Homework 2 – Preferences and Utility __________________________________ Name Econ 301, Spring 2020, Johnson Due at the beginning of class January 30, 2020. Turn in these pages, stapled, with your work on them. Double sided printing is fine. Extra pages may be inserted if needed. All work turned in for credit must be the student’s own work. Intermediate steps must be shown for full credit. If we observe a consumer choosing ( x1 , x2) when ( y1 , y2) is available one time, are we justified in concluding that ( x1 , x2) ≻ ( y1 , y2) ? 1. Consider a group of people A, B, C and the relation “at least as tall as,” as in “A is at least as tall as B.” Is this relation transitive? Is it complete? 2. Take the same group of people and consider the relation “strickly taller than.” Is this relation transitive? Is it reflexive? Is it complete? 3. What is the Marginal Rate of Substitution of $1 for $5 bills? 1 4. Draw representative indifference maps (three curves) for each of the following six different sets of preferences. Illustrate on each of your graphs the direction of increasing utility. a. Goods 1 & 2 are both good and preferences are well behaved. b. Goods 1 & 2 are both bads. c. Good 1 is neutral and good 2 is good. d. Good 1 and 2 are perfect complements, 1 to 4. e. Good 1 and 2 are perfect substitutes, 1 to 1. f. Good 1 is good and good 2 is bad. 2 5. Suppose that a utility-maximizing consumer must choose between the following bundles: Basket Units of Units of food clothing A 6 11 B 12 8 C 12 7 D 7 11 E 8 12 F 9 7 G 4 9 a. Which baskets can be ruled out with certainty? b. Why can we rule them out? 6. Which assumption is violated when indifference curves cross? Draw an example. 7. How does the indifference curve illustrate the marginal rate of substitution? 3 8. Suppose that there are two goods, soccer tickets and baseball tickets. Suppose the consumer is considering two baskets on the budget line, A and B. With basket A, the MRS for baseball tickets is greater than the relative price of soccer tickets and with basket B, the MRS for soccer tickets is less than the relative price. a. Draw the budget line and corresponding convex indifference curve. b. Should the consumer consume basket A? Why or why not? c. Should the consumer consume basket B? Why or why not? 4 9. Clay gets satisfaction from both movies and museums. His income is $540 per week. A museum ticket (with student I.D.) costs $15, and showing at the AMC costs $6. a. Graph the budget constraint Clay faces, with museum tickets on the vertical axis and movie tickets on the horizontal axis. b. If Clay spends all his income on museums, how much music can he afford? Plot a point that illustrates this scenario. c. If Clay spends all his income on movies, how many movies can he afford to see? Plot a point that illustrates this scenario. d. If he spends half his income on museums and half his income on movies, how much of each can he afford? Plot a point that illustrates this scenario. e. Connect the dots to create Clay’s budget constraint. What is the slope of the budget constraint? f. Divide the price of movies by the price of museums. Have you seen this number before? If so, where? g. Suppose a holiday bonus raises Clay’s income temporarily to $600 per week. Draw his new budget constraint. h. Indicate the new bundles of movies and museums that are feasible now if he spends all his money on movies. What about museums? 5
Purchase answer to see full attachment