Ch. 34 Suppose the utility possibility frontier for two individuals is given by UA + 2UB = 200. a) Draw the utility frontier for this function.
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- Marginal Utility MU, 0 $5,000 10,000 15,000 Income Singer Marginal Utility Multiple Choice MU, 0 $5,000 10,000 15,000 Income Catalano Refer to the above diagrams that show identical marginal utility from income curves for Singer and Catalano. If this initial distribution of $15,000 to Singer and $5,000 to Catalano is altered in favor of greater equality, it may be argued that: the combined total utility of the two consumers will decline because Catalano has a greater capacity to derive utility from income than does Singer incentives to produce will be weakened and total income will decrease.. incentives to produce will be enhanced and total income will increase. the combined total utility of the two consumers will decline because Singer has a greater capacity to derive utility from income than does Catalano.We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve exactlyonce. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)The price of X is $20 and the price of Y is $40. Y 30 Uz 24 40 Units of good X based on the graph, at point B, Multiple Choiİce < Prev B. 14 Units of good Y
- Explain why the lifetime budget constraint must be satisfied as a strict equalityConsider the following utility functions: a) U= xy b) U=(xy)l3 c) U=min(x,y/2) d) U=2x + 3y e) U=x?y? + xy 1. Check if any of utility functions a) – e) are homogeneous. If so, state the degree of homogeneity of each.9. Prove that if the consumer is indifferent between commodity bundles (q,.., q and (9. ,... ,q) and has a homothetic utility function, she will also be indifferent between the (1) bundles (tqi,., tq) and (tq (1) ***, tq,). .....
- Give examples of preference relation that is monotone but not continuous and is representable by a utility function.If the utility function of an individual takes the form: U = U ( x 1, x2) = (x1 + 2) 2 (x2 + 3) 3 Where U is total utility, and x1 and x2 are the quantities of two commoditiies consumed: (a) Find the marginal-utility function of each of the two commodities (b) Find the value of the marginal utility of the first commodity when 3 units of each commodity are consumed.Consider two individuals whose utility functions are given by