1. Is it impossible for two indifference curves to intersect one another? why? 2. What does it mean that preferences pre complete? Now would the real-life implica-
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- We claimed in the text that if preferences were monotonic, then a diag-onal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)3. We claimed in the text that if preferences were monotonic, then a diag- onal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (Hint: what would happen if it intersected some indifference curve twice?)Suppose utility can be measured by "utils" and that Jim buys both coffee and bagels. The price of coffee is $2 and the price of a bagel is $3. If Jim is currently consuming coffee and bagels such that the marginal utility from the last cup of coffee consumed was 6 utils and the marginal utility from the last bagel consumed was 12 utils, is Jim maximizing utility? Why or why not? If not, what should Jim do? Explain in detail.
- 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?)Suppose Ann likes both pancakes (P) and waffles (W) and is always willing to substitute two pancakes for one waffle. Write the equation for Ann's utility function. a. b. Given her preferences, what is Ann's marginal utility of an additional pancake? What is Ann's marginal utility of an additional waffle? с. With pancakes on the horizontal axis and waffles on the vertical axis, graph Ann's indifference curves for U=4 and U=8. d. What is Ann's marginal rate of substitution?1. Suppose that there are two breakfast options, pancakes and waffles. Kwame only cares about the calories he gets from his breakfast he wants to consume as much as possible, no matter the food. Suppose that a waffle has thrice as many calories as a pancake. What do Kwame's indifference curves look like, illustrated with waffles on the y axis and pancakes on the x - axis?
- (a) I like to consume two olives with every shot of vodka. If Ihave more olives or more vodka than that ratio, I just toss theextra in the trash (they are perfect complements). What is myutility function? What do my indifference curves look like? (b) I like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like? (c) Antonin notices he is currently spending all of his money ona bundle (x1, x2) where his marginal rate of substitution isgreater than the relative prices (p1/p2). Can Antonin reach abundle on a higher indifference curve with his current income?Explain clearly and provide a graph with your response. * Note that in (a) and (b), there are different utility…Donna and Jim are two consumers purchasing strawberries and chocolate. Jim’s utility function is ?(?,?) = ?? and Donna’s utility function is ?(?,?) = ?2? where x is strawberries and y is chocolate. Jim’s marginal utility functions are MUx=y and MUy=x while Donna’s are MUx=2xy and MUy=x2. Jim’s income is $100, andDonna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4?4. If we have the utility function, U(x)=(x−7)^2, and we know that there is an indifference set around x = 4 and an upper contour set of x = 6. How to graphically represent this function? I'm confused about how to draw the upper contour set on the graph? I know the concept that upper contour is the area over the convex line, but don't know how to put it on the graph. Could you draw a simple graph to help me identify the upper contour?
