21. Alfred's preferences are described by the following utility function U(X, Y) = 5X + 6Y,where the prices and income are Px = 3; Py = 5; M = 90.(a) What type of preferences does Alfred have and are they homothetic and/orquasilinear?(b) What will be Alfred's optimal bundle? Illustrate this in a diagram, with good Xmeasured on the horizontal axis, and explain your answer. (c) If Alfred's income increases to M = 120 and the price of good X is now Px = 5(with the price of good Y unchanged), what will Alfred do? Illustrate this in adiagram and explain your answer.Now consider a different utility maximising consumer, Cherrin, who does not have alinear utility function, but instead has strictly convex preferences. At the optimumbundle of (A*, B*), good A has a negative income elasticity of demand and good B has apositive income elasticity of demand.(d) If Cherrin's utility function was the same as Alfred's U (A, B) = 5A + 6B, and shefaced the same prices, such that PA = 3; PB = 5; what would her Engel curve nowlook like? Explain your answer.(e) Return to the original scenario for Cherrin, where she has strictly convexpreferences and where good A has a negative income elasticity of demand andgood B has a positive income elasticity of demand. If the price of good A increased,illustrate using a diagram and explain what would happen to Cherrin's consumptionof A and B due to the income and substitution effects. Make sure you are clearabout any assumption(s) you make.

Alfred's utility function is given by U(X,Y) = 5X + 6Y, where X represents the quantity of good X…

(a) What type of preferences does Alfred have and are they homothetic and/or quasilinear? (b) What will be Alfred's optimal bundle? Illustrate this in a diagram, with good X measured on the horizontal axis, and explain your answer.

(a) What type of preferences does Alfred have and are they homothetic and/or quasilinear? (b) What will be Alfred's optimal bundle? Illustrate this in a diagram, with good X measured on the horizontal axis, and explain your answer.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

1. Jim's preferences for pears and apples can be summarized by the following utility function: U(Xa,Xp)=XaXp where xa is the quantity of apples and xp is the quantity of pears. a) Draw an indifference curve for Jim by calculating a series of bundles that all produce the same level of "utility" and plotting them. Interpret the slope of the indifference curve (the marginal rate of substitution). b) Calculate the formula for Jim's marginal rate of substitution, as a function of apples and pears consumed.¹ c) What happens to the numeric value of Jim's marginal rate of substitution along an indifference curve (i.e., holds his utility constant) as he increases the number of pears he consumes and decreases the number of apples? For example, compare his MRS for a bundle consisting of 9 apples and 4 pears to his MRS for a bundle consisting of 9 pears and 4 apples and interpret the change. d) Suppose something increases Jim's desire for apples (for example, apples are found to reduce the risk of…
Q1. Consider a Cobb-Duglas utility function: log U = log A + a log X1 + b log X2 Given the prices of commodities X1, X2 as P, and P2 respectively and money income M a. Derive the marshallian demand function of X1 and X, b. Find the expression for the budget shares c. Show that the demand functions satisfy the properties of homogeneity and additive.
The figure below illustrates 3 indifference curves and two budget lines for a student whose budget for online gaming is $10/week. The red line illustrates this student's original budget line. After thanksgiving prices change, the blue (dash-dot) line illustrates the student's new (post-price change) budget line. a) What were the original hourly prices of FortDay and PokemonStop? What are the new prices? b) What is the students optimal bundle at the original prices? How about at the new prices?
4. Use the following information to calculate Wren's optimal bundle and his resulting utility: IC:U(x,y) = x0.5, 0.5 Px = 1, Py = 4, m = 48
Ben gets utility from apples and bananas such that U(A,B)=A+2B. If the price of bananas is $2, then Ben's ordinary demand curve for apples in the (x1, p1) plane is zero for pA>$2 and then downward sloping for pA$0.50 and then downward sloping for pA$0.50 and then vertical for pA$1 and then vertical for pA$4 and then downward sloping for pA$4 and then vertical for pA<$4.00
Help me
Cobb-Douglas Preferences] Asad lives in a world with two goods (N=2), apples and bananas. He has a Cobb-Douglas utility function over these goods U(a, b) = a 0.7 b 0.3 . Asad has an income I = 200, and faces prices pa = 2, pb = 1 (a) We know that if Asad is optimizing (and consumes a bundle that contains both apples and bananas), that the slope of the budget constraint should be equal to his MRS. Use this and his budget constraint to solve for his optimal bundle. (b) Suppose the price of apples rises to 4, and the price of bananas rises to 3. What is his new optimal consumption bundle? (c) Suppose Asad instead had a utility function given by U(a, b) = a 1.4 b 0.6 + 1. Given the same prices and income as in part (b), what is his optimal bundle?
Peter's preferences over two goods, x and y, are represented by the utility function u(x, y) = y + 2x. a) Peter is currently consuming bundle A = (2,4) with 2 units of good x and 4 units of good y. Calculate his current level of utility from consuming this bundle. b) Write the expression the indifference curve representing Peter's current level of utility (i.e., the one you found in part (a). Next draw this indifference curve. c) By looking at the indifference curve you drew in part (b), answer the following questions: Does Peter like good x? Good y? Explain. What can you say about the marginal rate of substitution of good x for y, MRSxy? Is it positive? Negative? Constant? Increasing? Decreasing? Interpret/explain your answer in terms of the tradeoffs Peter is willing to make between goods to keep the same utility level. d) On the same graph you drew in part (b), draw the indifference curve for a utility level of 10. Plot and label in the graph bundles B = (1,2), C = (1,6), and D =…
From the hypothetical data in table 1, provide the following requirements. Table 1. Total Utility & Marginal Utility for Chocolate Bars Quantity (Chocolate Bars) Total Utility Marginal Utility 0 0 1 7 2 11 3 13 4 14 5 14 6 13 Solve the marginal utility column. Show the graphical solution. What does your graph implies?
A consumer has $100 to spend on craft beer and Schweinefleischaft (pork shanks). Suppose craft beercosts $10 per 4-pack if the customer purchases up to five 4-packs. After that, it is $5 per 4-pack. SupposeSchweinefleischaft is $5 per order of pork shanks.(a) Draw the budget constraint for this consumer, with craft beer on the horizontal axis and Schweine-fleischaft on the vertical axis.(b) Will the consumer ever purchase exactly five 4-packs of craft beer? Explain why, using both thegraph in part (a) and words.
I. You only consume two goods and your preferences are represented by utility function 2 U(x₁, x₂) = (x1.5 + x2.5) for x₁ > 2 and x₂ > 0.
Rakhi likes to consume only two commodities X and Y, and nothing else. Both the commodities give her positive utilities, thereby giving rise to her preferences being well- behaved and convex. However, she treats commodity X as an inferior good. Suppose Rakhi earns an income of 1000 per month and the ongoing prices of commodities X and Y are 20 and 10, respectively. (a) Show, with the help of a diagram, what will happen to her optimal consumption of commodity X, in each of the following circumstances: Situation A: Price of X falls to 10, while everything else remains the same. Situation B: Her income increases to 2000, while prices remain the same. (b) What can you say about the demand curve for commodity X that Rakhi’s choice behaviour would produce? Elaborate, with the help of diagram.