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Antonio has strictly convex preferences. He is considering buying a bundle A with positive amounts of good X and good Y. Bundle A costs all of his income and the prices are Px=1 and Py=2. At bundle A his MRS=-3/4.

a. If you were to offer advice to Antonio would you tell him to buy more x and sell back some y or buy more y and sell back more x or to do nothing since he is already maximizing his utility. Explain.

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Namita kumari
Namita kumariLv6
28 Sep 2019

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Related questions

Louis has strictly convex preferences with MRS=-2y/3x. He is considering buying the bundle (8,4) which will exhaust all of his income. We also know that Px=2 and Py=1.

a. should he buy this bundle or not? If so, why? if not, explain why not and how he should alter his bundle (example: buy more X, less Y, or buy more Y and less X)

Consider an individual making choices over two goods, x and y with prices px = 2 and py = 6, and who has income I = 50.

(a) If the individual's preferences can be represented by the utility function u(x; y) = 2x+5y how much of each good does the individual buy in order to maximize his/her utility and what is his/her utility level? If py decreases to $4 (all other things staying the same), what are the individual'­s new utility-maximizing choices, and what is his/her new utility level? Explain.

(b) If the individual's preferences can be represented by the utility function u(x; y) = min( x2 ; y), how much of each good does the individual buy in order to maximize his/her utility, and what is his/her utility level? If py decreases to $4 (all other things staying the same), what are the individual'­s new utility-maximizing choices, and what is his/her new utility level? Explain.

PROBLEM 1 (This one is designed to give you lots of math practice!)

Consider the following individual utility functions:

Adam Smith: U(x,y) = xy

Jeremy Bentham: U(x,y) = xayb (Cobb-Douglas utility function)

Alfred Marshall: U(x,y) = ln x + ln y

John M. Keynes: U(x,y) = x + yb (Quasi-linear utility function)

Joan Robinson: U(x,y) = aX + bY (linear; perfect substitutes)

a. Solve for the MRS(XY) for each of the gentlemen (i.e., all but Joan Robinson). Show that Mr. Smith, Mr. Bentham, and Mr. Marshall all have diminishing MRS(XY), but that if a=b=2, their preferences exhibit constant, increasing, and decreasing marginal utility respectively. (Fortunately, diminishing MRS is the condition that guarantees convex indifference curves, so we can solve for their optimal consumption!)

 

b. What is the general formula for Mrs. Robinsons (constant) MRS?

c. Find demand functions for x and y for Smith, Bentham, Marshall, and Keynes. Assume that each man has income I and that the prices of x and y are px and py respectively.

d. Now assume that a=1/2, b = 1/4, I = 600, px = 10 and py = 20. Use these values to find the utility-maximizing quantities of x and y consumed by each man.

e. Find an expression for the share of income Mr. Bentham and Mr. Marshall each devote to the consumption of good x, where this share, sx, is defined as

(px x)/I.

f. Find expressions for the income elasticity of demand for good x for Mr. Bentham and Mr. Marshall. Find expressions for the (own) price elasticity of demand for good y for these two men.

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