Consider Jane's utility function: U = X0.5 + 0.5y with her income of M and prices, P & Py. Derive her ordinary demand curves. Create her indirect utility function and expenditure function.
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- A consumer is faced with the following utility function, U(x1 x2)=(xp1 1+xp2)1/p, where 0<p<1. The consumer also faces the prices p1 and p2 and has income level m. C) derive the the corresponding expenditure function for the consumer and the hicksian demand function.Consider an individual with the following utility function: Derive step-by-step both corresponding Hicksian demand functions depending on the different prices (P₁, P2) and a fixed utility level u. The equation given In picture.do This in 10 minutes.Consider a consumer with utility function u(x1, x2) = α_1x_1^( 2) + α_2x_2^( 2) where α1 > 0 and α2 > 0. Assume that p1, p2 > 0.? (a) Derive expenditure function e(p, u). Verify that it is homogeneous of degree 1 in p and increasing in u. (b) Using expenditure function and Hicksian demand, calculate Walrasian demand and indirect utility
- In Example 4.1 we looked at the Cobb-Douglas utility function U(x,y)=xay1-a, where 0<=a<=1. This problem illustrates a few more attributes of that function. a. Calculate the indirect utility function for this Cobb-Douglas case. b. Calculate the expenditure function for this case. c. Shos explicitly how the compensation required to offset the effect of an increase in the price of x is related to the size of the exponent a.Assuming a linear budget constraint, consider the following utility maximization problem:U (x1, x2) = 2x10.5 + 4x20.5 1. Compute the Marshallian demand functions for goods 1 and good 2.2. Find the compensated demand function.3. Derive the expenditure function and verify that h (p, u) = ∇pe (p, u)4. Derive the indirect utility function and verify Roy's IdentitA consumer has the following indirect utility function: u (x1, x2) = − 1/ x1 − 1 /x2 1. Compute the Walrasian demand functions.2. Obtain the indirect utility function.3. Obtain the expenditure function and the Hicksian demands.
- a. Utility function of Mr. Haroon is given by Find the optimal quantities of the two commodities (X and Y) by using Lagrangian method, if it is given that price of commodity X is Rs. 5 per unit, price of commodity Y is Rs. 10 per unit and income of Mr. Haroon is equal to Rs. 1000. b. Using indifference map elucidates at which point Mr. Haroon would be able to achieve maximum utility.A consumer is faced with the followlling Utility Function, U( x 1 x2) = ( xp +xp ) 1/ρ, where 0<ρ<1. The consumer also faces the prices and and has income level m. 1. Set up the Lagrangian 0ptimisation function for the consumer and Compute the optimal consumption bundle for the consumer. 2. The solution in (a) represents the Marshallian demand function for and . Using the solution in (a) compute the indirect utility function. 3. Derive the corresponding expenditure function for the consumer and the Hicksian demand function.the Marshallian Demands for the utility function U(x,y) =0.5x + 5ln ya) For this utility function calculate the Hicksian demand functions for x and y.b) Use your Marshallian and Hicksian demand functions to calculate the partial derivative of both Marshallian and Hicksian demand for x with respect to px and the partial derivative of Marshallian demand with respect to income.c) Use your answers for (b) to verify the Slutsky equation
- Economics Consider a household whose preferences are described by the utility function U(X1, X2) = X1X2 where X1 and X2 are household’s consumption of goods 1 and 2 respectively. Consider that household’s budget constraint is: P1X1 +P2X2 =I. (a) Derive the household’s demand functions for goods X1 and X2. (b) Derive the household’s compensated demand function for goods 1 and 2, i.e., obtain functions of the form Xi = fi (P1, P2, U) , I = 1, 2 where U is the household’s level of utility. (c) Assume that in the initial situation the commodity prices, P1 and P2, and the household income level, I, are given by P1 = $1, P2 = $1 and I = $2. Sketch the compensated and uncompensated demand curves for good 2 with P1 held constant at the initial level. In the compensated case, U is held constant at the initial level while in the uncompensated case, I is held constant. (d) By how much must I be increased if P2 increases to $2 (P1 remains at $1) and our household is to maintain its…The consumer has an incom Mand a utility function of the form u (x1; x2) = aInx1 + (1 - a)Inx2 If the prices of the two goods are given by p1 and p2, derive the Hicksian demand functions for a given utility level U: Derive the expenditure function. Using the concept of duality, derive the indirect utility function.Assume that utility is given by u(x, y) = x0.3y0.7 1. Derive the Walrasian demand function. Then use the derived Walrasian de- mand functions to compute the indirect utility function. 2. Derive the expenditure function and the Hicksian (compensated) demand functions for this case. Hint: Use Propositions 5 and 4.