Kofi's utility function is given by Ug (X,Y) = XY . The utility functions of his four friends - Esi (UE) John (U), George (UG) and Osei (Uo) are: a. Ug(X,Y) = 100XY b. U,(X,Y) = -XY c. Uc(X,Y) = XY – 10,000 d. Uo(X,Y) = X – Y Which of these friends have the same preference as Kofi.
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- uestion1:Donna and Jim are two consumers purchasing strawberries and chocolates. Jim’s utility function is U (x, y) = xy and Donna’s utility function is U (x, y) = x2y where x denotes strawberries and y denoteschocolates. Jim’s marginal utility functions are MUX=y and MUy=x while Donna’s are MUX=2xy and MUy=x2. Jim’s income is $100, and Donna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4? What is the optimal bundle for Jim, and for Donna, when the price of strawberries rises to $3?Question2:Consider a one-period ecoSuppose 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 30The following five individuals have different utility functions over food (good x) and clothing (good y): 1) u₁(x, y) = 3x²y 2) u₂(x, y) = 2√x + y 3) Uz(x, y) = x0.6y0.4 4) u₁(x, y) = x² + y² 1 5) us(x, y) = x + 3y For each of these people: a) Compute their marginal utilities of good x, MUx = Ju(x,y) MU, = ду du(x,y) ax b) Check whether the property of "more is better" is satisfied for both goods? Explain. [Hint: Check whether marginal utilities are positive assuming positive amounts of good x and good y] ƏMUX əx and marginal utility of good y, c) Does the marginal utility of good x diminish, remain constant, or increase as each of the individuals buys more x? Explain. [Hint: There are 2 ways to do it: 1) visually check what happens to the expression of MUx when x increases (does it decrease, keep constant or decrease?); or 2) take the partial derivative of this marginal utility with respect to x, that is ƏMUx .aMUX ƏMUX If 0, the marginal utility of x is increasing in x] d) Does the…
- Daniel and Kjell are writing a paper together. Daniel is the PhD supervisor and thus is the first to decide how many hours, hp. to put into the project. After observing the amount of time that Daniel contributes, Kjell decides how many hours, hK. to contribute. Daniel's utility function is 12(hp+ hx)5 -hp Kjell's utility function is 14(hp+hx)0.-hx How many hours does Kjell spend on the project? Select one alternative: O 49 O 26 O 32Sam's extended family spends $3,200 per month on wine and beer. Their utility function is given by U = 200WB, where W represents the number of bottles of wine that they buy, and B represents the number of cases of beer that they buy. Wine costs $25 per bottle and beer costs $32 per case. Sam's family wants to maximize their utility. Calculate how many bottles of wine and how many cases of beer they should buy. Show your calculation(s).I am unsure the direction the utility functions would go in , with this specific scenario
- Suppose that Bartolo and Emilio spend their incomes on two goods, food (F) and clothing (C). Bartolo's preferences are represented by the utility function: 16 15- U(F,C) 10FC 14- 13 while Emilio's preferences are represented by the utility function: U(F,C) 0.20F2C2 12 11 . 10- With food on the horizontal axis and clothing on the vertical axis, identify on a graph the set of points that give Bartolo the same level of utility as bundle (10,5). Do the same for Emilio. Then, identify the set of bundles that give Bartolo and Emilio the same level of utility as bundle (15,8) 8- 1.) Using the three-point curved line drawing tool, graph an indifference curve for Bartolo that includes bundle (10,5) and that also contains bundles with 4 and 5 units of food. Label the curve U 6- 2.) Using the three-point curved line drawing tool, do the same for Emilio including bundle (10,5) and bundles with 4 and 5 units of food. Label the curve U1 3.) Using the three-point curved line drawing tool, graph an…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.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.
- Anton, Betsy and Catherine are three college friends who regularly go the movies. At the movies, they can purchase skittles (x) and junior mints (y). The table below display the total utility each of them get from bundles of these two snacks (x, y). Bundle A = (1,1) B = (1,2) C = (1,3) D = (1,4) E = (1,5) Anton's Anton's Utility MUY (2) (1) 10 14 16 17 17.5 Betsy's Utility (3) 10 10 9 8 7 Betsy's MU, (4) Catherine's Utility (5) 10 12 15 19 24 Catherine's MUY (6) a) Yesterday the three friends went to watch the Barbie movie and they purchased the same bundle, bundle B = (1,2), with 1 bag of skittles and 2 bags of junior mints. Can you say who of the three friends experienced the highest utility from consuming bundle B? Explain. b) As you may have noticed, all bundles in the table contain 1 bag of skittles while they differ in the number of bags of junior mints. Fill in columns (2), (4) and (6) in the table by computing the marginal utility each friend receives from choosing a bundle…Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 -2 -2 2 Guitars 2$ Losses Losses i-600 -2 What is the least amount of money Jimi is willing to accept to sell one of his guitars? (just enter a dollar amount, i.e., "10o0", not "$1000"Ceja has utility function U=A2*B2 , where A equals the number of apples she eats each week, while B is the number of bananas she eats each week. Ceja has $20 to spend on fruit each week. The price of an apple is $1, while the price of a banana is $0.25. Find out the combination of Apples and Bananas that maximize Ceja’s satisfaction. If price of Banana is increased by $.25, what will be the new combination of A and B that would maximize her utility? Show graphically and drive the demand curve for Bananas