of three spends $2,000 on food (F) and other items (O). The family’s preferences are represented by the utility function U(F,O) = F1/5O4/5. The unit price of food and the unit price of other items are both $1. Find this family’s monthly food expenditure.The family could join a consumers’ club. At the club, food costs 20% less than in other stores (i.e., at the food club PF = $0.8)arrow_forward
- Problem 3 (10 points; 5 points for each part): Richard has a total utility function of: TU = 10q₁q₁²+24q2q2² +9192, where q₁ and q2 are goods. Richard is currently consuming at q₁ = 4 and q₂ = 6, which is also his utility maximizing consumption level. (Richard's optimal point is an interior solution). (a) How much additional utility would Richard receive if he were to increase his consumption of q2 from 6 to 7? (5 points). (b) How much q2 is Richard willing to pay (in terms of q2) in order to consume the 5th unit of q₁? (5 points).arrow_forwardEvery month, a family of three spends $2,000 on food (F) and other items (O). The family’s preferences are represented by the utility function U(F,O) = F1/5O4/5. The unit price of food and the unit price of other items are both $1.a) Find this family’s monthly food expenditure. The family could join a consumers’ club. At the club, food costs 20% less than in other stores (i.e., at the food club PF = $0.8). b) Suppose the club did NOT charge a membership fee: how much money would the family spend on food? How much food would the family buy? c) Would the family be willing to pay more than $80 to join the consumers’ club? Clearly justify your answer.arrow_forwardClarice has a utility function: U(Y) = 1000 - (100/Y), where Y is her income. clarice has just graduated from college and has a career choice for her first job of either working as a teacher and earning $40,000 or trying to become a theatre lighting director and earning $70,000 (if there is growth in the demand for theatre) or $20,000 (if there isn't growth in the demand for theatre). there is a 50% probability of growth. a consulting firm guarantees Clarice that it already knows whether there will be growth in the demand for theatre next year. what is the maximum amount Clarice should be willing to pay for this information?arrow_forward
- Q2. Lucas likes lemon soda (X) and chips (Y). His utility function is given by: U (X, Y) = X0.2Y0.8 He earns $40 per week to spend on lemon soda (X) and chips (Y). The prices of lemon soda and chips are $2 and $4 respectively. Find out Lucas’s utility-maximizing bundle of lemon soda and chips (X*, Y*). Set up the utility-maximization problem and find out the price ratio of these two goods. Find out Lucas’s marginal utility of lemon soda (MUX) and marginal utility of chips (MUY). Calculate the MRSXY . Set up the optimal tangency condition and solve for Y in terms of X. Solve for Lucas’s optimal consumption bundle of lemon soda (X*) and chips (Y*). Draw the optimal consumption bundle on the budget constraint BC1 in Q1. Denote it as Bundle A. Make sure to indicate the optimal consumption of lemon soda (X*) and chips (Y*). Draw an indifference curve that is tangent to the budget constraint at Bundle A. Calculate the value of the MRSXY (the value not the formula) at the optimal…arrow_forwardLet u(x) be a utility function that represents the preferences of a household. We say that the function v(x) is a monotonic transformation of u if f(·) is a strictly increasing function and v(x) = f(u(x)). (a) Show that if v(x) is a monotonic transformation of u, it represents the same preferences. (b) Can you explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (c) What kind of preferences are represented by a utility function of the form U(x1,x2) = ? What about the function U(x1,x2) = 13x1+13x2?arrow_forwardGreg has the following utility function: u = x49x9.51 He has an income of $75.00, and he faces these prices: (P1, P2) = (4.00, 1.00). Suppose that the price of x1 increases by $1.00. Calculate the compensating variation for this price change. Give your answer to two decimals. $arrow_forward
- 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…arrow_forwardTwo friends, Minrui and Jing, share a flat and both consume internet (i) and all other goods (g). The utility function for Minrui is U_m=i^(0.3)g^(0.7) whereas the utility function for Jing is U_m=i^(0.1)g^(0.9). Considering that the income of both individuals are the same $500 and that the prices are p_i = $80 and p_g = $5, what would be the optimal allocation of public good (i) and private good (g)? Interpret your answer.arrow_forwardMr. A derives utility from martinis (m) in proportion to the number he drinks: U(m) = m Mr. A is particular about his martinis, however: He only enjoys them made in the exact proportion of two parts gin (g) to one part vermouth (v). Hence we can rewrite Mr. A’s utility function as U(m) = U(g,v) = min (g/2, v). a. Graph Mr. A’s indifference curve in terms of g and v for various levels of utility. Show that, regardless of the prices of the two ingredients, Mr. A will never alter the way he mixes martinis. b. Calculate the demand functions for g and v. c. Using the results from part (b), what is Mr. A’s indirect utility function? d. Calculate Mr. A’s expenditure function; for each level of utility, show spending as a function of pg and pv. Hint: Because this problem involves a fixed-proportions utility function, you cannot solve for utility-maximizing decisions by using calculus.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Economics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning
Exploring EconomicsEconomicsISBN:9781544336329Author:Robert L. SextonPublisher:SAGE Publications, Inc
Economics (MindTap Course List)
Economics
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Cengage Learning
Exploring Economics
Economics
ISBN:9781544336329
Author:Robert L. Sexton
Publisher:SAGE Publications, Inc