Question

(1) Explain why the assumption of convex preferences implies that “averages are preferred to extremes.” Make both a formal argument and an intuitive one (that is, an explanation that can be understood by the “man on the street.”)

(2) What does the negative slope of an indifference curve imply about a consumer’s tastes for the two goods? How would this change if one of the goods wasn’t a “good” at all (but instead a “bad”…something people do not like)?

(3) For the following sets of goods draw two indifference curves, U1 and U2, with U2 > U1. Draw each graph placing the amount of the first good on the horizontal axis and the second good on the vertical axis.

a) Hot dogs and chili (the consumer likes both and has diminishing marginal rate of substitution of hot dogs for chili).

b) Sugar and Splenda (the consumer likes both and will accept an ounce of Splenda or an ounce of sugar with equal satisfaction).

c) Peanut butter and jelly (the consumer likes exactly 2 ounces of peanut butter for every ounce of jelly).

d) Nuts (which the consumer neither likes nor dislikes) and ice cream (which the consumer likes).

e) Apples (which the consumer likes) and liver (which the consumer dislikes).

(4) The utility that Julie receives by consuming food (F) and clothing (C) is given by U(F, C) = FC. For this utility function, the marginal utilities are given by MUF = C and MUC = F.

a) On a graph with F on the horizontal axis and C on the vertical, draw indifference curves for U = 12, U = 18, and U = 24.

b) Do the shapes of these indifference curves suggest that Julie has diminishing MRSFC ? Explain.

c) Using the marginal utilities, find the MRSFC. What is the slope of the indifference curve U=12 at the basket with 2 units of food and 6 units of clothing? What is the slope at (4, 3)? Does this support your answer to b?

(5) Consider the utility function U(x, y) = x – 2y2, MUx = 1, MUy= -4y. a) Graph some typical indifference curves and show the direction of increasing utility. b) Which of the three basic assumptions of consumer preferences does this function violate?

Answer 1

Q1. Averages are preferred to extremes because indifference curves are convex. This means that to keep the individual's utility constant decrease in the quantity of one good must be compensated with greater quantity of another good. Now intutively, averages are preferred to extremes because averages represent a balance of both goods, for instance if an individual can choose one of three bundles;

a. 100 shoe and 0 socks

b. 0 shoe and 100 socks

c. 50 shoe and 50 socks

Now from the point of view of a 'rational' individual, one can easily conclude that 99% of the people( if not 100%) will prefer option C as both goodsa are available in suficient / average quantity in this bundle.