# Mary has utility over Goods 1 and 2 given by U(x1, x2) = x12x2. What is the value of MRS(2, 3)?

## Question:

Mary has utility over Goods 1 and 2 given by U(x1, x2) = x12x2. What is the value of MRS(2, 3)?

## Marginal Rate of Substitution ( MRS )

The absolute value of the slope of indifference curve, that is {eq}-\frac{x1}{x2} {/eq} is the MRS between x1 and x2. So {eq}\frac{x1}{x2} {/eq} is the MRS. This indicates the amount of x2 that is to be sacrificed in order to enjoy one extra unit of x1.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

View this answerU(x1, x2) = x12x2.

Differentiating the utility function,

=> dU = x1 d( 2x2) + 2x2 dx1

=> 0 = 2x1 dx2 + 2x2 dx1

=> 0 = x1 dx2 + x2 dx1

=&...

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

Chapter 3 / Lesson 51Learn how to calculate the marginal rate of substitution and its application in economics. View examples of the formula in use with real world application.

#### Related to this Question

- Suppose Vanessa has a utility function U(X,Y) = X^0.2 Y^0.8 , which X and Y are two goods. The prices for X and Y are $8 and $2, respectively. She has $200 in her pocket. (1) Please explain why Vanes
- There are two goods in the world, x and y. William's utility function is u(x,y) = min(x,y) and Mary's utility function is v(x,y) = x+y. If a tax is imposed on good x, how does William's utility chan
- Mary's preferences can be represented by the following utility function: u(X,Y) = min{3X,7Y} The price of good X is Px= 3 and the price of good Y is Py=7. If Mary has $84 to spend, she will buy_____
- Jane's utility function on bundles of two commotities (x,y) is given by: U(x,y)=4x^2y^3. What is the value of MRSxy(x,y) when x=2 and y=1? 1/3 3 1/6 2/3 7/3
- Do public goods come under the umbrella of merit goods?
- Consider Mary's utility function U = 10C^{0.5}T^{0.5} , where C is the quantity of coffee and T is the quantity of tea Mary consumes. For each additional coffee Mary consumes, she receives additional utility equal to 5C^{-0.5}T^{0.5} and for each addition
- Suppose Mary's utility function for Wegman's ice cream (W) and Top?s ice cream (T) is U = W + T. Wegman's ice cream costs $5 each and Top?s ice cream costs $4. Mary has $100 income. Find Mary's opti
- Jared has utility over Goods 1 and 2 given by u(x1, x2) = min{x1, x2} where x1 and x2 are the quantities of Goods 1 and 2 Jared consumes (respectively). If Bundle A = (4, 4), Bundle B = (4, 16), which
- Say Anna's utility function was given by UA=(MA)(MM), where MA is Anna's wealth and MM is Marie's wealth. Initially, Anna has 160 units of wealth and Marie has 40. In order to maximize her utility Anna should: a. Transfer all her wealth to Marie, b. Trans
- Kelly's preferences over goods X and Y can be represented by the following utility function: U(X,Y) = X^0.75 Y^0.25 Given prices and income, Kelly optimally chooses to consume X* = 3 and Y* = 2. There
- A big concern with trying to measure utility is that a. each individual has a unique personal scale for his or her utility measures. b. to measure utility, you need monetary values of the goods and
- Assume that a person's utility over two goods is given by: U(x,y) = x^(alpha)y^(1 - alpha). The price of Good X is p_x and the price of Good Y is p_y. The total income of the individual is given by M.
- Maureen has preferences for two goods to be consistent with the utility function. The price of good 1 is $4 each, and the price of good 2 is $12 each. For what incomes will good 1 be normal?
- From a utility function (e.g., U = 2X + 3Y or U = X0.5Y0.5), which of the following may be determined? i. The utility derived from all bundles of goods and services. ii. The bundles of goods and ser
- You have two goods, X & Y, and two consumers named Aaron (a) and Bill (b). Suppose their utility functions are Ua(X,Y) = min{X,Y} and Ub(X,Y) = min{2X,Y}, respectively. Total Endowments of goods X
- The Utility that Amy receives by consuming food F and clothing C is given by U (F,C) = C+F. Marginal utilities of food and clothing are respectively MU f = C + 1 and MU c = F. Food costs $1 a unit and
- Suppose Jane has chosen a combination of two goods, A and B, such that MU/P of good A is 10 (MUA/PA = 10), and the MU/P of good B is 10 (MUB/PB = 10). To increase utility with the same amount of money
- In the use of contingent valuation under cost-benefit analysis: A.people's travel costs determine the value of a public good. B.the value of similar market-traded goods estimates the value of a publ
- Can utility be measured as the price you're willing to pay divided by your total wealth?
- Pierre has the utility function U(F, C) = 10FC, and Marie has the utility function V(F, C) = 20F^2 C^2, where F and C represent the quantities of food and clothing. A) What is the set of market basket
- Mary purchased a stuffed toy animal for $5. After about a week, someone offered her $100 for the toy. Mary refused. One can conclude that Mary's consumer surplus from the toy is: a) less than $5. b) at least $95. c) at least $100. d) $105.
- If the utility function is: U=99x_1 + 78x_2 and considering the following bundles: A=(64,46) B=(58,17) C=(80,83) D=(48,21) E=(97,65) How much utility does the consumer get from bundle A?
- The utility that Ann receives by consuming food F and clothing C is given by U(F,C)= FC + F. Food costs $1 a unit, and clothing costs $2 a unit. Ann?s income is $22. Ann is currently spending all of
- Chris has a utility function U(F,C) = 10FC , and Joe has the utility function V(F,C) = 20F^2C^2 , where F and C represent the quantities of food and clothing? a) What is the set of market baskets tha
- Ella s utility function is min{5x, y}. If the price of x is $10 and the price of y is $15, how much money would she need to be able to purchase a bundle that she likes as well as the bundle (x, y) = (10, 25)? A) $209 B) $440 C) $425 D) $475 E) $85
- Given the following Utility function for two goods, "x" & "y:
- Consider the endowment economy. There are 2 goods, apples (A) and bananas (B). The price of apples (bananas) is P_A (P_B). Preferences are represented by the utility function U(D_A,D_B) = D_A^{\frac{1
- Sally the Sleek's preferences can be described by the utility function U(x, y)={x^2y^3}/{1000}. Prices are p_x=4 and P_y=3; she has an income of $80 to spend. (a) If Sally initially consumed 5 units o
- The consumer is choosing between two goods- good1 and good2. Good 1 is priced at $2 and good 2 is priced at $3. The consumer has a total of $600 to spend on both the goods. Let the utility function of the consumer be U (X1, X2) = Min (X1,X2) a) Calculat
- Consider a rational utility maximizing consumer who is choosing between two goods clothing (C) and food (F), where the total utilities of the two goods are independent so that total utility (U) = Util
- Mary owns holds property in fee simple. Mary would like to lease the property to Jack, who wants to farm the land. Because Mary holds the property in fee simple, she: a. cannot buy or sell the land,
- Mary spends all her budget on statistical software (S) and office supplies (O). Her preferences can be represented by the utility function: U(S, O) = 2 ln(S) + 3 ln(O). Find Mary?s demand functions for software and office supplies, QS(pS, pO, I) and QO(pS
- Is going to art school rational because the expected utility of art is greater than the expected utility of intransitive goods and services offered by the market at any given time?
- Mary invested $100,000 in a hardware store. Business has been good, and the store shows an accounting profit of $10,000 for the last year. This profit is after taxes and after payment of a $25,000 salary to Mary. This salary is less than the $40,000 she c
- a.Tom spends all his $100 weekly income on two goods, X and Y. His utility function is given by U(X, Y) = X^2Y^2. If PX= 4 and PY=10, how much of each good should he buy? b.Same as part a, except no
- If the utility function is: U=121x1 + 155x2 and considering the following bundles: A=(138,119) B=(108,157) C=(169,111) D=(111,194) E=(116,186) How much utility does the consumer get from bundle C
- A medium of exchange is a. anything that is generally accepted in exchange for goods and services. b. a common measurement in which relative values are expressed. c. an item's ability to hold value
- John has a risk asset worth Y and derives utility from the consumption of his wealth. His Utility function is: U(Y) = ln(Y) There is the probJohn has a risk asset worth Y and derives utility from the
- Mary's salary increased from $36,000 last year to $38,000 this year. If the economy experienced 4 percent inflation over the last year, has Mary's purchasing power increased along with her salary? Calculate the real value of Mary's current salary in terms
- Mary's salary increased from $36000 last year to $38000 this year. If the economy experienced 4 percent inflation over the last year, has Mary's purchasing power increased along with her salary? Calculate the real value of Mary's current salary in terms o
- Jim's utility from leisure and consumption of all-other-goods (Y) is U=30 L0.5Y0.5, so that the marginal utility of leisure is MUL=15L-0.5Y0.5 and the marginal utility of all-other-goods is MUY=15L0.5
- Opportunity cost is the alternative that must be sacrificed in order to get something else. a. lowest-valued b. middle-valued c. highest-valued d. median-valued
- List five sets of two goods each (i.e., each set is composed of two goods; for example, diamonds and water make up one set) such that the good with the greater value in use has a lower value in exchange than does the good with the lower value in use.
- Donna and Jim are two consumers purchasing strawberries and chocolate. Jim's utility function is U(x, y) = xy and Donna's utility function is U(x, y) = x^2y, where x is strawberries and y is chocolate. Jim's marginal utility functions are MU_x = y and MU_
- Suppose that Angie's MUx=Y^2 and MUy=2XY. The price of good X is $ 10 and the price of good Y is $ 2. If Angie is consuming 8 units of good X and 16 units of good Y, is she maximizing utility?
- What objects have value in and of themselves and are also used as money?
- Andy purchases only two goods, apples (q1) and kumquats (q2). He has an income of $40 and can buy apples at $2 per pound and kumquats at $4 per pound. His utility function is U(q1,q2) = 3(q1) + 5(q2). What is his marginal utility for apples and what is hi
- Andy purchases only 2 goods, apples (q_1) and kumquats (q_2). He has an income of $40 and can buy apples $2 per pound and kumquats at $4 per pound. His utility function is U(q_1, q_2) = 3q_1 + 5q_2. What is his marginal utility for apples and what is his
- Contingent valuation is used to estimate the a. perceived valuation or existence value of environmental goods. b. cost of the closest alternative program for achieving the public goal. c. value of
- A consumer has preferences for two goods, 1 and 2, which can be represented with the utility function u(x_1, x_2) = 4x_1 + 3x_2. A. If a consumer has a budget of 20 AZN while prices of goods 1 and 2 are 2 AZN and 4 AZN, respectively, calculate the bundle
- By selecting a bundle of good X and good Y where MRS = MRT, the consumer is saying A) I value my last unit of each good equally. B) I will equate the amounts spent on all goods consumed. C) I am willing to trade one good for the other at the same rat
- A consumer has preferences between two goods, hamburgers (measured by H) and milkshakes (measured by M). His preferences over the two goods are represented by the utility function U = sqrt(H) + sqrt(M
- Donna and Jim are two consumers purchasing strawberries and chocolate. Jim's utility function is U ( x , y ) = x y and Donna's utility function is U ( x , y ) = x 2 y where x is strawberries and y is chocolate. Jim's marginal utility functions are
- Laura's total utility from consuming 8, 9, and 10 Hershey's chocolate kisses is 35, 42, and 45, respectively. What is her marginal utility from the 9th kiss?
- The consumer is choosing between two goods: good 1 and good 2. Good 1 is priced at $2 and good 2 is priced at $3. The consumer has a total of $600 to spend on both the goods. 1. Let the utility function of the consumer be U (X1, X2) = X1(1/2)X2(1/2). a)
- Jack and Phil both like apples and oranges. Jack's preferences over these two goods are represented by the utility function U(x_a, x_o) = log(x_a) + log(x_o), where x_a is the number of apples consumed and x_o is the number of oranges consumed. Phil's pre
- The salary John's grandfather earned in 1962 is a a. purchasing power parity adjusted value. b. cost of living adjusted value. c. real value. d. nominal value
- Once again you've impressed your parents and because of your marks you have convinced them that your happiness as expressed by your utility function should be 125,000 utils. What income is required for you to achieve this utility when your utility functio
- Alessandro purchases two goods, X and Y, and the utility gained for the last unit purchased of each is 16 utils and 23 utils, respectively. The prices of X and Y are $1 and $1.75, respectively. Is Alessandro in consumer equilibrium? Explain your answer.
- Suppose Mary?s income is $100 per week, which she allocates between sandwiches and books. Sandwiches cost $2 each. Books cost $10 each if she purchases between 1 and 5 books. If she purchases more tha
- John's marginal utility for consuming muffins and doughnuts in utils are as follows. If he spends $4 for breakfast every morning, the price per muffin is $100 and the price per doughnut is $0.50.
- Sally the Sleek's preferences can be described by the utility function U(x, y) = x^3y^2/1024. Prices are P_x = 2 and P_y = 4. (a) If Sally initially consumed 10 units of : and 5 units of y, how much
- An essential characteristic of a public good is that it is non-excludable. This means that A. public goods are of equal benefit to all consumers. B. there is no opportunity cost in the provision of public goods. C. people could consume the good without pa
- If the ulitity function is: U=19x1 + 23x2 and considering the following bundles: A=(97,44) B=(28,44) C=(40,63) D=(6,69) E=(9,97) How much utility does the consumer get from bundle E?
- Can public goods be treated as commercial commodities and still be nonrivalrous and nonexcludable?
- Julie has preferences for food, f, and clothing, c, described by a Cobb-Douglas utility function u(f, c) = f c. Her marginal utilities are MUf = c and MUc = f. Suppose that food costs $1 a unit and that clothing costs $2 a unit. Julie has $12 to spend on
- Deborah spends all of her money on comic books and donuts. In 2012, she earned $27.00 per hour, the price of a comic book was $9.00, and the price of a donut was $3.00. Which of the following give the nominal value of a variable? Choose all that apply. A)
- Jane's utility function has the following form: U(x,y) = x^2 + 2xy. The prices of x and y are p(sub-x) and p(sub-y) respectively. Jane's income is I. a) Find the Marshallian demands for x and y a
- For each utility function, find the preferred bundle between X = (4 cloths, 3 pens) and Y = (5 cloths, 10 pens). i. U(x_1, x_2) = x_1 + x_2 ii. U(x_1, x_2) = x_1x_2
- When Kelly Ziegenfuss buys five units of a particular good or service, __________. a) she has no consumer surplus b) she has a consumer surplus c) there is no way of knowing whether she has a consumer surplus
- The utility function and the prices are the following: U = 80 x(1) + 31 x(2) P1=4, P2=63 and I =3,273 What is the MRS?
- Consider an economy with apples and oranges. Dustin's endowment of two commodities is given by omega{K}=(8,2) and Kate's endowment is omega{K}=(2,8) The utility functions of Dustin and Kate are the s
- Arther has preferences over amounts of commodities 1 and 2 represented by the utility function u(x_1, x_2) = sqrt{x_1} + sqrt{x_2}, where x_1 denotes how much commodity 1 he has and x_2 denotes how much of commodity 2 he has. A. Show that Arthur's prefere
- In Ozland, the price of milk is 2/L, and the price of water is 7/L. Ozland is famous for equality because every resident in Ozland has a wealth of $11. Chelsea has the utility function u(x1,x2) = x1
- A consumer has the utility function U(x1, x2) = x1x2 and an income of 24 pounds. Initially, the price of good 1 was 1 pound and price of good 2 was 2 pounds. Then the price of good 2 rose to 3 pounds while price of good 1 stayed the same. Find the consume
- Jim's utility function is u(x_1, x_2) = x_1x_2. Jerry's utility function is u(x_1, x_2) = 1000x_1x_2 + 2000. Tammy's utility function is u(x_1, x_2) = x_1x_2(1 - x_1x_2). Oral's utility function is u(x_1, x_2) = -\frac{1}{10 + 2x_1x_2}. Marjoe's utility f
- Sev and Mary have the following valuations for a set of goods. Sev and Mary are given the following baskets of goods: Sev gets 2 bubble gum, 0 chainsaws, 1 Volvo, and 4 Snickers bars. Mary gets 4 bubble gum, 2 chainsaws, 5 Volvos, and 1 Snickers bar. Prop
- If a consumer receives 18 units of utility from consuming two donuts and 24 units of utility from consuming three donuts, what is the marginal utility of the third donut?
- Are all goods that are provided by the government, ?public goods?? Name one that is a public good and three that are not.
- Using a two good (Apples, Oranges), two person (Ed, Mary) economy, suppose that at a given allocation, Ed's MRS(AO) is 3 and Mary's MRS(AO) is 1.
- Julio receives utility from consuming food (F) and clothing (C) as given by the utility function U(F,C) = FC. The price of food is $5 per unit, the price of clothing is $7 per unit, and Julio's weekly
- Julie has preferences for food, f , and clothing, c , described by a Cobb-Douglas utility function u ( f, c ) = f \cdot c . Her marginal utilities are M U f = c and M U c = f . Suppose that food costs
- What is the opportunity cost of buying a new car? A. The value of other goods and services you could have purchased with the money you spent on the car. B. The price you paid for the car. C. The cost of operating and maintaining the car. D. The differ
- Please only do part b. a) A consumer has utility give by U(x,y)= \sqrt {xy} subject to the budget constraint 100=4x+y. Find the bundle that maximizes utility. b) Suppose the original utility is not wr
- Leonid consumes bundles of food and transportation. His utility from bundle (10,10) has a value of 4. If for Leonid more is better, then among the following options, which can be the value of utility of bundle (20,20)? a. 3 b. 2 c. 1000 d. 1 e. 0
- The paradox of value notes that: a) The price obtained from selling any commodity may bear little relationship to the cost of producing it. b) There is no rational explanation why people should set a high value on objects such as diamonds, which have litt
- Sev and Mary have the following valuations for a set of goods. Sev and Mary are given the following baskets of goods: Sev gets 2 bubble gum, 0 chainsaws, 1 Volvo, and 4 Snickers bars. Mary gets 4 bubble gum, 2 chainsaws, 5 Volvos, and 1 Snickers bar. Wha
- Suppose Jimmy and Rita are in an exchange economy. Their endowments: apples and oranges. Suppose further that both Jimmy and Rita's utility functions are concave in the two goods. Draw an Edgeworth bo
- Goods that are nonrival in consumption and that have benefits that are nonexcludable are _____. A. private goods B. neighbor effects C. public goods D. none of the above
- A consumer's budget is M=300, which she spends on buying two goods, X and Y. Her utility from consuming x units of good X and y units of good Y is given by the following Cobb-Douglas utility function
- Hanna consumes only edamame and kale. Her utility function over these two goods is given by: U(x_1,x_2) = 3x_1 + 2x_2. A) If her income is $30 and p_1 = p_2 = 3, how much of each good will she consume
- (30) Consider the following utility function, which specifies Carina's preferences over two goods, donuts (D) and brownies (B). (Please note that we call this type of utility function quasi-linear.) U
- The utility function for Morris is U = min\{4M, T\}, where M is pints of milk and T is cans of tuna. Morris has $90 to spend on tuna (priced at $2 per can) and milk (priced at $1 per pint). What is Morris's utility-maximizing consumption bundle?
- Danny is a utility-maximizing farmer with a utility function of U=I(.5), where I is income. If weather is good, he will earn $100,000. If there is a hailstorm, he will earn only $50,000. The probabili
- Rob has the utility function of U (x_1, x_2) = x_1(x_2 + 1). 1) Rob's utility function is quasiconcave. What does the mean for Rob's preferences? 2) The price of Good 1 is 2 and the price of Good 2 is
- Question: Janet's utility function is u(x1,x2)=min(4x1,x2) if the price of good 1 is $2, the price of good 2 is $3 and Janet's income is $28, what is the optimal consumption bundle for Janet?
- We do not need to actually measure the level of satisfaction derived by a consumer from the consumption of goods. we only need a ranking among the alternative bundles. Thus utility is what kind of con
- If a consumer receives 20 units of utility from consuming two candy bars and 25 units of utility from consuming three candy bars, the marginal utility of the second candy bar is: A. 25 utility units B. 20 utility units C. 5 utility units D. unknown as mor
- Electric generating and transmission equipment is placed in service at a cost of $2,975,000. It is expected to last 30 years with a salvage value of $250,000. 1. What is the MACRS-GDS property class?
- A consumer's utility is given by U(X,Y)=X^0.25*Y^0.75. (To be clear, ^ denotes exponentiation, so the utility function is X to the 0.25 power multiplied by Y to the 0.75 power.) Given this utility fun