Consider the following utility function: ху U(x,y): х — у (a) Derive the MRS of x to y. Show your work. (b) Is this function quasi-concave? [Hint. You need to check the conditions for quasi-concavity].
Q: Consider the following utility function: U=100X^0.75 Y^0.10. A consumer faces prices of Px = $5 and…
A: Given, U=100x0.85y0.10
Q: Suppose a consumer’s preferences over two goods x1 and x2 are given by u = root(x_1 x_2). Her…
A: Answer: Given, Utility function: u=x1x2 Price of good 1 = p1 Price of good 2 = p2 Income = M The…
Q: An individual preference scale for two goods x and y is defined by the marginal rate of substitution…
A: Utility functions define the level of satisfaction or welfare of consumer with the given level of…
Q: Suppose that the following a quasi-linear utility function is given U(X,Y) = U(X,)=-x-²-y-,Find…
A: We are going to solve above question using Marginal Rate of Substitution formula.
Q: Walt has utility function u = x + y. He has an income of $240. If the price of good x changes from…
A: The given utility function is of perfect substitutes and in this type of utility function consumer…
Q: Suppose Pizza (P) and Hamburgers (H) are perfect substitutes to Kate. Two slices of Pizza always…
A: Given Pizza (P) and Hamburgers (H) are perfect substitute and utility from 2 slices of Pizza =…
Q: The marginal rate of substitution (MRS) is not dependent on the transformation of a particular…
A: Answer: True, Explanation: A monotonic transformation of a particular utility function does not…
Q: Which of the following utility functions represent preferences which do not satisfy monotonicity? U=…
A: Monotonic preferences refer to such consumer preferences towards the greater consumption of goods…
Q: The following statement is true for consumer preferences: a) The axiom of weak monotonicity implies…
A: Consumer preference: It refers to the items that a consumer wants to buy. The change in consumer…
Q: indifference curve at utility level equal to 20 is?
A: Utility means the satisfaction that a consumer gains from consuming a product or service. Utility…
Q: For the utility u(x1, 2) = xf + x verify the Slutsky equation
A: Utility function : U(x1 , x2 ) = x11/3 + x21/3 Let the prices be p1 & p2 Income be (m) Budget…
Q: Calculate the MRS for the following utility function U (x1, X2) = 2x + x; + e³x1 (in text mode, the…
A: Utility function : U(x1 , x2 ) = 2x12 + x22 + e3x1 Marginal Rate of substitution refers to the rate…
Q: Suppose that the consumer has a utility function u(a, b) = min (2a, b). The price of both goods is…
A: Recall that the utility function of the form u(a, b) = min(2a, b) represents goods which are perfect…
Q: Assume a consumer with the utility function U(X,Y)=X²Y² and the typical budget constraint M= PxX+…
A: Given Consumer's utility function: U(X,Y)=X²Y² Consumer's budget line: M= PxX+ PyY
Q: For the utility function U(X,Y)= 6X0.50.5, the marginal rate of substitution MRSxy is: O Y/X. O X/Y.…
A: Given:- Utility function, U(X,Y)=6X0.5Y0.5 To calculate:- MRSxy=?
Q: Jane receives utility from days spent traveling on vacation domestically (D) and days spent…
A: Given; Utility function; U(D, F)=10DFPrice of a day spent traveling domestically=$100Price of…
Q: Mary has the utility function u(x, y) = Inx + x^2. Are her preferences strongly convex?
A: u (x,y) = ln x +x2
Q: Using a graph, draw a set of indifference curves that are not locally non- satiated. Explain in…
A: An indifference curve refers to a graphical depiction of a combined product that offers a buyer a…
Q: Consider the indifference curve map and budget constraint for two goods, X and Y. Suppose the good…
A: Normal goods are those goods whose quantity demanded increases, when the income of the consumer…
Q: Consider a consumer, he has the utility function: u(x1, X2) = xỉ * Could you find a monotone…
A: A utility function represents homothetic preferences when it is homogeneous of degree n.
Q: The marginal rate of substitution is the maximum number of units of good Y that the consumer would…
A: Option -: All of the above is correct The marginal rate of substitution is defined as the…
Q: Q2. Mary makes cheese sandwiches for herself every week, and she has her own receipt with two pieces…
A:
Q: Calculate the marginal rate of substitution (MRS12) for the following utility function: U(q1, 92) =…
A: "Marginal rate of substitution indicates the rate at which a consumer can give up some units of a…
Q: When utility function U(q1, q2)=min{ 34.6 q1, 17 q2} and q1= 33 and q2= 60 are given, find…
A: A utility function represents the preferences of a consumer if the consumer has a preference…
Q: A sports bar charges $5 per drink (good X) and $10 per plate of appetizers (good Y). Victor, a…
A:
Q: Suppose Jane is always willing to give up one apple for one orange. Then, the MRS for apples to…
A: In economics, an individual has the face the trade-off between the alternatives to make different…
Q: Suppose Elizabeth’s preferences can be described by the Cobb-Douglas utility function, u(x_1, x_2 ).…
A: Given information Elizabeth has Cobb-Douglas utility function U=u(X1,X2) P1 =price of X1 P2=price…
Q: Jane’s utility function on bundles of two commodities (x,y) is given by: U(x,y)=4x2y3. What is the…
A: To calculate the value of Marginal Rate of Substitution.
Q: Q1. Bob has a utility function defined over goods 1 and 2: u(x1; x2) = min{6*x1 + x2, x1 + 2*x2}…
A: u(x1; x2) = min{6*x1 + x2, x1 + 2*x2}
Q: he marginal rate of technical substitution Group of answer choices is the rate at which one input…
A: The marginal rate of technical substitution (MRTS): MRTS is the rate at which the firm can trade…
Q: In Problem 6, Elmer's utility function is U(x, ) = min{x, y²}. If the price of x is $20, the price…
A: From the utility function, we know x and y are complements Thus, x=y2 When y= 8 x = (8)2 = 64if 8…
Q: An individual utility function is given by U(x,y) = x·y. This individual demand (optimal purchase)…
A: Given Individual utility function: U(x,y) = xy ......... (1) Let px and py be the price of good x…
Q: The following statement is true for consumer preferences. a) /The axiom of weak monotonicity…
A: Consumer preference: It refers to the items that a consumer wants to buy. The change in consumer…
Q: Bridget's preferences for apples( X) and bananas(Y) can be represented by the utility function…
A: Utility refers to the satisfaction obtained by the consumers from a good or service. While ,…
Q: What is the marginal rate of substitution (MRS) for the utility function U(x, y) = x° + y®? The…
A: Given: The utility function is: Ux, y = xp + yp To Find: The marginal rate of substitution of Good x…
Q: Consider the following utility function U(x1, x2) = Min{x1, x2} + 1/2Max{x1, x2} Calculate the…
A: U(x1,x2) = Min{x1, x2} + 1/2Max{x1,x2}
Q: A consumer has GH¢600 to spend on two commodities, A and B. Commodity A costs GH¢20 per unit and…
A:
Q: Suppose an individual had a utility function given by: U = X0.6 y 0.8. Calculate this individual's…
A: utility function is an important concept that measures preferences over a set of goods and services.…
Q: Bob lives in San Diego and loves to eat desserts. He spends his entire weekly allowance on pudding…
A: Marginal rate of substitution can be explained as the rate at which a consumer is willing to give up…
Q: Diogo has a utility function, 0.2. 0.8 where q, is chocolate candy and q2 is slices of pie. If the…
A: The measure that illustrates satisfaction or welfare of a consumer being a function of the real good…
Q: x0.25 y0.75 and has an income of As in question 2a, A consumer has a utility function given by U…
A: U = x0.25y0.75 MRS = MUxMUy = 0.25x-0.75y0.750.75x0.25y-0.25 = 1y3x Before Price change: MRS =…
Q: Consider the following utility function: U= 100x0.50,0.50 A consumer faces prices of P, = $2 and P,…
A:
Q: Suppose the function for the utility from good c is denoted as U(c)=2c2. Which of the following…
A: The total utility is defined as the total satisfaction a consumer is able to get by consuming a…
Q: marginal rate of substitution (MRS) can be defined as: Select one or more: a. The amount of one…
A: Marginal rate of substitution depicts the relative price of two goods.
Q: Consider the following utility function: U= 4X+Y. A consumer faces prices of P,= $2 and P, =1. %3D…
A: Answer: Given, Utility function: U=4X+Y The formula of the marginal rate of substitution (MRS) is…
Q: Consider the following utility function: U= 100x 50,0.50 %3D A consumer faces prices of P, = $2 and…
A: U=100X^0.5Y^0.5 Px=$2 Py=$1 MRS=1.83 MRS is the ratio of marginal utilities of the two goods In a…
Step by step
Solved in 3 steps with 1 images
- Consider the following utility function: ху υ(x, y) х —у (a) Derive the MRS of x to y. Show your work. (b) Is this function quasi-concave? [Hint. You need to check the conditions for quasi-concavity].Select the function that represents the marginal utility of X for the utility function: U = X³y². Select one: а. 3Х2ү2 b. 0.33X²Y с. 3X-3ү2 d. 2x²y² е. 3Х3ү2a good is normal, then an increase in the price of the good will lead to which of the following to be true for this good? (Assume that there are only two goods, the individual's preferences lead to well-behaved preferences with strictly convex indifference curves and an interior solution for all budgets). Let SE = substitution effect, IE = income effect) (a) The magnitude of the IE for this good must be larger than the magnitude of the SE (b) The magnitude of the SE for this good must be larger than the magnitude of the IE (c) The good could be a Giffen good d) The good must be an ordinary good ( (e) None of the above
- Anna has an income of 1000 euros and utility function U(x,y)=x²y³. The prices of the two goods are P₁=5 and Py-20. a) Define the budget constraint and represent it graphically. (If Utility =.5lnX+3Z+10+4√W then Marginal utility from X is....;. and the Mu of Z is ..For the utility function U(X,Y)= 6X0.50.5, the marginal rate of substitution MRSxy is: O Y/X. O X/Y. 3Y/X. O3X/Y.
- Define the Marginal Rate of Substitution between two goods (X and Y).If a consumer’s preferences are given by U(X,Y) = X1/4Y 3/4, compute the consumer’s marginalrate of substitution as a function of X and Y. Calculate the MRS if the consumer has chosen toconsumer 12 units of X and 30 units of Y.Consider the following utility function и(х, у) %3 3х + 4y a. Is the utility function homothetic? Explain. b. Under what condition will the consumer purchase good x alone?1 Consider a consumer who consumes only two goods, 21 and z2. His utility function is u (21, 22) = In z1 + 2. where In represents the natural logarithm. 1.a Derive the consumer's MRS of good 1 for good 2 using calculus to calculate his marginal utility from z and his marginal utility from z2. 1.b If the price of z1 is $2 per unit and the price of z2 is $4 per unit, and the consumer's income is $100, What is the equation of this consumer's budget line? 1.c What are the optimal consumption choices, z and z5, for this consumer? Show your work.
- You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.A utility function is called separable if it can be written as U(x, y) = U (x) + U,(y), where U > 0, U" < 0, and U1, U, need not be the same function. a. What does separability assume about the cross-partial derivative U„? Give an intuitive discussion of what word this condition means and in what situations it might be plausible. b. Show that if utility is separable then neither good can be inferior. c. Does the assumption of separability allow you to con- clude definitively whether x and y are gross substitutes or gross complements? Explain. d. Use the Cobb-Douglas utility function to show that separability is not invariant with respect to monotonic transformations. Note: Separable functions are examined in more detail in the Extensions to this chapter.0.8 A consumer's utility function is given by the expression: U = (0.6X0.5 +0.4Y0.5) ². Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.