1. The consumer has Cobb-Douglas preferences for two goods x and y: u(x, y) = Py> 0 and m> 0 is given. a) Set up the Expenditure Minimization Problem. b) Calculate MU and MUy. 10x¾y³. px > 0, c) State the condition that explain why Cobb-Douglas preferences will guarantee an interior solu- tion. c) Give the two optimality conditions for x and y. i)

1. The consumer has Cobb-Douglas preferences for two goods x and y: u(x, y) = Py> 0 and m> 0 is given. a) Set up the Expenditure Minimization Problem. b) Calculate MU and MUy. 10x¾y³. px > 0, c) State the condition that explain why Cobb-Douglas preferences will guarantee an interior solu- tion. c) Give the two optimality conditions for x and y. i)

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter21: The Theory Of Consumer Choice

Section: Chapter Questions

Problem 2CQQ

See similar textbooks

Similar questions

TOTAL AND MARGINAL UTILITY Reset E UTILITY CALCULATIONS Total Utility Quantity Consumed 70 Total Marginal Utility Utility 60 50 40 22 30 22 20 18 10 40 14 4 6. 8 54 Quantity Consumed Marginal Utility 10 20 4 64 6. 10 5 70 1 3 4 2 -10 72 -20 -2 Quantity Consumed 70 Quantity Consumed -6 64 1 6. 8.
3 8. Let be the utility function U(x, y) =(xi + 2ya), , where x and y are the quantities consumed of two goods. (a) Show that the functional equation U(x,y) U(2, 2) defines y as a function of x in a neighborhood of point (2, 2). (b) If the quantity consumed of good x increases by 1 unit, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant? (c) If the quantity consumed of good x increases by 1%, by how much does the quantity have to increase or decrease? Consumed of the good and to keep utility constant?
1/Muhammad’s perceives canned tuna (Y) as an inferior good and fresh tuna (X) as a normal good. If his income increases by 100%, and his income elasticity of both types of tuna is 1. Show the effect of this increase in income on the change in his optimal choice of canned and fresh tuna, highlighting his income-consumption curve. Clearly label your graph. Reflect the proportional changes in your graph 2/ Assume a piece of jewelry and 2 consecutive drops in its price. Also consider Alia’s demand to be relative elastic in the price range from ?1 to ?2, and that she perceives jewelry as a Giffen good in the price range from ?2 to ?3. Draw her price-consumption curve with well-behaved preferences. Clearly label your graph.
2. Suppose John's utility function is UX,Y) = 4/XY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2Y/X and MUy = 2\X/Y ) a) Suppose Y=3. Calculate John's utility for X=4,9,16, and 25. For a given level of Y, does good X display diminishing marginal utility?
A consumer has the following utility function: Ulx, y) = xy -y, *21 where x and y represents the quantities consumed of goods X and Y. y 20 What will be the substitution and income effects for X and Yassuming that the consumer attempts to maintain the same level of utility achieved before price of Y increased (that is, when price of Y was $1)? SEx= +0.5 IEx = -0.5 SE, = -0.25 IE- = -0.25 SEx= +0.293 IE = -0.293 SEy = -0.414 IE, = +0.414 SEr= +0.25 IE SE, = -0.75 IE, = -0.75 = -0.25 SEx= +0.414 IEx = -0.414 SEy = -0.293 IE, = -0.207 Income = $3 Px= $1, Py= $2
1.Let x and y denote the amount of goods X and Y. Find the demand functions of X (do not need to ﬁnd that of Y) when your preferences are represented by the utility function U = x^2y. Is X normal good? Can you conﬁrm law of demand for X? What is the relationship of X with Y? Answer all of them by using the demand curve you derived. 2.Let x and y denote the amount of goods X and Y. Find the demand functions of X (do not need to ﬁnd that of Y) when your preferences are represented by the utility function U = x + xy + y. Is X normal good? Can you conﬁrm law of demand for X? What is the relationship of X with Y? Answer all of them by using the demand curve you derived 3.There are two goods F and C. Let MU and P denote marginal utility and price of each good. SupposeMUF = 3, MUC = 4, PF = 2, PC = 2.Are you maximizing your satisfaction? If not, what would you do to increase your satisfaction? Explain.
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)
Answer the following short questions:a. Suppose that a consumer’s preferences between goods x andy are represented by the utility function u(x, y) = x^2 + 16xy + 64y^2. If these two goods have the same price, describe the optimal consumptionchoice of this consumer.b. Suppose that when the price of a good change, the incomeand substitution effects change the consumer’s demand for that goodin opposite directions.i. Is this good a normal or an inferior good? Explain.ii. Is this good a Giffen or an ordinary good? Explain.c. Is the following statement true or false? The differencebetween a monopolist’s marginal cost and its profit-maximizing price issmaller when the demand is more elastic.
You are choosing between two goods, X and Y, and your marginal utility from each is as shown below. Units of X MUX Units of Y MUy 10 8. 2 2 7 3 4 4 4 4 6. 6 Instructions: Enter your answers as whole numbers. a. If your income is $18.00 and the prices of X and Y are $4.00 and $2.00, respectively, what quantities of each will you purchase to maximize utility? X = units. Y =O units. b. What total utility will you realize? c. Assume that, other things remaining unchanged, the price of X falls to $2.00. What quantities of X and Y will you now purchase? units. X =O units. Y = d. Using the two prices and quantities for X, derive a demand schedule (a table showing prices and quantities demanded) for X. Instructions: Start with the highest price first. Quantity Price Demanded
3. Finding the optimal combination of two goods - $2. Suppose that Larry buys Larry enjoys consuming both cheese and fruit. Each pound of cheese costs Pc = $1, and each pound of fruit costs PF 300 pounds of cheese and 200 pounds of fruit per year. The following graphs show his marginal utility curves for cheese and fruit. At his current consumption level, Larry's marginal utility from consuming the last pound of cheese he bought is MUC S 30 utils per pound, and his marginal utility from consuming the last pound of fruit he bought is MUF = 30 utils per pound. 60 40 30 IL 20 10 400 500 600 50 40 A 30 B C D 20 10 0 0 100 Is Larry currently maximizing his utility? Combination 200 300 CHEESE (Pounds per year) 300, 30 (Pounds per Year) 200 400 300 No; he could buy less cheese and more fruit, not spend any more money, and be better off. O No; he likes fruit and cheese more than other goods, so he should buy more of both. O No; he could buy more cheese and less fruit, not spend any more money,…
1..Calculate the optimal quantity of each of two goods (x and y) and the consumers’ total utility given Px=1, Py=2, I=80, and U(x,y) = x1/2y. How would you represent this graphically? What is value of the utility received by consumer at optimal consumption? Explain all your steps. N.B. You can attach your explanations
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?