Question

1. True or False, and explain briefly. 1) The assumption that more is better implies that the indifference curves are upward sloping 2) Convexity of indifference curves implies that consumers are willing to give up more to get an extra the more they have 3) Consider the following three bundles. Bundle Good Goody If Bundles A and B are on the same indifference curve, preferences satisfy all the usual assumptions introduced in the lecture, Bundle Cis preferred to Bundle A 4) The utility functions U(x,y)=xy' and (x.y) = 2 logx +3logy +3 represent the same preferences over goods and y. Consider two goods, A and B. For each of the following scenarios, develop the utility function U(A,B) that matches the given information 1) The consumer believes that goods A and B are perfect substitutes with one unit of A equivalent to two units of B. 2) The consumer believes that goods and B are perfect complements and always uses two units of for every unit of a Suppose a consumer has preferences over two goods that can be represented by the utility function U=X+3Y 1) What are MU, and MU, ? Describe the relationship between good X and good Y. 2) Describe the shape of the indifference curves. 3) Describe the special properties of the MRS . Suppose a consumer has preferences over two goods that can be represented by the utility function U = min(X.3Y). 1) Describe the relationship between good X and good Y. 2) Describe the shape of the indifference curves 3) Describe the special properties of the MRS Consider the utility function U(x,y)=2x+y. 1) Is the assumption that more is better" satisfied for both goods? 2) What is MRS for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.

Answer 1

1.

1. False

An indifference curve is downward sloping not upward sloping, Assumption that more is better is also true only in case of 'good' goods, not 'bad' good.

2. False

Convexity of the indifference curve is a result of the increasing marginal utility of substitution (MRS). Hence to acquire more and more amount of x, given one already has more x with him/her and less amount of y, it is going to be difficult. That is consumers would be willing to give up less and less y in lieu of x because MRS for y would be increasing as it is a scarce resource.

3. False

Given that bundles A and B lie on the same indifference curve. Now one cannot deduce that C lies on the same IC or other IC. Reason being the convex shape of the IC. So if the quantity of one good remains the same, while quantity of other good increases or quantity of both goods increases /decreases at the same time then we can say that we moved from one IC to another IC. Also, this is only true in the case of both goods being 'Goods' not 'Bads'.