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- 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.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.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.
- Consider a three-commodity consumer setting with the expenditure function: e(p, u) = up1α p2βp3γ Find the indirect utility function Find the Walrasian demand function Verify Roy's identity Recover consumer's direct utility functionQuestion 3 Consider the utility function of the form: ?=?1?1?2?2 Given the budget constraint: ?1?1+?2?2=? Show that the implied Marshallian demand curves are: ?1=?1(?1+?2)??1 ?1=?2(?1+?2)??2Consider the following function describing the utility of a consumer: U(x1, x2, x3) = a1*ln(x1) + a2*ln(x2) + a3*ln(x3), where ln = natural logarithm and a1, a2, a3 constants a. Pose the primal problem (using Langrange's method), obtaining the Marshallian demands for each good and the individual's indirect utility function. b. From the results obtained from question a., find the minimum expenditure function and the Hicksian demands.
- Suppose the consumer solves the following UMP: max (x1)^2 + (x2)^2 , s.t. p1x1 + p2x2 ≤ w where p1,p2 > 0. a) Plot the indifference curves b) Find the Marshallian demand functions. Show graphically the utility maximizing choices.Existence of representative consumer Suppose households 1 and 2 have one-period utility functions u(c1) and w(c2), respectively, where u and w are both increasing, strictly concave, twice-differentiable functions of a scalar consumption rate. Consider the Pareto problem: Subject to the constraint c1 + c2 = c. Show that the solution of this problem has the form of a concave utility function vθ(c), which depends on the Pareto weight θ. Show that vθ(c) = θu (c1) = (1 − θ)w (c2). The function vθ(c) is the utility function of the representative consumer. Such a representative consumer always lurks within a complete markets competitive equilibrium even with heterogeneous preferences. At a competitive equilibrium, the marginal utilities of the representative agent and each and every agent are proportional.Given the utility function: U = X3/4 .Y1/4 Estimate the demand functions of commodity X and commodity Y using Lagrange method, if it is given that price of X is Px and price of Y is Py and Income is M.
- Which of the following statements is true? Select one or more options: a-If two different individuals have exactly the same budget constraint but different preferences (different appearance of the indifference curves) then they will have different equilibrium conditions for optimal choice b-The marginal substitution ratio is always equal to 1 for perfect substitutes c-If item X costs SEK 10, item Y costs SEK 20 and if the marginal benefit for X is 20 and the marginal benefit for Y is 30, then the individual should buy more of Y and less of X d-In the case of a corner solution for an individual, the marginal substitution ratio for two goods is not equal to the relative price of the two goodsWhich of the following statements is true? Select one or more options: -If two different individuals have exactly the same budget constraint but different preferences (different appearance of the indifference curves) then they will have different equilibrium conditions for optimal choice -The marginal substitution ratio is always equal to 1 for perfect substitutes -If item X costs SEK 10, item Y costs SEK 20 and if the marginal benefit for X is 20 and the marginal benefit for Y is 30, then the individual should buy more of Y and less of X -In the case of a corner solution for an individual, the marginal substitution ratio for two goods is not equal to the relative price of the two goodsA 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.
