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ECON 351x Study Guide - Final Guide: Substitute Good, Indifference Curve, Normal Good

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pearrat167
28 Nov 2017
School
USC
Department
Economics
Course
ECON 351x
Professor
Seda Durguner

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Document Summary

Indifference curve curve representing all combinations of market baskets. If mrs(f,c) 2q: f(2k,2l) < 2q doubled. If mp(l)/w > mp(k)/r then goods are perfect substitutes and you will only consume l.

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Related Questions

18. Which of the following statements is false? A) A consumer possesses a preference map. B) An indifference curve is a line that shows combinations of goods among which a consumer is indifferent. C) A consumer has only one indifference curve. D) The marginal rate of substitution is the rate at which a consumer will give up good y to get an additional unit of good x and remain on the same indifference curve. E) If the indifference curve is steep, the marginal rate of substitution is high.

1. Assume that beer is an inferior good for Wei. If the price of beer goes up, then the total effect results in Wei buying _______ beer and the substitution effect results in Wei buying ______ beer.

a.

more, more

b.

more, less

c.

less, more

d.

less, less

e.

not enough information to determine

2. A consumer has preferences that are complete, transitive and satisfy the "more is better" property. Which of the following statements are necessarily true?

a.

Indifference curves are negatively sloped.

b.

Indifference curves do not cross.

c.

Indifference curves exhibit diminishing marginal rates of substitution.

d.

Both a) and b) are true.

e.

a), b), and c) are true.

3. Suppose an individual has preferences over two goods - good X and good Y. In response to changes in the price of good X, the individual has a positively sloped price consumption curve, where good X is drawn on the horizontal axis. Which of the following statements is true?

a.

Good Y is a normal good.

b.

Good Y is a Giffen good.

c.

Good Y is a complement for good X.

d.

Good Y is an inferior good.

e.

Good Y is a substitute for good X.

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.