Suppose Bilbo Baggins is deciding on whether to buy a sword or a bag of golden cups. If he has a utility function of U(C,S)= √(4C+S) and treasures amounting to 200, while the prices of the sword and bag of golden cup are 4 coppers and 5 coppers, respectively, how many swords and bags of cups can he buy?
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Suppose Bilbo Baggins is deciding on whether to buy a sword or a bag of golden cups. If he has a utility function of U(C,S)= √(4C+S) and treasures amounting to 200, while the prices of the sword and bag of golden cup are 4 coppers and 5 coppers, respectively, how many swords and bags of cups can he buy?
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- You have k20per week to spend and two possible uses for this money,:telephoning friends back home and drinking coffee. Each hour of phoning costs k2 and each cup of coffee costs k1. Your utility functions U(X,Y)=XY,where X is the hours of phoning you do and Y the number of cups of coffee you drink. Now suppose the price of telephone calls drops to k1 per hour. What are your optimal choices? What is the resulting utility levelYou have £20 per week to spend, and two possible uses for this money: telephoning friends back home, and drinking coffee. Each hour of phoning costs £2, and each cup of coffee costs £1. Your utility function is U(X,Y) = XY, where X is the hours of phoning you do, and Y the number of cups of coffee you drink. What are your optimal choices? What is the resulting utility level? You can use the standard result on the constrained maximization of such a function, but must state it clearly. Now suppose the price of telephone calls drops to £1 per hour. What are your optimal choices? What is the resulting utility level? How much income per week will enable you to achieve the same quantities at the new prices as the ones you chose before? What income will enable you to attain the same utility as you did before? Comment on your answer in the context of equivalent variation and compensating variation.At a different table, Juan wins $600 in a blackjack game. Similarly, he has to choose between $600 or the chance to play a new game. In this game, Juan has a 60% chance of winning nothing and a 40% of winning $1,000. The following graph presents the utility function of Juan with respect to money: U(w) U(w) U(1,000) U(700) U(600) U(400) 400 600 700 1,000 w 10.2.2 1.0 point possible (graded, results hidden) By how much money would his winnings need to increase or decrease so that Juan is indifferent between the $600 and the new game? (in case of an increase, insert a positive number; in case of a decrease, insert a negative number).
- When Katerina goes running, she can either take water (W) or coconut water (C) with her to drink. She believes coconut water is three time more hydrating than plain water. Katerina just cares about the hydrating power of the drink. (i) Can Katerina's utility function be represented by U(W,C) =3C + W? (ii) Given U(W,C) =3C + W, Katerina has £28 pounds to spend on these two drinks. If a bottle of water costs £1 and a bottle of coconut water costs £2 what is Katerina's optimal choice? Note that MUw = 1 and MUc=3. %3D (iii) Explain under which conditions the tangency condition does not work. Given that the tangency condition does not work, discuss how we can find out the optimal consumption bundle for a consumer.You have k20 per week to spend and two possible uses for the money: telephoning friends back home and drinking coffee. Each Hour of phoning costs k2 and each cup of coffee costs k1. Your utility function is U(X,Y)=XY,where X is the hours of phoning you do and Y the number of cups of coffee you drink. What are your optimal choices? What is the resulting utility levels? You can use the standard result on the constrained maximization of such a function, but must state in clearlyYou have the Cobb-Douglas utility function u(x,y) = xy over apples (x) and plums (y) and you have $120 budget to spend and can carry at most 480 ounces in weight in your backpack going back to the dorm. Each apple costs $1 and weighs 8 ounces, and each plum costs $3 and weighs 4 ounces. You can only leave the store with a bundle of fruits you can afford and carry. (a) Drawing the relevant lines, intercepts, marking the points and hence identifying the feasible set of bundles, calculate the optimal bundle. (b) Forget about (a). If you were to choose a backpack before going on this shopping trip, for the weight constraint not to be an issue for you, how many ounces of weight capacity would you need for your backpack? HINT: That is, for this weight capacity of the backpack, you’d be able to carry the best bundle you can afford, i.e, the weight constraint is not binding for your decision. ( c) Forget about (b). In (a), just before going out for shopping with your backpack to buy the…
- 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.Roman loves corn bread. He buys corn meal and wheat flour in order to make corn bread. His recipe calls for two cups of corn meal and one cup of flour for each batch that he bakes. More corn bread is better for Roman. He can bake fractions of a batch, but has no use for corn meal or flour that is left over. What of the following is Roman’s utility function on cups of corn meal, denoted by c, and cups of flour, denoted by f?Julio loves gardening. His favourite plants are tulips and hydrangeas. His utility function is ' u(t,h)= t +100h -h^2 where t is the number of tulipsin his garden and h is the number of hydrangeas in his garden. suppose he has a 500 square feet for his garden. each tulip takes up 1 square foot of space and each hydrangeas takes up 4 square feet. he gets both plants for free.If he wanted to maximize his utility, how many tulips should he plant, what about hydrangeas? b) if his yard was only 144 square feet, how many tulips would he plant? How many hydrangeas? C) In order to plant both tulips and hydrangeas, how big does his garden need to be. carfeully explain.
- You live a fun life, consuming a yummy composite good, and a lot of cellphone The cell provider offers you two contracts: service! Deal #1: Up to 300 minutes per month, for a fixed fee of $20, and extra minutes for 20 cents. Deal #2: Up to 600 minutes per month, for a fixed fee of $55, and extra minutes for 15 cents. Your utility function is U = x" y"2 MUX = (1/2) x12 y2 You have a budget of $100 to spend. -1/2. MUy = (1/2) x2y2 a) Which plan do you choose, and what are your optimal choices of x and y? Confirm that your choice in part a) is correct by comparing the slopes of the budget b) line and the indifference curve at the optimum.Steve's utility function is U = q, +4 q,, where q, = veggie burgers per week and q, = packs of cigarettes per week. The price of a veggie burger is p,-$1.00. If Steve's optimal choice is (q,, 92) = (3,5), then the price of cigarrets is $Zeynep is at the supermarket buying her bi-weekly groceries. As she arrived at the store right before closing, not much is left on the shelves; so her purchases are limited to beef, B, and an assortment of organic vegetables, V. Beef costs £50/kg and vegetables Ł10/kg. Her utility function is expressed as U(B,V) = B0-6v0.3. She has ±150 to spend. Please answer the following questions using this information: A) Given the vegetables cost less than beef, explain why Zeynep would not only buy vegetables. B) Write Zeynep's constrained maximization problem (objective function subject to her budget constraint). C) Using the Lagrangian technique, find how much beef and vegetables would Zeynep buy? D) Show that for the preferences represented as above, demand for beef is a function of only its own price, pg, and income, m, but not the price of vegetables, py. Note: Rather than using the given prices and income, use PB, Py and m. Find and comment on the comparative statics, i.e., how do changes…