Carla has utility function U (x, y) = vx + 2y over goods x and y a) Do we have a name for this type of utility function? Are Carla's preferences well-behaved? b) Let Carla have budget I=$40, and let prices be Px=$2, Py=$8. What bundle will Carla consume? c) What if Carla's budget drops to $20? [Think about: could this utility function describe Carla's preferences over bread and ice cream?]
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![Carla has utility function U(x, y) = vx + 2y over goods x and y
a) Do we have a name for this type of utility function? Are Carla's preferences well-behaved?
b) Let Carla have budget I=$40, and let prices be Px=$2, Py=$8. What bundle will Carla consume?
c) What if Carla's budget drops to $20?
[Think about: could this utility function describe Carla's preferences over bread and ice cream?]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa1f2822-8ee5-4468-b761-4648e25887d9%2Fc516f041-8b83-4fd5-a477-6944665e49da%2F8ayo59_processed.png&w=3840&q=75)
Well-behaved preferences are those that are monotonic and convex.
The equilibrium is established where the MRSxy = Px/Py
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- Considering the following Diagram of consumer equilibrium, answer the following questions. If consumer has $100 to spend on X and Y at Budget line DE, what are the prices of X and Y products. What combination of X & Y maximizes the consumer’s total utility at Budget line DE? Why a consumer has moved to point B on Budget line DE1 from Point A of Budget line DE? Derive the demand curve of X product. What is relationship between X and Y products13. Shawn likes to consume pineapple smoothies and hotdogs. His preferences are represented by the utility function U(x,y) = 34x - x²/2 + y where x is his consumption of pineapple smoothies and y is his consumption of hotdogs. The price of pineapple smoothies is $2 and the price of hotdogs is $1. If the price of pineapple smoothies increases to $6, the change in Shawn's consumer surplus is: A) -144 B) -128 C) -120 D) -112 E) -90Calculate marginal utility and marginal utilty per dollar for the data provided in the table below: (round to two decimal places) The Price of wine is 3 The Price of Cheese is 0.14 The Consumer's budget for wine and Cheese is 9.69 (CHEESE) (CHEESE) (CHEESE) WEDGES OF CHEESE GLASSES (WINE) (WINE) (WINE) MARGINAL UTILITY MARGINAL MARGINAL UTILITY MARGINAL UTIUTY/dollar OF WINE TOTAL UTILITY TOTAL UTILITY UTIUTY/dollar 70 Number Number Number Number 160 35 Number 65 Number 225 3. 41 Number Number Number Number 45 288 Number 61 Number 48 349 The Quantity of Wine this consumer would buy to maximize utlity is: Number Number The Quantity of Cheese this consumer would buy to maximize utilit is : What is the consumer's Total Utility when optimized: Number 10
- Explain why it is that as the consumer purchases more of a good, her marginal utility falls while her total utility rises.Anatoly's marginal utility for DVDS (D) is MU X and his marginal utility for Xbox games (X) is MUx D. Anatoly's income is $120, the price of a DVD is $20.00, and the price of an Xbox game is $10.00. How many DVDS and Xbox games does Anatoly consume to maximize his satisfaction? Anatoly consumesDVDs andXbox games. (Enter your responses using integers.)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?
- Currently, Paula is maximizing utility by purchasing 5 TV dinners (T) and 4 Lean Cuisine meals (L) each week. Graph Paula’s initial utility-maximizing choice. Suppose that the price of T rises by $1 and the price of L falls by $1.25. Can Paula still afford to buy her initial consumption choices? What do you know about her new budget constraint? Use your graph to show why Paula will choose to consume more L and less T given her new budget constraint. How do you know that her utility will increase? Some economists define the ‘‘substitution effect’’ of a price change to be the kind of change shown in part c. That is, the effect represents the change in consumption when the budget constraint rotates about the initial consumption bundle. Precisely how does this notion of a substitution effect differ from the one defined in the text? If the substitution effect were defined as in parts, how would you define ‘‘the income effect’’ to get a complete analysis of how a person responds to a…3. Suppose Mary enjoys Pepsi and Coke according to the functionU(P;C) = 4C + 5P. What does her utility function say about her MRS of Coke for Pepsi? What do her indi§erence curves look like? What type of goods are Pepsi and Coke for Mary? If Pepsi and Coke each cost $1 and Mary has $20 to spend on these products, how many units of each product should she buy in order to maximize her utility? Show this utility maximiz- ing combination combination of Pepsi and Coke on the graph. how would her consumption and utility maximizing bundle of Coke and Pepsi change if the price of Coke decreases to 50 cents. 4. Vera is an impoverished graduate student who has only $100 a month to spend on food. She has read in a government publication that she can assure an adequate diet by eating only peanut butter and carrots in the Öxed ratio of 2 pounds of peanut butter to 1 pound of carrots, so she decides to limit her diet to that regime. a) If peanut butter costs $4 per pound and carrots cost $2 per…Suppose that Dale consumes only coffee and cheese, both of which have diminishing marginal utility. For each of the following cases, determine whether Dale should 1Consume more coffee and less cheese, or2Consume less coffee and more cheese: 1.The marginal rate of substitution of cheese for coffee is 3 (i.e., the marginal utility of cheese is three times the marginal utility of coffee), while the price ratio is 2 (i.e., cheese costs twice as much as coffee). 2.The marginal rate of substitution of cheese for coffee is 1 (i.e., the marginal utility of cheese is equal to the marginal utility of coffee) while the price ratio is 2 (i.e., cheese costs twice as much as coffee). 3.The marginal rate of substitution is initially equal to the price ratio, but the price of coffee increases. 4.The marginal rate of substitution is initially equal to the price ratio, but the price of cheese decreases. 5.The marginal rate of substitution is initially equal to the price ratio, but Dale enters exam…
- 5. Janice consumes two goods, X and Y. Janice has a utility function given by the expression: U=4X05Y05 and current prices of X and Y are $25 and $50, respectively. Janice currently has an income of 750 unit per time period. a. Write an expression for Janice's budget constraint. b. Calculate the marginal rate of substitution of X for Y. (horizontal line X, vertical line Y). c. Calculate the values of X and Y that will maximize utility. d. Graph your answers (budget line, indifference curve)[2. John likes 3 sugar packets (S) in his coffee (C). Assume that Ps is the price of sugar, Pc is the price of coffee and I is John’s income. (a) Write down John’s budget set and utility Solution Budget set: (Ps)S + (Pc)C = I Utility function: u(S,C) = S + 3C] For the answer above, I don't understand why the utility function of S and C is performed in the form of perfect substitutes instead of perfect compliments.Joyce drinks both coffee (x) and tea (y). Her preferences over these two goods can be represented by the utility function U(x,y) =x + 3y^1/2 where x represents the number of pounds of coffee and y represents the number of cups of tea. a) Given her preferences, find her demand functions for coffee (x) and tea (y). b) Suppose that the price of a pound of coffee is $4 and that she has $56 to spend on coffee and tea. Write her demand curve for tea. Illustrate her demand curve. c) Suppose that the price of a cup of tea is $1 (the price of coffee and income remain $4 and $56, resp.). Use your demand functions to find her best bundle. In an indifference curve diagram illustrate her best bundle at these prices. For the remainder of the question, assume that her income rises to $60 and that the prices of coffee and tea are unchanged at = $4 and =1.
