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- Alice is going to Wonderland and needs supplies. She has $100 and can buy only walnuts and raisins. The price of walnuts is $20 per kg and of raisins is $10 per kg. Alice's preferences are described by the utility function u(x1,x2)=min{0.5*x1+2*x2,x1}, where x1 is the quantity of walnuts, and x2 is the quantity of raisins. Given her budget constraint and preferences, if Alice were offered a choice only among the bundles listed below, which one would she buy? Выберите один ответ: a. x1=3, x2=4 b. x1=2, x2=0.5 c. x1=4, x2=3 d. x1=1, x2=8Suppose an individual is currently spending all of their income on a bundle of books and pizza, but they are not sure whether the bundle maximizes their utility. Assume the individual has a strictly diminishing marginal rate of substitution over these two goods. At their current bundle of books and pizza, the individual's marginal utility from consuming books is 6 utils and their marginal utility from consuming pizza is 3 utils. If the current price of a book is $12 and the price of a pizza is $7, which of the following statements must be true: A. The individual can increase their utility by consuming more books and less pizza B. The individual is maximizing their utility C. The individual can increase their utility by consuming more pizza and fewer booksThe 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…
- Andrea has a budget of £21 to spend on toothbrushes and tooth paste. He does not receive any utility from owning a toothbrush, but for the consumption of every tube of tooth paste he gains a utility of 2 utils – but only if he owns a tooth brush. Without a tooth brush, Andrea gains no utility from consuming tooth paste. In addition, after consuming 10 tubes of tooth paste, a toothbrush needs to be replaced, i.e., Andrea needs to buy a new one. The current price of tooth brushes on the market is £5 and the current price for tooth paste is £1 per tube. Assume that Andrea aims to maximise consumer surplus. wwwwwww a) In a graph, draw total utility as a function of number of toothpaste tubes, assuming that Andrea buys 1 tooth brush. b) How many tubes will Andrea buy if he wants to maximise consumer surplus, assuming that Andrea can buy any amount of tooth brushes? What is Andrea's total consumer surplus? c) How many tubes will he buy if the current price is £0.50 per tube? d) Find Andrea's…Suppose we are able to model the total utility function for the consumption of two goods, good x and good z. The utility function is structured as U(x, z) = 3x2 + z2 - 2xz. The consumer is faced with the prices of goods x and z. The price for each unit of good x and z is $1 each. The consumer has an income $1 (in thousands). How many units of each good should the consumer consume so as to maximize his/her utility?Please refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by Your marginal utility function for apples is . Your marginal utility function for oranges is U (A, O) = AO³ MUA = 0³ MUO 3A0² . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. = When you set up the optimal decision rule for your consumer problem, which of the following statements best describes how much you will buy of apples and oranges at your consumer equilibrium? For each peck of apples, you will buy 1/3 pounds of oranges. For each peck of apples, you will buy 1 pounds of oranges. O For each peck of apples, you will buy 3 pounds of oranges. O For each peck of apples, you will buy 6 pounds of oranges.
- 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.While visiting family in Mexico, your professor has a budget of $ 255 ($ = pesos) that he spends on tacos and tequila. The price of tacos is $ 6 and a shot of tequila is priced at $ 16. During his visit the price of tacos changes to $ 5. Assume your professor has a Cobb-Douglas utility function with (tacos) parameter a = ( 27 / 100). How many shots of tequila does your professor purchase ? (Assume both goods are commodities.) (Answer is : 11.63)Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…
- Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices…Andrea has a budget of £21 to spend on toothbrushes and tooth paste. He does not receive any utility from owning a toothbrush, but for the consumption of every tube of tooth paste he gains a utility of 2 utils – but only if he owns a tooth brush. Without a tooth brush, Andrea gains no utility from consuming tooth paste. In addition, after consuming 10 tubes of tooth paste, a toothbrush needs to be replaced, i.e., Andrea needs to buy a new one. The current price of tooth brushes on the market is £5 and the current price for tooth paste is £1 per tube. Assume that Andrea aims to maximise consumer surplus. a) In a graph, draw total utility as a function of number of toothpaste tubes, assuming that Andrea buys 1 tooth brush. b) How many tubes will Andrea buy if he wants to maximise consumer surplus, assuming that Andrea can buy any amount of tooth brushes? What is Andrea's total consumer surplus? c) How many tubes will he buy if the current price is £0.50 per tube? e d) Find Andrea's…Consider Gary's utility function: U(X,Y) = 5 XY, where X and Y are two goods. If the individual consumed 10 units of X and received 250 units of utility, how many units of Y must the individual consume? 5 25 0 10