Allen has a utility function U=xy², where x is the consumption of apples and y is the consumption of bananas. Price of apple is 1 and price of bananas is 4. Allen has 30 dollars in his pocket, so how many apples and bananas will he purchase to maximize his utility? options: 10 apples and 5 bananas. 3 apples and 10 bananas. 30 apples only. none of above.
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- Assume that Bob's utility function over beer x and pizza y is U(x,y) = 4x+12y. Which of the following statements is false? a) If the price of pizza is 12 and the price of beer is 3, then we can't determine how much pizza relative to beer Bob purchases. b) If the price of pizza is 16 and the price of beer is 5, then Bob only purchases pizza. c) If the price of pizza is 15 and the price of beer is 5, the own price elasticity of the demand for pizza as well as beer is infinite. d) It the price of pizza is 15 and the price of beer is 4, Bob purchases only beer e) Pizza and beer are perfect substitutes.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 BananasAn Individual values two goods, X and Y, according to the following utility function: -1.14 U(X,Y)= 6 (0.5 X-0.88 +0.5 Y-0.88) The price of X is P4, and the price of Y is Py-4. The individual has 16 dollars. How much X and Y should this individual buy? (Round answers to the nearest two decimals. For example, 1.666 rounds to 1.67.) X Number Y Number
- Tom went to a pizza by the slice bar with Jerry. Tom loves pizza (x), and prefers it, even more, when he can eat them with Coke (y). While Jerry is super hungry and will devour any amount of pizza and Coke available to him, Tom knows that there is a sweet spot for him, that is, an amount of pizza and Coke that maximizes his satisfaction. Tom’s preferences are represented by the utility function: u(x,y) = min{5,min{x,2.5y}}Tom took $30 with him to the pizza joint, and when he got there he saw the prices for a slice of pizza or a cup of Coke were $3 and $1.50, respectively. a.) What is Tom’s budget constraint? b.) How many slices of pizza and cups of Coke will Tom choose, in order to maximize his utility? Also, how much money does Tom uses? Assume Tom will not spend any money that does not increase his utility. c.) If Jerry needed money from Tom, what is the most money Tom can lend him? Explain.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 that the price of good X is $6 and the price of good Y is $2. You have $144 to spend and your preferences over X and Y are defined as: U(x,y) = x2/3y1/3 Calculate the marginal utility of X Calculate the Marginal Utility of Y What is the optimal Choice of X and Y given the PX = $6, PY = $2 and I = $144 If Income is increased to $150 calculate how the optimal choice of X and Y change
- Assume someone has a utility function of U = Min[3X, Y]. They currently have 8 units of X and 3 units of Y. The price of X is $12 and the price of Y is $3. If this person could sell some units of X and/or Y what level of utility could they achieve?Rafe is optimally choosing to consume 6 apples and 3 bananas. The prices of apples and bananas are p. = 7 and pb - 7. Which of the following utility functions over quantities of apples (a) and bananas (b) could represent Rafe's preferences? = u(a, b)-a4/5 61/5 Ou(a, b) = a¹/5 64/5 Ou(a, b)-a2/3 b1/3 Ou(a, b)-a¹/3 2/3Biwei’s utility function U=4XY, where X is consumption of beer and Y is consumption of pizza. For this utility function, the marginal utility of X is MUx = 4Y; the marginal utility of Y is MUY = 4X. 1) Suppose Y = 3. Calculate Biwei’s utility for X = 2, 3, 10, and 11. For a given level of Y, does good X display diminishing marginal utility? 2) Suppose X = 3. Calculate Biwei’s utility for Y = 2, 3, 10, and 11. For a given level of X, does good Y display diminishing marginal utility?