Suppose that Romeo in Problem 8 has the utility function U= S6 RS, and Juliet has the utility function U= SRS6, where SRis Romeo's spaghetti consumption and S, is Juliet's. They have 70 units of spåghetti to divide between them. a) Juliet would want to give Romeo some spaghetti if she has more than 42 units of spaghetti. b) Romeo would want to give Juliet some spaghetti if he had more than 35 units of spaghetti. C) Romeo and Juliet would never disagree about how to divide the spaghetti. d) Romeo would want to give Juliet some spaghetti if he has more than 38 units of spaghetti. Juliet would want to give Romeo some spaghetti if she has more than 40 units.
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- 1) Suppose that Abel and Eden spend their incomes on two goods, food (F) and clothing (C).Abel’s preferences are represented by the utility function U(F,C)=10FC, while Eden’spreferences are represented by the utility function U(F,C)= 0.20F2C2A) With food on the horizontal axis and clothing on the vertical axis, identify on a graph theset of points that give Abel the same level of utility as the bundle (10, 5). Do the same forEden on a separate graph.B) On the same two graphs, identify the set of bundles that give Abel and Eden the samelevel of utility as the bundle (15, 8).C) Do you think Abel and Eden have the same preferences or different preferences? Explain 2. Graphically show the effect of an increase in price of Coca Cola on the demand of PepsiCola 3. Assume a budget line is drawn for two commodities: X on the x-axis and Y on the y-axis. Ifthe income of the consumer is 120 Birr, the y-intercept is 3, and the slope of the budget lineis -0.5 then determined the price of commodity…John likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does John show diminishing marginal utility for Coke, or does he show increasing marginal utility for Coke? Supposethat John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke?Suppose that Romeo in Problem 8 has the utility function U= S° RS2, and Juliet has the utility function U= S2RS5, where SRis Romeo's spaghetti consumption and Sj is Juliet's. They have 42 units of spaghetti to divide between them. Juliet would want to give Romeo some spaghetti if she has more than 28 a) units. Romeo would want to give Juliet some spaghetti if he has more than 26 units of spaghetti. C) Romeo and Juliet would never disagree about how to divide the spaghetti. d) Romeo would want to give Juliet some spaghetti if he had more than 21 units of spaghetti. Juliet would want to give Romeo some spaghetti if she has more than 30 units e) of spaghetti.
- Suppose that Abel and Eden spend their incomes on two goods, food (F) and clothing (C).Abel’s preferences are represented by the utility function U(F,C)=10FC, while Eden’spreferences are represented by the utility function U(F,C)= 0.20F2C2A) With food on the horizontal axis and clothing on the vertical axis, identify on a graph theset of points that give Abel the same level of utility as the bundle (10, 5). Do the same forEden on a separate graph.B) On the same two graphs, identify the set of bundles that give Abel and Eden the samelevel of utility as the bundle (15, 8).C) Do you think Abel and Eden have the same preferences or different preferences? ExplainEnrique 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 moviesThe following table shows the marginal utility per dollar of apples and pears for five consumers: Consumer Marginal Utility Per Dollar Apples Pears Darnell 8 5 Eleanor 7 8 Jacques 6 6 Kyoko 5 4.5 Musashi 4 4 Darnell, Eleanor, and Kyoko are not optimizing over their choice of fruit. In the following table, indicate which fruit each consumer should increase consumption of in order to achieve the optimal fruit consumption bundle. Consumer Apples Pears Darnell Eleanor Kyoko
- John likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does John show diminishing marginal utility for Coke or does he show increasing marginal utility for Coke? Suppose that John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke? *use tables and/or graphs if possible, please original work2. Jie has the utility function U, (a, b) = 2a + b and Daokui has the utility function U,(a, b) = v2ab, where a is the number of apples consumed and b is the number of bananas consumed. There are 10 units of apple and 10 units of banana in total. We draw an Edgeworth box with apple on the horizontal axis and banana on the vertical 4 axis and we measure Jie's consumptions from the lower left corner of the box. We assume that both apple and banana are infinitely divisible. Please answer the following questions. (a) Write down all pareto optimal allocations (you do not need to explain why). (b) If social welfare function is W min{U,(a, b), U(a, b)}, derive the social optimal allocation. Is this allocation pareto optimal? Suppose the endowment of Jie is 7 units of apple and 0 units of banana, and the endowment of Daokui is 3 units of apple and 10 units of banana. Please answer the following questions. (c) Assume that the price of apple is p, and the uniform price of banana is 1. Derive the…Matthew Hamming is stranded on an island. He has decided that he will spend exactly 10 hours a day gathering food. He can either spend this time gathering coconuts or catching fish. He can catch 2 fish per hour and he can gather 3 coconuts per hour. Matthew's utility function is U(FC) = 3F0.60.3 a. How many fish should Matthew catch and how many coconuts should he gather so that his consumption maximizes his utility? Illustrate the equilibrium with a graph b. One day a native inhabitant of another island arrives on the island. The visitor offers Matthew trade of 3 fish for 1 coconut. The trade fee costs 1 fish (that must be paid prior to the exchange). Will Matthew decide to trade? What will Matthew produce and consume? Justify your answer and provide a graph.
- Carol has very weird preferences. She only cares about quantity. When evaluating a bundle, Carol only looks at the highest amount of a good she can consume in each bundle, regardless of whether it is of eggs or dumplings. She is indifferent between two bundles only when the largest consumption of a good within each bundle is the same across bundles. So, for instance, if a bundle offers 5 eggs and 1 dumpling she finds that bundle indifferent to a bundle offering 4 eggs and 5 dumplings. These preferences are transitive. But are they monotone? And convex?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 30Julio 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.