Answered: The preferences of a consumer are… | bartleby

Microeconomics A Contemporary Intro

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 6QFR

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Question

The preferences of a consumer are represented by the following utility function:
U = min (×1, 2x2)
If income is 100 and p1=p2=1
a) What is the optimal bundle?
b) If p₁=4, what is the new optimal bundle?
c) If p2=4, what is the new optimal bundle?
d) Decompose the price effect into income and substitution effect and provide a graphical representation of your results.

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Consider the following utility function that expresses the preferences of any consumer for good x and good U(x, y) Min {2x, y) Consider that the price of x is $4, the price of y is $2, and the income R is $100. Reply: a) What is the marginal rate of substitution for x? b) What is the marginal rate of substitution for y? c) What is the expression of demand ( demand function) of x? d) What is the demand expression (demand function) for y? e) What is the basket composition that maximizes this consumer's satisfaction given the given restriction? f) What is the utility achieved with this basket?
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?]
The question is in the attached image. Thank you!
consumers view 100 quires of paper (each quire contains 25 sheets) and a bale of paper (each bale has 5,000 sheets) as perfect substitutes. Assume a quire and bale prices are $12 and $2,000, respectively, and consumer weekly budget is $4,000. Using a graphical analysis in a 2-dimensional commodity plane (i.e., draw indifference curves and a budget constraint), show how consumers identify an optimal bundle. Explain. Repeat the exercise in part (a), assuming a quire price is $6 (everything else is as before). Explain. Repeat the exercise in part (a), assuming a quire price is $25 (everything else is as before). Explain.
Problem 1 Consider the following utility function: U(x₁, x₂) = (x₁)²x₂. Task 1 : Suppose a consumer with the above utility function faces prices p₁ = 2 and P2 = 3 and he has an income m = 18. What's his optimal bundle to consume? Illustrate it in the commodity space with the budget line and the optimal bundle's indifference curve. * * Task 2: Suppose that you observe that this consumer chooses x = 1 and x2 = 4 but you cannot observe the prices, and you know that he is a utility maximizer with income m = 18. What can you infer about the prices he faces? If so, what are the prices?
a)Assume that the typical consumer always spends a small share of her overall budget on Vietnamese meals and use the utility maximization conditions to find the demand for Vietnamese food of the typical consumer (keep in mind that since utility is quasi-linear, you can find demand without information about the consumer’s weekly budget). b) Sum across consumers to find the weekly market demand for Vietnamese meals in NYC.
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A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizza
1.3. Consider the following utility function for a consumer who consumes two goods, x1 and X2, and answer the questions below: u(x1, x2) = In(x1)+ x2 (a) Calculate the marginal rate of substitution (MRS) for this utility function. (b) Does u(x) exhibit strictly monotonic preferences? Explain. (c) Is u(x) a homothetic function or not? Explain. (d) Is u(x) quasi-concave/quasi-convex/neither where x1 0? Provide support for your an- swer.
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 =…
Q: A consumer’s preferences for food (F) and clothing (C) are given by U(F,C) = F0.2C0.8. The price of food is $4, and the price of clothing is $8. The consumer has an income of $3600. a) What is the utility maximizing choice of food and clothing? b) How would the utility maximizing choice change if price of clothing increased to $14? c) Given the answers to the previous parts plot a linear approximation to the demand function for clothing.
Consider the following utility function. U=U(X,Y)=X0.2Y0.8 Find the marginal utilities. Determine their signs. Provide the economic interpretation of the signs of these marginal utilities. Determine whether the law of diminishing marginal utility holds for both goods.

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