Caroline has a $10 dessert budget that she uses to buy pie and cake. Assume the price of pie (Pp) is fixed at $2. Table A shows Caroline's marginalMUutility (MU) and marginal utility per dollar () she receives from the first through fifth slices of pie she buys each week. Table B shows the sameinformation for cake when the price of a slice of cake (Pc) is either $4 or $2. Assume that Caroline isrational consumer who wants to maximize herutility.Table AMU/P(If P=2)PieMU(Slices)(Utils)3015124122010147Table BCakeMUMU/P(Slices)(Utils)(If P=$4)(If P=$2)40102032816224121648412.964.4 51. If the price of a slice of cake is $4, the price of a slice of pie is $2, and Caroline spends her entire budget of $10, she will choose to buyof pie andof cake.Now, suppose that cake goes on sale, and its price decreases to $2. Caroline's utility is now maximized if she buysof pie andof cake.Suppose the price of pie is fixed at $2, and Caroline's budget is fixed at $10.On the graph, use the blue line (circle symbols) to plot Caroline's demand for cake. Do this by placing one blue point (circle symbol) on Caroline'sdemand for cake when the price is $4 and the second blue point on Caroline's demand for cake when the price is $2.Caroline's DemandPRICE (Dollars per slice)4)

If the price of the slice of cake is $4....., she will choose to buy 3 slices of pie and 1 slice of…

Answered: Caroline has a $10 dessert budget that…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.
Every month, a family of three spends $2,000 on food (F) and other items (O). The family’s preferences are represented by the utility function U(F,O) = F1/5O4/5. The unit price of food and the unit price of other items are both $1. Find this family’s monthly food expenditure.The family could join a consumers’ club. At the club, food costs 20% less than in other stores (i.e., at the food club PF = $0.8)
QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x2). Linguini has utility function UA = x4x4 and Colette has utility function UB = 2xfx. Linguini is endowed with 10 éclair (x,) and 3 profiterole (x), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x2). (a) Draw an Edgeworth box with x, on the horizontal axis and x, on the vertical axis. Position Linguini on the bottom left corner and Colette on the top right comer. Indicate the total number of units of x, and x2. Label the endowment allocation. (b) Derive the equation of the contract curve, ie., find x(x). In your graph in (a), draw the contract curve.
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.
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?
A consumer has an income of $400 and is deciding between two products: X and Y. Assume that the X product is the horizontal axis product. The price of X is $10 and the price of Y is $2. Assume the consumer currently wants to consume 50 units of product Y to maximize his utility. a) Write out the equation to this consumers budget line. What is the slope to this budget constraint? b) How much of X and Y will the consumer consume to maximize his utility subject to his budget constraint. C) Now assume the price of X changes to $5 and price of Y and Income stays the same. At the new price, the consumer wants to buy 60 units of product X to maximize her utility given her budget. How much X and Y will the consumer consume to maximize utility. g in the before and after the change of the budget constraint and indifference graph on the same graph space. Show all necessary points. Label clearly. ead oubstitutiofs. Draw d) Write out the expression of the utiiity maximizing ruie here.?
Another instance when people are likely not to spend a dime (or a minute) on an item is when they have a dislike for mixing the item with other items available. In this case, we say the consumer has ‘non-convex preferences’ and indifference curves are bowed out from the origin. In plain language, the consumer has a preference for binging. We often feel this way towards our favorite social media app. Consider a kid who has four hours a day to spend on social media. They enjoy spending time on Snapchat (x) or spending time on Twitter (y). a) Write the kid’s time constraint and illustrate it in a graph where you measure time spent on Snapchat along the horizontal axis and time spent on Twitter along the vertical axis. This kid’s utility from time spent on Snapchat and time spent on Twitter is U(x,y) = 4x2+ y2. b) In your graph, draw a couple of the kid’s indifference curves. Notice how the kid’s |MRSY,X| increases along each curve as he spends more time on Snapchat and less time on…
Lisa consumes only two goods, pizzas and burritos. In equilibrium, her marginal utility per slice of pizza is 10 and her marginal utility per burrito is 8. Instructions: Enter your answer rounded to two decimal places. If a slice of pizza costs $3, then the price of a burrito must be $
Suppose that U(f,c) = f + 8c^(1/2)is a utility function that describes Amelia’s preferences over two goods: fish(f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis.a. Derive an expression for her marginal utility (Uf)from a small increase in f holding c fixed. Also find themarginal utility for custard (Uc).b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitivedescription of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, howmany units of custard would she be willing to give up in order to get one more unit of fish?c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goodson the indifference curve.d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5properties of indifference curves? Briefly support your answer.e. Give another utility function that represents…
Ellie spends £20 on Energy drink (E) and Juice (J). Her preferences for these goods can be described by the following utility function: U ( E,J) = 2E + J^2 ( J squared) - J (MUt = 2, MUj = 2J - 1) Suppose that one energy drink costs £1.60 while one carton of Ellie’s favourite Juice costs £4.00. a) Find Ellie’s optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how Ellie’s optimal consumption choice would change when her disposable budget changes. c) If the price of energy drinks increases to £2.00 per can, how should the price of Juice change so that Ellie can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ellie’s optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ellie’s demand for Energy drink and/or Juice.
Q2. Suppose a consumer seeks to maximize the utility function U (x, y) = (x + 2) (y + 1), where and y represent the quantities of the two goods consumed. The prices of the two goods and the consumer's income are pa, py, and I. Write out the consumer's budget constraint and the Lagrangian function for the problem.
Huang is determining how much Coke and Pepsi he will buy. Use the information in italics to answer the bolded question below. • Huang's preferences for Coke (C) and Pepsi (P) are represented by the following utility function: U = 2C + 3P • Huang has $12 to spend on soft drinks. • The price of Coke (P) is $0.50/can. • The price of Pepsi (Pp) is $1.00/can. Which of the following statements referring to Huang's preferences is incorrect. O Huang does NOT experience diminishing MRS. If Huang gives up two cans of Pepsi, he needs to purchase 3 cans of Coke to remain equally satisfied. Pepsi and Coke are perfect substitutes for Huang O None of the above statements are incorrect.

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