1. Pindyck and Rubinfeld (2018) Chapter 4 Appendix, Exercise #5 Jae has the following utility function: U(X,Y)= 20X + 80Y – X² – 2Y², where X is consumption of CDs, with a price of $1, and Y is consumption of movie videos, with a rental price of $2. Jae plans to spend $41 on both forms of entertainment. а. Determine the number of CDs and video rentals that will maximize Jae's utility.
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- 2. Eren's two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V²M Last year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. a. b. C. Calculate the change in consumer surplus from consuming the expensive meals considering the price change (Hint: you need to compare his optimal consumption bundle before and after the price change to get the change in CS). Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV). Calculate for the equivalent variation (EV) for the price change.Anatoly's marginal utility for DVDS (D) is MU X and his marginal utility for Xbox games (X) is MUx D. Anatoly's income is $120, the price of a DVD is $20.00, and the price of an Xbox game is $10.00. How many DVDS and Xbox games does Anatoly consume to maximize his satisfaction? Anatoly consumesDVDs andXbox games. (Enter your responses using integers.)George consumes two goods, milk, and cookies. He has maximized his utility given his income, Milk costs $2 per gallon and he consumes it to the point where the marginal utility he receives from drinking a gallon of milk is 6. Cookies cost $3 per bag and the relationship between the marginal utility that George gets from eating a bag of cookies and the number of bags he eats per month is as follows: Bags of cookies Marginal Utility 21 How many bags of cookies does George buy each month? 2 3 4. 5. 18 15 12
- Mariah consumes music downloads (M) and concert tickets (C). Her utility function is giveh by U = 0.5M? + 2C². a. Using calculus, what is the marginal utility of music downloads? b. Using calculus, what is the marginal utility of concert tickets? Write the equation for the MRSMC (i.e., the MRS of C for M; M is increasing, C is С. decreasing). d. Would the bundles of (M = 4 and C = 1) and (M = 2 and C = 2) be on the same %3D %3D %3D %3D indifference curve? How would you know? e. Calculate the MRSMC when M = 4 and C =1 and when M = 2 and C = 2. Explain why the %3D %3D values of MRSMC differ across these two bundles. f. Based on your answers above, are Mariah's indifference curves convex? Explain using the values calculated. er thisThe table shows the total utility (TU) that James receives from consuming different amounts of two goods X and Y, per month. Quantity TUx MUx MUx/Px TUy MUy MUy/Py 0 0 0 0 0 0 0 1 50 50 16.67 75 75 25.00 2 88 38 12.67 117 42 14.00 3 121 33 11.00 153 36 12.00 4 150 29 9.67 181 28 9.33 5 175 25 8.33 206 25 8.33 6 196 21 7.00 225 19 6.33 7 214 18 6.00 243 18 6.00 8 229 15 5.00 260 17 5.67 9 241 12 4.00 276 16 5.33 d.How much total utility will James experience by buying the utility-maximizing combination? e.Suppose the price of good Y increases to $6. How many units of X and Y will he buy to maximize his utility now?1. Doug consumes two goods, electricity, e, and a composite commodity z. Doug has the following utility function: U = z²-e Last week, he clicked on a Facebook ad and got free solar panels put on his roof! Now Doug has solar panels on his roof that generate 50 units of electricity per day. For the going price of electricity, if Doug demands more than 50 units of electricity, he can buy more at that price. If he demands less than 50 units, he can sell the extra electricity (50 - his consumption) back to the grid, and earn the going price as extra income. a. What are his Marshallian demand functions for e and z? b. Currently, Doug's income is $100 per day, the price of z is $1 and the price of electricity is $0.50. How much electricity is he consuming and what is his utility? (note, the utility numbers may get a bit large). C Calculate quantity demanded for electricity and his utility if the price of electricity rises to $1. And then calculate the quantity demanded and utility when the…
- Suppose Al is currently consuming five movies and two concerts per month. If his utility function is given by U = 15MC, where Mrepresents the number of movies seen and C represents the number of concerts attended, Al's total utility is equal to: 75 15 150 10 30Enrique is a movie buff. He likes to watch on demand movies from his cable company, which cost $5 each, and so likes to go to the local movie house, which charges $15 a ticket. Suppose that given his budget and his tentative spending plans, the marginal utility from a cable movie is 15 utils and the marginal utility of a movie at the local cinema is 45 utils. Assuming he is spending his entire budget, Enrique is currently maximizing his utility Enrique can increase his utility by buying more cable movies and watching fewer cinema movies Enrique can increase his utility by buying more cinema movies and fewer cable movies