ECO102 Lecture 19: ConvexityQuasiConvexityandLevelCurveShapeHANDOUT

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3 Nov 2017

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Quasiconcavity: consider the function f : d r, where d is a convex subset of rn and let c be a number in the range of f . De ne the upper level set of f for c to be the following subset of d: Pc {x d : f (x) c} (so pc consists of all points in d at which the value of f is equal or greater than c. ) Then: a fuction f (de ned on a convex set) is quasi-concave if every upper level set of f is convex (that is, if pc is convex for all c. ) Using graphs: quasiconcavity refers to properties of the level map (all the level curves) of f . Suppose f is a two-variable function and it increases as we move north-east from the origin (in the domain of f ). To be more precise, consider the function f (x1, x2) = x1x2, which has this property.

Related Questions

Suppose all consumers are maximizing utility with convex indifference curves. All face the same prices, and are perfectly rational. According to microeconomic models, at the maximization bundle they should

A. All have the same marginal rate of substitution

B. All buy more of the least expensive good

C. All end up with the same bundle of goods

D. All have the same level of satisfaction

Consider an indifference map with food on the vertical axis and shelter on the horizontal axis.

If a consumer is willing to give up 3 units of food in exchange for 1 unit of shelter and food is priced at $5 per unit and shelter at $10 per unit, then the consumer is:

A. Purchasing too much food for utility maximization

B. Purchasing too much shelter for utility maximization

C. Purchasing just the right amount of each good for utility maximization

D. Purchasing less than the budget would allow

If a consumer with convex indifference curves moves along her budget line, closer and closer to the horizontal axis, as she is moving:

		A. The marginal utility she gets from good Y declines.
		B. The marginal utility she gets from good X declines.
		C. The marginal utility she gets from good X increases.
		D. The price ratio of the two goods changes.

1.The Phillie Phanatic always eats his ballpark frank in a special way; he uses a foot-long hot dog together with precisely half a bun, 1 ounce of mustard, and 2 ounces of pickle relish. He only gains utility/satisfaction from these 4 items, any extra of a single item without the others is worthless.

What can we say about the relationship among these goods for the Phillie Phanatic and the shape of his indifference curve with respect to these goods?

2. Consider a person with convex indifference curves. When she optimally chooses a consumption bundle of a particular amount of fruit on the Y-axis, and vegetables on the X-axis, her marginal rate of substitution equals:

A. 1

B. PV_/PF (The price of vegetables divided by the price of fruit)

C. P_F/P_V (The price of fruit divided by the price of vegetables)

D. 0

3. A consumer has a budget for food (F) and shelter (S). With income M, and prices PF and PS, the budget constraint for this consumer may be represented as:

A. PSS + PFF = M

B. F = M/PF - (PS/PF)S

C. S = M/PS - (PF/PS)F

D. All of the above

burgundyalpaca580

True or False. If False explain why it's false.

1. If all prices are doubled an money income is the left the same, the budget set does not change because the relative prices do not change.

2. A decrease in income pivots the budget line around the bundle initially consumed.

3. If preferences are well-behaved, then for any commodity bundle (x1,x2), the set of commodity bundles that are worse than (x1,x2) is a convex set.

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

5. If someone has the utility function U= 2min(x, y), then x and y are perfect complements for that person.

6. At the boundary optimum, a consumers indifference curve must be tangent to her budget line.

7. If two goods are substitutes, then an increase in the price of one of them will increase the demand for the other.

8. An Engel curve is a demand curve with the vertical and horizontal axes reversed.

9. An inferior good is less durable than a normal good.

10. When other variables are held fixed, the demand for a Giffen good rises when income increase.

ECO102 Lecture 19: ConvexityQuasiConvexityandLevelCurveShapeHANDOUT

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