Ellie enjoys basketball (b) and soccer (s) according to the function U(b, s) = 3b + 4s. She has $120 to spend on lessons and each basketball or soccer lesson costs $30. a. What does Ellie's utility function say about her MRS of basketball for soccer? What do her indifference curves look like? b. How many basketball and soccer lessons should Ellie buy to maximize her utility? c. Would the number of basketball lessons Ellie buys change if she had more money to spend? Explain your answer.
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- Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.EXERCISE 6 If Ginna spends her entire budget, she could buy a chosen set of groceries and also buy 10 notebooks. If she spends only half of her budget, she could only buy a set of groceries and could not afford any notebooks. Suppose Ginna's budget is £150. Her preferences for groceries (G) and notebooks (N) can be described by the following utility function: U(G, N) = 30G + 2N (MUG = 30, MUN = 2). a) Find Ginna's optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how the price of a notebook should change for Ginna to change her optimal consumption choice. c) If the price of a notebook increases by 50%, how should the price of the groceries drop so that Ginna can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ginna's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ginna's demand for groceries and/or notebooks.Becky needs to decide how many cups of coffee and pieces of cake she will buy for a meeting with an office mate. She estimates her total utility for different quantities of coffee and cakes below. A cup of coffee is $1.00, and each piece of cake is $0.50. Becky has a total of $3 to spend. What is Becky's total utility if she buys 1 cup of coffee and 4 pieces of cake? Cups of Coffee 1 2 3 4 5 6 Utility from Consumption Pieces of Cake 1 2 3 4 5 6 A B C D Total Utility from Cups of Coffee 33 56 79 Total Utility from Pieces of Cake 15 32 48 63 77 90 Total Utility of Different Consumption Bundles Consumption Bundle Cups of Coffee Pieces of Cake Total Utility 3 0 2 2 1 4 0 6
- Styles 15. Damian Matthews is busy. He allocates his free time between watching movies and working out at the gym. The table below shows his utility from the number of times per week he watches a movie or goes to the gym. Damien has 14 hours a week to spend on movies or the gym (think of hours like $ of income here). Each movie takes 2 hours. Each gym trip takes 2 hours. Q of Gym Total Q of Movie Total Utility visits Utility from visits from Gym Visits movies 100 1 60 180 110 3 240 3 150 4 280 4 180 310 190 330 195 340 7 197 a) What bundles of gym visits and movies can Damien consume if he spends 1) all his time in the gym or 2) all his time watching movies? b) Calculate the marginal utility of each gym visit'and movie. Then calculate the Marginal Utility per hour of each activity. c) How should he allocate his time to maximize his utility? 12Define Economic utility3. Sam has set aside $480 for entertainment this month, which is golf (x) and/or bowling (z). A round of golf is $40 and a night of bowling is $30. His utility function is U = 3x + 2z. What is his MRS? a. b. c. Solve for the optimal choice of golf and bowling. Draw a graph of the budget line (including intercepts), a few indifference curves, and the optimal choice for Sam.
- How can one's choice of purchases/consumption be infuenced by utility or marginal utility?Rick eats only french fries and burgers at his office cafeteria. His weekly lunch budget is $48. Each burger costs $6 and each order of fries costs $3. When deciding how much of each good to buy, Rick knows that 2 burgers and 4 orders of french fries will give him a utility of 8. At his utility-maximizing point, Rick's utility is:You have $4,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and theprice of a pizza and a movie (M) is $20. Suppose that your utility function is U(T, M) = T3/4M1/4.a. What combination of T and M will you choose? b. Suppose that the price of day trips rises to $50. How will this change your decision?
- 1. Pindyck and Rubinfeld (2018) Chapter 4 Appendix, Exercise #5 Jae has the following utility function: U(X,Y)= 20X+ 80Y – X² – 2Y?, 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. Determine the number of CDs and video rentals that will maximize Jae's utility. а.4 Emily goes camping on the weekend and eats marshmallows (M) and crackers (C) there. She wants to match 1 marshmallow with 2 crackers, but does not eat in different proportion (i.e., perfect com- plement). The price of a marshmallow is 10 cents and the price of a cracker is 5 cents, and she spend up to $3 in total. a) Write down a utility function which represents Emily's preferences over marshmallows and crackers. b) How many marshmallows and crackers is she going to consume? (Hint: the first-order conditions will not help; draw the budget constraint and the indifference curves and look at the highest one that intersect the budget constraint). c) What is the exact value of Emily's indirect utility?Suppose you had a budget of $20.00 and the prices of a burger and a slice of pizza are $4.00 and $2.00 respectively. What is the marginal utility per dollar spent for the fourth burger?