16. A consumer's utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A,B) = A!5 B45. The price of goods A and B are $5 and $10, respectively. The consumer has a budget of $300 that he can use to consume the two goods. a. Write down the budget constraint and plot it. b. Calculate the optimal bundle and maximized utility for the consumer. c. Price of good B increases by 20%. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the price increase?

16. A consumer's utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A,B) = A!5 B45. The price of goods A and B are $5 and $10, respectively. The consumer has a budget of $300 that he can use to consume the two goods. a. Write down the budget constraint and plot it. b. Calculate the optimal bundle and maximized utility for the consumer. c. Price of good B increases by 20%. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the price increase?

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

b. A consumer purchases two goods, the amounts of which are x and y. Her marginal utility of consuming good x is Ux , while that of consuming good ? is Uy. If the two marginal utility functions are given by Ux = y2 + 2xy and Uy = 4xy + 3x2 − 3 and the consumer is known to stay on the same utility curve, find the total utility function of this consumer buying the two goods
9. A consumer has the utility function u(x,y) = =x+6y and the price of x is $1 and the price of y is $5. If the consumer's income is $40, what bundle of goods will maximize her utility? x = 20, y = 4 x=40, y = 0 x = 0, y = 8 x= 10, y = 6 A a. b. c. d.
What happens to the original budget line if the price of good ? falls to 4$? (i.e., Will there be a change in the slope and/or intercepts of the original budget line? If yes, what are those changes?). Interpret economically how the change in the price of good ? affects the consumption decision of the consumer.
27. Mike spends all his income on films (F) and concerts (C). Films cost $10 and concertscost $30. Mike’s preferences can be described by the utility function: U = F C and hence themarginal utility of films is C and the marginal utility of concerts is F. Which of the followingbundle will Mike purchase? (Hint: You do not need to know income in $ amount. Answerthe question using the tangency condition.)(a) Mike purchases 30 concerts and 10 films a month.(b) Mike purchases 10 concerts and 30 films a month.(c) Mike purchases 20 concerts and 20 films a month.(d) Mike purchases 5 concerts and 10 films a month.
Question 3: Samantha has $3,000 to spend on two goods: sandwiches and beer. The price of a sandwich is $6 and price of a beer is $5. a) Draw Samantha's budget line. Put beer on the horizontal axis. b) If Samantha's optimal consumption bundle contains 400 sandwiches, how many beer does her optimal consumption bundle contain? Show her optimal consumption in the graph above. c) Draw Samantha's indifference curve crossing her optimal consumption bundle.
Need explanation
4. Suppose that a consumer with the utility function U =X0.25 Y0.75 choses a bundle where X=5 and Y=10. If the prices of the two goods are Px= $1, and Py = $3. Calculate marginal utility per dollar spent on each good. Can this consumer increase utility without increasing expenditure and if so how?
Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $1,000 and can buy apples at $10 per pound and kumquats at $10 per pounc utility function is U(a, k) = 4a + 3k. What is his marginal utility for apples and his marginal utility for kumquats? Andy's marginal utility for apples (MU) is MU, = and his marginal utility for kumquats (MU) is MU, = (Enter your responses as whole numbers.) What bundle of apples and kumquats should he purchase to maximize his utility? Andy should consume apples and kumquats. (Enter your responses as whole numbers.) React tv MacBook Air 80 DI DD F1 F2 F3 F5 F6 F7 F8 F9 F10 @ #3 $ % & 1 2 4 7 8. 9 Q W E Y { A S F G H. J C V M ption command command option .. .. V B
illustrate diagrammatically how the optimal choice of a consumer changes as a result of a decrease in the consumer’s income, when one of the two goods on offer is a normal good. To complete this activity you must have a clear understanding of how the optimal choice is determined, what happens to the budget constraint as the consumer’s income decreases, and the concept of a normal good.
Answer the question on the basis of the following marginal utility data for products X and Y. Assume that the prices of X and Y are $4 and $2 respectively and that the consumer's income is $18. Marginal Utility, Y Units of X Marginal Utility, X Units of Y 1 20 1 16 2 16 2 14 3 12 3 12 4 8 4 10 5 6 5 8 6 4 6 Refer to the data. What quantities of X and Y should be purchased to maximize utility? 2 of X and 1 of Y 2 of X and 5 of Y 4 of X and 5 of Y 2 of X and 6 of Y
A consumer has income of $15,000. Masks costs $35 per mask, and sanitizers costs $70 per bottle. solve questions 4 and 5 Draw the consumer’s budget constraint (put mask on the horizontal axis). What is the slope of this budget constraint? Suppose his income increases from $15,000 to $20,000. Illustrate what happens if both masks and sanitizers are normal goods. Illustrate what happens if a mask is an inferior good. The price of masks rises from $35 to $40 per mask, while the price of sanitizers is unchanged. For a consumer with constant income of $15,000, show what happens to consumption of both goods (assume both goods are normal goods). Decompose the change into income and substitution effects. Under what circumstance(s) if any can an increase in the price of sanitizers induce a consumer to buy more of that good? Explain. Explain how a consumer should allocate expenditure in order to achieve maximum satisfaction and analyse how a rise in income might affect that allocation.