Suppose you have following utility function :U(x,y)=(xª + yª )a wherex > 0, y > 0 and a + 0, a < 1 The price of commodity x is P, >0 and the price of good y is P, >0. Let us denote income by M, with M> 0 a) Compute the marginal utilities of x and y. b) Write down the utility maximization problem and corresponding Lagrangian function. c) Solve for optimal bundle, x+ and y* as a function of Px, Py, and M.

Q: A consumer B has a utility function of the form u(x1,x2) = Vx1 + V2x, where x s the basic food…

A: Utility indicates the satisfaction consumers earn from consumption.

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 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: Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F Suppose as Case 1, Total income…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Assume that Rossi consumes only bananas and avocado. Fortunately, she likes both goods. The…

A: At optimal condition MRS = Price ratio.

Q: Suppose Pacó has an annual entertainment budget of I. He spends his entertainment budget on only 2…

A: Utility Function is given as U(v,m) = 4v1/2m. Price of Video games: Pv Price of Movies: Pm

Q: suppose that a consumer has a utility function U=AX^2Y^2 Which of the following statements is false?…

A: The given infomation:The utility function can be written as follows:

Q: Suppose that we have a utility function involving two goods that is linear of the form U(x, y) = ax…

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Q: Paris has a utility function over berries (denoted by B) and chocolate (denoted by C) as follows:…

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Q: Which of the following are true regarding the law of diminishing marginal utility? The more a person…

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Q: Suppose that the consumer has a utility function u(a, b) = min (2a, b). The price of both goods is…

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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: Consider the following utility function.   U=U(X,Y)=X0.2Y0.8   Find the marginal utilities.…

A: Utilty is defined as the satisfaction which the consumer gets by consuming the homogeneous units of…

Q: Suppose the utility function is represented by the following equation: U (X, Y) = XY + X + 2Y + 2…

A: A budget limitation refers to the different combinations of goods and services that a consumer can…

Q: An economy described in an edgeworth box consists of 2 goods, namely X and Y and two consumers,…

A: Given, a two good and two-person economy: Utility functions: A: UA = XAYA B: UB = XBYB Endowments:…

Q: Consider a consumer who purchases two goods, x and y. The consumer’s utility function is U(x, y) =…

A: The budget constraint of the consumer shows the different combinations of two goods that an…

Q: Suppose that a consumer with the utility function U = X0.75 Y 0.25 choses a bundle where X=10 and…

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Q: . Construct an indirect utility function that corresponds to the direct function U = a In q1 + q2.…

A: We have  Utility function: U=αlnq1+q2          .... (1) First, we will find the Marshallian demand…

Q: Suppose that the utility function for two commodities is: U(q1, q2) = q1α q2(1-α) Let the prices…

A: A consumer consumes a good as it gives it is a utility. The utility is the want satisfying power of…

Q: A utility maximizing consumer purchases two commodities, Q1 & Q2. The consumer’s utility function is…

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Q: Consider an individual whose preferences are represented by the utility function U(x1,x2) = min…

A: Since you have posted multiple parts question, we will solve the first three parts for you. If you…

Q: Diogo has a utility function, U(a,, 92) =q, 02., 0.8 where q, is chocolate candy and q2 is slices of…

A: Optimal condition is that condition where MRS is equal to price ratio.

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: Consider the following utility function: u(x1,x2) = x1 + x2. (A): i) Restate the consumer problem.…

A: * Hi there , as there are multiple questions posted . Following our guidelines we can only solve the…

Q: Suppose you have following utility function :U(x,y)=(x“ + yª )a where x > 0, y > 0 anda ± 0,a 0 and…

A: We will use utility maximization method to answer this question

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: Jess has the utility function U(x₁, x₂) = min{3x1, 6x2}. The price of x₁ is px₁, Px₂, and his income…

A: This is a case of complementary function where both goods are consumed in the fixed proportion.

Q: Suppose there are two goods, x1 and x2, with unit prices p1 and p2. Consider a consumer with vealth…

A: (a) The objective of the consumer is to maximize his utility subject to the budget constraint. The…

Q: Sandy receives utility from consuming berries (X) and nuts (Y) as given by utility function u(X,Y) =…

A: Given nuts/ barriers ratio = 62/17 = 3.647

Q: Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F Suppose as Case 1, Total income…

A: Given, U (F,C) = FC MUF= C MUC = F Income (I) = $100 Price of food (PF) = $2 Price of cloth (PC) =…

Q: The Slutsky matrix below belongs to a consumer with a regular utility function of three goods, with…

A: As we know that Slutsky matrix is symmetric matrix. Therefore, By solving the metrics we can find…

Q: Suppose that the preferences of the consumer are represented by the following functions of utility:…

A:

Q: Let there be two goods x and y with prices p,x and py respectively, and let M be the consumer's…

A: The indifference curve of the consumer shows the different combinations of two goods that give an…

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: Consider a consumer with the utility function U(X,Y) = In(vX + vY) and suppose that the prices of…

A: Given prices and income, the budget constraint is given by pXX+pYY=I⇒2X+4Y=120 To solve the utility…

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: Bob has utility function U(x,y)=x+y over goods x and y. a) If P,-$30, Py-$10, draw the income…

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Q: If the utility function (U) between food (F) and clothing (C) can be represented as U =2F + 9C, the…

A: The utility is the amount of satisfaction received by the consumers from the consumption of goods…

Q: U = U ( x 1, x2)  = (x1 + 2) 2 (x2 + 3) 3

A: The Marginal utility is a satisfaction which consumer derive by consuming one more unit of…

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: Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F Suppose as Case 1, Total income…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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 a consumer whose preferences are given by the utility function U (x, y) = (x + 1)² (y +…

A:

Q: Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F Suppose as Case 1, Total income…

A: Given, U (F,C) = FC MUF= C MUC = F Income (I) = $100 Price of food (PF) = $2 Price of cloth (PC) =…

Q: Suppose that consumer has the following utility function: U(X, Y) = X/2y/+. What would be the demand…

A: