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- 10. Ken has a utility function for tennis rackets (X) and tennis balls (Y) of the form U(X,Y)=min(4X,2Y). His Hicksian demand for X is given by a. X = 4Px b. X = 2Px c. X == d. X =For the utility function U = Qx0.22Qy(1-0.22) find the trade-off rate between good X and good Y at Qx= 9 and Qy=19 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).Show whether or not the following utility functions are monotonic transformation of each other u = X,X2: u = lnX,lnX, %3! u = X, + X2: u = (X, + X,) u = X, + X2: u = (X1 + X2)? Show whether or not the following utility functions are convex U = x,°X, U = x, + X,2 U = X, + X,X2X
- Suppose that we can represent Joyce's preferences for cans of pop (the x-good) and pizza slices (y-good) with the utility function min[4x,5y]. a) Find her Marshallian Demand Functions. b) Find her Hicksian Demand FunctionsGiven the following utility function: U(Q,Q2) = 100LN(4Q1/2 + 2Q,/2) %3D a. Show that the function is cardinal. b. Show that the function is ordinal. c. Derive the demand functions for the two goods. d. For Q1 show that the law of demand holds. e. Show that Q1 is normal. f. What is the relationship between the two goods.Derive Ryan's demand function for q₁, given his utility function is where o = = (9₁) P + (9₂)P, 1 1-p The demand curve for q₁ as a function of P₁, P2, and Y is (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a subscript can be created with the_ 9₁ = character.) U= Let the price of q₁ be p₁, let the price of q2 be p2, and let income be Y.
- Suppose that an individual has a Utility function represented by a CES function. The utility function of the individual is given as: U(x,y) = x1/2 + y1/2 b. Calculate the own price elasticity using the "share elasticity" of any good. Let us assume that the prices of both goods are equal.A) Suppose a quasilinear utility function is given by u(x₁, x₂) = 2√√x₁ + 4x₂. 1. For this utility derive the demand functions xi (P₁, P2, 1) and x₂ (P₁, P2, 1). 2. For this utility derive the Engle function I = 1(x₂, P₁, P₂) for good 2. B) Do the same for the Cobb-Douglas utility function u(x₁, x₂) = x₁x². That is, 1. For this utility derive the demand functions x₁ (P₁, P2, 1) and x₂ (P₁, P2, 1). 2. For this utility derive the Engle functions I = 1(x₁1, P₁, P₂) and I = = 1(x₂, P1, P2).Consider the following indirect utility function:ʋ(P,y) = y(P1r + P2r)-1/r Wherer = ρ/(ρ-1, Pi are parametric prices, and y is the consumer’s budget a) Solve for the Marshallian demand functions xi (P, y) and verify that these functions are homogenous of degree zero (Hint: you can also use Roy’s Identity). b) Derive the Hicksian demand functions xih (P,u)
- QUESTION 1 For the utility function U = Qx0.69Qy(1-0.69) find the trade-off rate between good X and good Y at Qx= 7 and Qy=11 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 1.2, 1.14 = 1.1).= Problem 3. Consider the Cobb-Douglas utility function u(x, y) = x²y². Let the budget constraint be Pxx+PyY I where pa, py are the prices and I denotes the income. (a) Write the Lagrangian for this utility maximization problem and solve the first-order con- ditions to find the demand functions for both good x and good y. [Hint: Your results should only depend on the parameters pr, Py, I.] (b) In the optimal consumption bundle, how much money is spent on x? How much on y? Express your answer in proportion of the total income I. (c) Check the second order conditions. (d) Assume the price p, increases. How does the optimal consumption bundle change? (e) Assume the income doubles. What is the new optimal consumption bundle? How does your answer in (b) change?A consumer chooses non-negative consumption levels of two goods x1 and x2 and has a utility function given as: U = = 0xfx% where 0 < a <1 and 0 is a constant. Assume that the prices of goods x1 and x2 are respectively Piand p2 Set up the expenditure minimization problem of the consumer and derive the Compensated (Hicksian) demand function for goods 1 and 2 and investigate whether the two goods are complements or substitutes. i.