16. Linda consumes two goods: x and y, has preferences that are smooth(utility maximi zation is characterized by the tangency rule), andincome Y=$150.If px $25 and py $5, what is the marginal rate ofsubstitution for Linda at her optimal bundle?5 x5y150+a. -1/2b. 1/5C. -3d. 7/2e. 5

Marginal rate of Substitution: In economics, the marginal rate of substitution states the point at…

Answered: 16. Linda consumes two goods: x and y,…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
You are choosing between two goods, X and Y, and your marginal utility from each is shown in the following table. Units of X MUX Units of Y MU 1 20 16 14 16 3. 12 3. 12 4 8. 4. 10 6. 4. 8. 6. 6. Instructions: Enter your answers as a whole number. 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? units of X and units of Y b. What total utility will you realize? utils
4. John has a utility for the quantity of sandwiches, Xs, and quantity of burgers, Xp, that he consumes, represented by the following equation: U(X,X) = XX His income is Y = $24. The price of a sandwich changes from X, = $1 to X, = $4 while the price of a burger remains at X, = $6. Solve for the compensating variation and equivalent variation associated with this price increase.
10. Assume an individual's preferences are represented by the following indifference map and he has an income of S400. Which of the following is shown when the price of Good I is $20 and the price of Good 2 increases from $10 to S16? Note: Even though the price of Good 2 is increasing, the steps to determine the income and substitution effects are the same. 50 45 40 35 30 25 20 15 10 10 15 20 25 30 35 40 45 50 Good 1 Good 2 is a normal good. Good 2 is an inferior good, but not a Giffen good. Good 2 does not satisfy the Law of Demand. • Ignoring the Income Effect, the Substitution Effect will cause the individual to consume more of Good I. A. B. 21 C. 3 None of the above statements are true. D. Good 2
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.
2. Anne's preference can be represented by the following utility function: U(x, y) = x® y". a) Find the optimal bundle for Anne that minimizes her expenditure. b) Write down the expenditure function. c) In a graph, show how her optimal bundle would change if the price of x increases (assume price of y remains the same).
II. Your preferences are represented by the utility function U(x₁, x₂) = (x² − x²)0.5 for x₁ > 0, x₂ > 0, and x² > x².
13. Sylvester has an income of $110 that he spends on two goods: X and Y. The price of a unit of Y is $5. The price of a unit of X is $14 for the first four units, but after the fourth unit the price of a unit of X is $9. Sylvester's utility function is U-3X+Y. Sylvester's level of utility when he consumes his optimal consumption basket is utils.
8. Fabian consumes X and Y and the following utility function represents his utility: U = 2XY a. With a utility function of U = 2XY, Fabian's MU, = 2Y and his MU, = 2x ,where MU is marginal utility. Write an equation for Fabian's marginal rate of substitution (MRS). b. Suppose Fabian's income is $120 and Px = S6 and Py-$2, where Px is the price of X and Py is the price of Y. Write an equation for Fabian's budget constraint. c. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve: d. If Fabian is spending all of his income, how much X and how much Y will he choose? Use the equations you wrote in part's b and c to answer this question. e. What will Fabian's utility be with this combination of X and Y? f. Now suppose the price of X increases to P.=10. Write the equation that equates the slope of Fabian's budget constraint to the slope of Fabian's indifference curve. How will this change the optimal combination of X and Y? What…
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?
Bob views apples and oranges as perfect substitutes in his consumption, and MRS = 1 for all combinations of the two goods in his indifference map. Suppose the price of apples is €2 per pound, the price of oranges is €3 per pound, and Bob's budget is $24 per week. What is Bob's utility maximizing choice between these two goods? A. 12 pounds of apples and no oranges B. 8 pounds of oranges and no apples C. 4 pounds of oranges and 6 pounds of apples D. 12 pounds of oranges and no apples Fiona uses her entire budget to purchase food and clothing. The price of food is €1 per unit and the price of clothing is €2 per unit. Fiona's marginal utility from food is 2 and her marginal utility from clothing is 6. She currently spends all her money on food and clothing. Her objective is to maximise her utility. Which of the following statements is correct? Fiona should buy more food and more clothing. A. B. C. D. E. Fiona is currently maximsing her utility and should continue to consume her current…
2 3 1. The consumer has Cobb-Douglas preferences for two goods x and y: u(x, y) = 10x¾yš Py> 0 and m > 0 is given. a) Set up the Expenditure Minimization Problem. b) Calculate MU and MUy. Ꮖ 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) ii) Px > 0, e) Solve for the compensated demand functions for good x and y.

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16. Linda consumes two goods: x and y, has preferences that are smooth (utility maximi zation is characterized by the tangency rule), and income Y=$150. If px $25 and py $5, what is the marginal rate of substitution for Linda at her optimal bundle? 5 x 5y 150 + a. -1/2 b. 1/5 C. -3 d. 7/2 e. 5