Microeconomic Theory

12th Edition

ISBN: 9781337517942

Author: NICHOLSON

Publisher: Cengage

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Suppose a consumer has utility function U(X, Y) = X2/3Y1/3. Suppose the consumer has M =$90 to spend and the prices of goods X and Y are PX = $15 and PY = $6 .
a. Carefully express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint).
b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve.
c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the…

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1) Suppose that a person consumes two goods, x and y, in fixed proportions. He or she always consumes 1 unit of x together with 3 units of y no matter what the relative prices are.a) What is the mathematical form for this person's utility function?b) Calculate the Marshallian demand functions for both goods for this person.c) Calculate the indirect utility function and the expenditure function for this person.d) In class we discussed why expenditure functions are concave in prices. Is the expenditure function you calculated in part (c) concave in ???

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a. Suppose Fiona’s income is $100 per week, which she allocates between chocolates and books. Chocolates cost $2 each. Books cost $10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to $5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Fiona might have more than one utility-maximizing solution?
b. Confirm that if a consumer’s utility function is described by U = 2X + Y, and prices are px = 2 and py = 1, there is no unique utility maximizing solution regardless of income level. What does this tell you about X and Y as commodities? (Hint: draw a graph showing a budget constraint and indifference curve using the information provided.)

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Please can i get help with the illustrating the graphs?
An individual has a utility function, U(x, y) = x ∙ y, with a budget constraint, 120 = 2x + y.(a) Derive the individual’s optimal consumption for x and y, as well as the utility level associated with them. Graph the utility function and budget line. Indicate the point corresponding to your answer.(b) Evaluate the price effect when the budget constraint changes to 120 = 4x + y, specifying the income and substitution effect. Illustrate these on the graph indicating the points corresponding to your answer.(c) Based on (b), what type of goods are x and y?

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EXERCISE 5
Loise spends £20 on tea (T) and coffee (C). Her preferences for these goods can be described by the following utility function: ( , ). Suppose that one cup of tea costs £1.60 while one cup of Loise’s favourite coffee costs £4.00.
Find Loise’s optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning.
Discuss how Loise’s optimal consumption choice would change when her disposable budget changes.
If the price of tea increases to £2.00 per cup, how should the price of coffee change so that Loise can be as well off as before this change in prices?
Discuss the implications of the price change from c) on Loise’s optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Loise’s demand for tea and/or coffee.

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Answer the question on the basis of the following two schedules, which show the amounts of additional satisfaction (marginal utility) that a consumer would get from successive quantities of products J and K.
Units of J
MUj
Units of K
MUk
1
56
1
32
2
48
2
28
3
32
3
24
4
24
4
20
5
20
5
12
6
16
6
10
7
12
7
8
If the consumer has money income of $52 and the prices of J and K are $8 and $4 respectively, the consumer will maximize her utility by purchasing
Multiple Choice
3 units of J and 7 units of K.
5 units of J and 5 units of K.
4 units of J and 5 units of K.
6 units of J and 3 units of K.

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Utility maximization under constraint Lucas gets utility (satisfaction) from two goods, A and B, according to the utility functionU(C, D) = 25[C−3 +4D−3]−4 +25. While Lucas would like to consume as much as possiblehe is limited by his income. Maximize Lucas’ utility subject to the budget constraint usingthe Lagrangean method.

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Answer the question on the basis of the following two schedules, which show the amounts of additional satisfaction (marginal utility) that a consumer would get from successive quantities of products J and K. Units of J MUj Units of K MUk 1 56 1 32 2 48 2 28 3 32 3 24 4 24 4 20 5 20 5 12 6 16 6 10 7 12 7 8 What level of total utility is realized from the equilibrium combination of J and K, if the consumer has a money income of $28 and the prices of J and K are $8 and $4, respectively?
Multiple Choice
a. 172 utils
b. 168 utils
c. 188 utils
d. 72 utils
Note:-
Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism.
Answer completely.
You will get up vote for sure.

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Question 3Draw indifference curves for the following sets of preferences and indicate the direction inwhich the individuals’ satisfaction (or utility) is increasing. Be specific about slopes when itis necessary. Assume for both parts (a) & (b) that soft drinks are measured on x-axis andhamburgers on the y-axis. (a) Mary always gets twice as much satisfaction from an extra hamburger as she does froman extra soft drink. (b) Bob loves soft drinks but dislikes hamburgers.

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No written by hand solution
Assume Fred has the following preference relation on [0, 1]: x ≿ y if and only if x ≤ y for all x ̸= 1 and y ̸= 1; and 1 ≻ z for all z ∈ (0, 1), 1 ∼ 1 and 0 ≻ 1. Does there exists a utility representation for this preference relation? If yes, provide a utility function. If no, explain. Show your work.

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7
which following statement is true or flase with explaination
1. for a cobb douglas utility function, the slope of its income offer curve is constant while the slope of its price offer curve is not .
2. monotonic transformation of a utility function is possible because utility itself ordinal.

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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.

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