Exam 2: Preferences

Ambrose has indifference curves with the equation x₂ = constant - , where larger constants correspond to higher indifference curves. If good 1 is drawn on the horizontal axis and good 2 on the vertical axis, what is the slope of Ambrose's indifference curve when his consumption bundle is (16, 17)?

Belinda loves chocolate and always thinks that more is better than less. Belinda thinks that a few piano lessons would be worse than none at all, but if she had enough piano lessons to get good at playing the piano, she would prefer more lessons to less. Draw a graph with piano lessons on the horizontal axis and chocolate on the vertical axis. On your graph sketch two indifference curves for Belinda that would be consistent with this story. Label the better of the two indifference curves AA and the worse one BB.

In Professor Meanscore's class, the first midterm exam and the second midterm exam are weighted equally toward the final grade. With the first midterm's score on the horizontal axis, and the second midterm's score on the vertical axis, indifference curves between the two exam scores are

Josephine buys 3 quarts of milk and 2 pounds of butter when milk sells for $2 a quart and butter sells for $1 a pound. Wilma buys 2 quarts of milk and 3 pounds of butter at the same prices. Josephine's marginal rate of substitution between milk and butter is greater than Wilma's.

Steven's indifference curves are circles, all of which are centered at (15, 13). Of any two indifference circles, he would rather be on the inner one than the outer one.

Suppose that there are two commodities and a consumer prefers more to less of each good. If the consumer has transitive preferences, can her in difference curves cross? Sketch a brief proof of your answer, and illustrate with a diagram.

Professor Goodheart's colleague Dr. Kremepuff gives 3 midterm exams. He drops the lowest score and gives each student her average score on the other two exams. Polly Sigh is taking his course and has a 60 on her first exam. Let x₂ be her score on the second exam and x₃ be her score on the third exam. If we draw her indifference curves for scores on the second and third exams with x₂ represented by the horizontal axis and x₃ represented by the vertical axis, then her indifference curve through the point (x₂, x₃) = (50, 70) is

If two goods are perfect complements,

If there are only two goods, if more of good 1 is always preferred to less, and if less of good 2 is always preferred to more, then indifference curves

Mac Rowe doesn't sweat the petty stuff. In fact, he just cannot detect small differences. He consumes two goods, x and y. He prefers the bundle to the bundle if and only if . Otherwise he is indifferent between the two bundles. a. Show that the relation of indifference is not transitive for Mac. (Hint: Give an example.) b. Show that the preferred relation is transitive for Mac.

The relation "is preferred to" between commodity bundles is just one example of a binary relation. Another example is the relation "is a full brother of" defined over the set of all human beings. Let xRy mean person x is a full brother of person y.

If preferences are convex, then for any commodity bundle x, the set of commodity bundles that are worse than x is a convex set.

Tim consumes only apples and bananas. He prefers more apples to fewer, but he gets tired of bananas. If he consumes fewer than 29 bananas per week, he thinks that 1 banana is a perfect substitute for 1 apple. But you would have to pay him 1 apple for each banana beyond 29 that he consumes. The indifference curve that passes through the consumption bundle with 30 apples and 39 bananas also passes through the bundle with A apples and 21 bananas, where A equals

If there are two goods, if a consumer prefers more of each good to less, and if she has a diminishing marginal rate of substitution, then her preferences are convex.

If two goods are both desirable and preferences are convex, then

Recall that Tommy Twit's mother measures the departure of any bundle from her favorite bundle for Tommy by the sum of the absolute values of the differences. Her favorite bundle for Tommy is (2, 7), that is, 2 cookies and 7 glasses of milk. Tommy's mother's indifference curve that passes through the point (c, m) = (5, 4) also passes through

Ambrose has indifference curves with the equation x₂ = constant - , where larger constants correspond to higher indifference curves. If good 1 is drawn on the horizontal axis and good 2 on the vertical axis, what is the slope of Ambrose's indifference curve when his consumption bundle is (9, 5)?

If we graph Mary Granola's indifference curves with avocados on the horizontal axis and grapefruits on the vertical axis, then whenever she has more grapefruits than avocados, the slope of her indifference curve is 22. Whenever she has more avocados than grapefruits, the slope is . Mary would be indifferent between a bundle with 22 avocados and 37 grapefruits and another bundle that has 37 avocados and

The marginal rate of substitution measures the distance between one indifference curve and the next one.

A consumer with convex preferences who is indifferent between the bundles (5, 1) and (11, 3) will like the bundle (8, 2) at least as well as either of the first two bundles.