Exam 2: Preferences-Part A

Toby Talkalot subscribes to a local phone service that charges a fixed fee of $10 per month and allows him to place as many local phone calls as he likes without further charge.Let good 1 be an aggregate of commodities other than local phone use and let good 2 be local phone use.(Measure good 1 on the horizontal axis and good 2 on the vertical axis.)On Monday, Toby didn't use the telephone at all.The slope m of his indifference curve at the consumption bundle he chose on Monday was

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.

Angela consumes goods x and y.Her indifference curves are described by the formula y = k/(x + 3).Higher values of k correspond to better indifference curves.

Bill Katz prefers more of good 1 to less and he prefers less of good 2 to more.Bill has convex preferences.If we draw his indifference curves with good 1 on the horizontal axis and good 2 on the vertical axis, then his indifference curves have positive slope but get steeper as they rise.

Nancy Lerner is taking a course from Professor Goodheart who will count only her best midterm grade and from Professor Stern who will count only her worst midterm grade.In one of her classes, Nancy has scores of 20 on her first midterm and 70 on her second midterm.When the first midterm score is measured on the horizontal axis and her second midterm score on the vertical, her indifference curve has a slope of zero at the point (20, 70).Therefore this class could

If preferences are transitive, more is always preferred to less.

Blanche Carter has devised a system for rating the males in her economics class.She cares about their intelligence and their looks.She has ranked each male on a scale of 1 to 5 for intelligence and 1 to 3 for looks.She defines a preference relation, R, as follows: xRy if boy x scores at least as high as boy y in either looks or intelligence.Give an example to show that Blanche's method of determining preferences might not lead to transitive preferences.

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

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 -4x^1/2₁, 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)?

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

Explain how it would be possible to cheat someone who had intransitive preferences.Be explicit about what you would offer him if you were trying to exploit his intransitivity and what he would do in response.

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.

Ambrose has indifference curves with the equation x₂ = constant - 4x^1/2₁, 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)?

Nick's indifference curves are circles, all of which are centered at (12, 12).Of any two indifference circles, he would rather be on the inner one than the outer one.

If someone has the utility function U = 1,000 + 2min {x, y}, then x and y are perfect complements for that person.

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.

Preferences are said to be monotonic if

Colette consumes goods x and y.Her indifference curves are described by the formula y = k/(x + 7).Higher values of k correspond to better indifference curves.

If Melody has more classical records than rock and roll records, she is willing to exchange exactly 1 classical record for 2 rock and roll records, but if she has more rock and roll records than classical records, then she is willing to exchange exactly 1 rock and roll record for 2 classical records.Melody has convex preferences.