Unit 2C Practice Problems

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Econ 207: Unit 2C. Practice Problems Multiple Choice: 1. With typically shaped indifference curves, utility maximization requires a consumer do what two things? a. set MUx = MUy; spend all their income b. spend all their income; set MRS = Px/Py c. spend as little as possible; maximize the MRS d. set MRS = Px/Py and spend as little as possible 2. The figure above shows Sarah’s budget constraint and three of her indifference curves. Which of the following statements is FALSE? a. at bundle D, Sarah’s marginal rate of substitution of X for Y is equal to P X / P Y b. Sarah would be spending less than her full income on bundle B, exactly her full income on bundles A, D, and C, while bundle E is not affordable for her. c. Sarah’s optimal consumption bundle is bundle D d. Sarah prefers bundle D to either bundle A or bundle C, and she prefers either bundle A or bundle C to bundle B 3. Jenny has the “usual-shaped” downward sloping, convex indifference curves for pizza slices and sodas. The price of a pizza slice is $2 and the price of a soda is $1. In general, Jenny’s optimal consumption bundle will be one for which her marginal rate of substitution of pizza slices for sodas (the quantity of soda he is willing to trade for one more pizza slice) is equal to: a. ½ b. 1 c. 2 d. 3 4. Jimmy spends his entire income on carrots and cookies. At his optimal consumption bundle, he would consume positive amounts of both goods. At his CURRENT consumption bundle, Jimmy’s MRS of cookies for carrots (the amount of carrots he’s willing to give up to obtain an additional cookie) is 3. The price of a cookie is $0.25 and the price of a carrot is $0.10. Which of the following statements is correct? a. Jimmy can improve his utility by consuming more cookies and fewer carrots b. Jimmy can improve his utility by consuming fewer cookies and more carrots c. Jimmy is maximizing his utility d. whether or not Jimmy is maximizing his utility cannot be determined from the information given 5. Frank's utility function is U = 10 X + 6 Y . Frank has a budget of $60 to spend on goods X and Y . The price of good X is $3 and the price of good Y is $2. To maximize utility, Frank should purchase _____ units of good X and _____ units of good Y. a. 20; 0 b. 6; 10 c. 10; 15 d. 0; 30 6. Annie is currently spending all of her income on movies and shows. The MU of the last movie seen was 15, the MU of the last show seen was 25, the price of a movie is $10 and the price of a show is $50. To maximize utility, Annie should: a. Watch more shows and fewer movies b. Watch more movies and fewer shows c. Keep their consumption of movies and shows the same d. Watch fewer movies and fewer shows 7. To maximize utility, this consumer will buy _____ hockey tickets and _____ soccer tickets. a. 8; 0 b. 5; 3 c. 3; 5 d. 0; 8 8. Suppose that a consumer’s utility function is given by: U = XY. The price of good X is $5 and the price of good Y is $4. How many units of good X does the consumer buy if she has $360 of income (you can assume typically shaped indifference curves)? a. 9 b. 36 c. 45 d. 72 9. Kangbo is maximizing utility by consuming movies and concerts. If the price of movie tickets doubles and Kangbo continues to maximize utility, what will the marginal rate of substitution of movie tickets for concert tickets be after the price change? a. -1 b. 1 c. -2 d. 2 e. none of the above 10. David gets $90 per month as an allowance to spend any way he pleases. Because he likes only peanut butter and jelly sandwiches, he spends the entire amount on peanut butter (at $1 per ounce) and jelly (at $2 per ounce). Bread is provided free of charge by a concerned neighbor. David is a picky eater and makes his sandwiches only one way-- with exactly one ounce of peanut butter and two ounces of jelly. He is set in his ways and will never change his preferences. To maximize utility, David should consume _____ ounces of peanut butter and _____ ounces of jelly each month. a. 18; 36 b. 0; 45 c. 90; 0 d. 15; 30
Short Answer Questions: 1. (Basic Utility Maximization) The utility that Sarah receives by consuming fries (F) and cake (C) is given by: U(F,C)=FC a. Carefully draw the indifference curves ( put fries on the x-axis ) for utility levels of 24 and 48. Use a table to show at least 5 points on each curve. Use increments of 2 on both axes. b. Suppose fries costs $2 per unit, cake costs $3 a unit, and Sarah has $24 to spend on fries and cake. Graph the budget constraint she faces. You do not need to show any work. c. Calculate (and show your work) the equation of the budget constraint. Your final answer should start with C= d. List the two criteria that must be met for utility maximization with typically shaped budget constraint and indifference curves. e. Label the utility-maximizing choice of fries and cake point B in your graph. How many fries and how much cake will she consume at this point? f. Solve this problem using calculus and verify that the answer in (e) is correct. Be sure very clearly show all your work.
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