Microeconomics
2nd Edition
ISBN: 9780073375854
Author: B. Douglas Bernheim, Michael Whinston
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 5, Problem 5CP
To determine
Explain Person N’s marginal rate of substitution for MRSCF, values of PF is her best choice an inferior solution, and the price of the boundary choice.
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[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?
Rui's utility function is
Let the price of good X be px, the price of good Z be normalized to $1.00, and U be her level of well-being.
What is her expenditure function?
Rui's expenditure function (E) is
E = 2.
U=X+4XZ+Z.
PX(U+0.25)
2
- 0.25 (Px +1) · (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the _ character.)
Derive her unco pensated demand curve for X. Let Y be her income.
Rui's uncompensated demand curve for good X is
(Properly format your expression using the tools in the palette.)
X=
Joyce drinks both coffee (x) and tea (y). Her preferences over these two goods can be represented by the utility function U(x,y) =x + 3y^1/2 where x represents the number of pounds of coffee and y represents the number of cups of tea.
a) Given her preferences, find her demand functions for coffee (x) and tea (y).
b) Suppose that the price of a pound of coffee is $4 and that she has $56 to spend on coffee and tea. Write her demand curve for tea. Illustrate her demand curve.
c) Suppose that the price of a cup of tea is $1 (the price of coffee and income remain $4 and $56, resp.). Use your demand functions to find her best bundle. In an indifference curve diagram illustrate her best bundle at these prices. For the remainder of the question, assume that her income rises to $60 and that the prices of coffee and tea are unchanged at = $4 and =1.
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
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- A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizzaarrow_forwardWhich of the following is not a required characteristic for a function U(.) to be considered a valid utility function? (Select all that apply) U(.) must be monotonically increasing in all possible bundles U(.) must be able to assign a utility to every possible bundle of goods For any two bundles, A and B, either U(A) ≥ U(B) or U(B) ≥ U(A) must be true For any three bundles, A, B, and C, if U(A) ≥ U(B) and U(B) ≥ U(C), then U(A) ≥ U(C)arrow_forwardPlease answer sub-part d) of the question.arrow_forward
- Khamzat consumes burgers (x1) and sodas (x2). Consider the CES utility function u(x1, x2) = (x + x)UP), for a constant p > 0, where the price of burgers is 20 and soda is 2. Khamzat's income is 100. What is the demand functions for burgers and sodas? Khamzat becomes famous and the store owner recognizes him and decides to give him the burgers at cost, $12. What is the income and substitution effect?arrow_forwardCarla has utility function U(x, y) = vx + 2y over goods x and y a) Do we have a name for this type of utility function? Are Carla's preferences well-behaved? b) Let Carla have budget I=$40, and let prices be Px=$2, Py=$8. What bundle will Carla consume? c) What if Carla's budget drops to $20? [Think about: could this utility function describe Carla's preferences over bread and ice cream?]arrow_forwardYou consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.arrow_forward
- Q10. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F. In Case 1, Total income is $100 , per unit prices of Food (F) are $2 , per unit prices of Cloth (C) are $10In Case 2, Total income is $100 , per unit prices of Food (F) are $2 , per unit prices of Cloth (C) are $15 Find the following for both cases, and contrast Case 2 with Case 1:a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e. (F*, C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space (draw both case budget lines and point of optimality on one diagram)arrow_forwardHelp mearrow_forwardPlease get correctarrow_forward
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