Use the following information to solve the next two questions: Suzette's preferences for x1 and x2 areconsistent with the utility function U(x1,X2) = Vx1 + x2. She can purchase good 1 for $2 each and good 2 for$32 each. She has $160 to spend on the two goods.(4) What is the marginal rate of substitution at the point (4, 4)? Find the absolute value.(a) 1/8(b) 1/4(c) 1/2(d) 1(e) None of the above(5) How many units of good 2 will she purchase to maximize her utility?(a) 1(b) 2(c) 3(d) 4(e) None of the above

The indifference curve of the consumer shows all the combinations of two goods that give an…

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Christin has a monthly income of $500 that he allocates between two goods: food and clothing. Suppose food costs $8 per pound and clothing cost $5 per piece. a) Draw her budget constraint properly labelling the axes. 0.5 b) Suppose also that her utility function is given by ?( f,c)= 2f ^2 + c^2 . What combination of food and clothing does she buy in order to maximize her utility? Show your work mathematically. Round your answer to two (2) decimal points.
1. Consider a consumer who consumes two goods. The utility function is given by u(x1, x₂) /2x1+1+√√√x₂, - where x > 0 denotes the amount of good i = the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. 1,2 consumed. Unless stated otherwise, (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x₁, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its derivative with respect to p2, i.e., v'(P2), at p2 = 3. (4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demand for each good.
Julie, who has $64, consumes only two goods: whistles (w), which cost $6 each and xylophones (x), which cost $7 each. Her preferences over these two goods can be represented by the utility function u(w, x) = 3w0.75 0.25 a) What is the optimal number of whistles for Julie to consume given this scenario? b) What is the level of utility Julie attains at this level of consumption? c) Suppose now that the price of whistles rises from $6 to $7. What is the magnitude of this price effect on whistles?
b) As in question 2a, A consumer has a utility function given by U = x°.25 y0.75 and has an income of £100, the price of good x is £5 and the price of good y is £10. Suppose the price of good y falls from £10 to £5. By how much does the demand for good y fall and how much of the resulting change in demand for good y is due to the substitution effect and how much is due to the income effect? Take a picture of your diagrams and upload with your answer
Consider the following utility function: U= 100x0.50,0.50 A consumer faces prices of P, = $2 and P, =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X and 11 units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y O étv MacBook Air 80 esc F1 F2 F3 F4 F5 F6 F7 F8 # $ % & 1 2 7 Q W E T Y tab S D F G caps lock C V M ft control option command つつエ B N
Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices…
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Please tell me which of the multiple choices in question 1.6)1.7)1.8) are correct.State only the correct ones please. 1.6) The marginal rate of substitution (MRS) can be defined as: Select one or more: a. The amount of one good that the consumer is willing to trade for one unit of the other. b. The ratio of the amounts of two goods. c. The change in the consumer’s utility when one good is substituted for another. d. The absolute value of the slope of the indifference curve. 1.7) (SEE ATTACHED PICTURE) The diagram shows that: Select one or more: a. If Angela works 24 hours a day she can still survive. b. There is a technically feasible allocation where Angela does not work. c. A new technology that produced more grain would give a larger technically feasible set. d. If Angela needed less grain to survive the technically feasible set would be smaller.
Consider the following utility function: U = 100x.50,0.50 A consumer faces prices of P, = $2 and Py =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X an units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y 15 tv MacBook Air 80 esc DII F1 F2 F3 F4 F5 F6 F7 F8 @ #3 % 2 7 8. Q W E Y tab s lock A S F G H J Z C V N M Onteel 8 : < CO T D
The goods in the next question are not ale and bread. To solve this question, you are going to have to evaluate the condition The price p is defined for you, but you will have to define the marginal rate of substitution for yourself. What ratio of marginal utilities should you use? You will know the answer to this question once you have defined the marginal rate of substitution – that is, decided which good is being given up and which good is being given in compensation. When making this decision, remember that both sides of this equation refer to the same kind of trade. The right-hand side describes the rate at which one good can be traded for the other in the marketplace; and the left-hand side describes the rate at which someone is willing to trade that good for the other. Thus, the definition of the price determines the manner in which the marginal rate of substitution must be defined. Pierre lives on red wine and blue cheese. His utility function is. where w is his…
John has $300 as income and he uses his income only for apples and bananas. If he uses his income only for apples, he can buy 10 pounds. If he uses his income only for bananas, he can buy 15 pounds. Which one is the correct formula for his budget constraint when X=pounds of apples, Y=pounds of bananas and the prices are per pound? a) More information is needed to answer the question. b) 15X + 10Y = 300 c) 10X + 15Y = 300 d) 20X + 30Y = 300 e) 30X + 20Y = 300
4. Assume Megan has preferences represented by utility function U (x₁, x2) = (x₁)¹/4 (x2)³/4 Good 1 is electricity (1) while good 2 is gasoline (x2). Suppose the consumer has an income level of m= 1000 dollars. In addition, the price of good 1 is p₁ = 5 and the price of good 2 is p2 = 5. (a) Compute the Marginal Rate of Substitution (MRS). (b) Find the optimal levels of electricity (x) and gasoline (x2) consumption for Megan. (c) Suppose the government imposes a per-unit tax of t = 5 dollars on gasoline. Find the optimal levels of electricity (x) and gasoline (x2) consumption for Megan with the tax.

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