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 c. Is the demand more elastic or inelastic than a Cobb-Douglas Utility function? Use the Slutsky matrix to illustrate.
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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
c. Is the
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- 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 c. Is the demand more elastic or inelastic than a Cobb-Douglas Utility function? Use the Slutsky matrix to illustrate.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 c. Is the demand more elastic or inelastic than a Cobb-Douglas Utility function? Use the Slutsky matrix to illustrate.PLEASE SKIP IF YOU ALREADY DID THISSuppose 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.
- You are given the following utility function (and there is obviously an income constraint). Derive the Marshallian demand function (half the points) and identify the income elasticity of both goods (half the points). u=x1x2Given utility function and prices of the good along with income U = x2 + y2 +2x + 2y P x = 1 P y = 1 M = 4 Find out ordinary demand functions and expenditure function.Consider the indirect utility function: v(p1; p2; m) = m /(p1 + p2). What is the Hicksian demand function?
- A consumer has the following utility function:u(x) = (xρ1 + xρ2)1/ρ 1. Derive the Walrasian demand function x(p, w) and compute the indirect utility function.2. Write down the expenditure minimization program.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 a. Derive the Marshallian Demand for both goods, in terms of Income and the prices of both goodsAssume you spend your entire income on two goods X & Y with prices given as PX & PY, respectively. Prices and income (I) are exogenous and positive. Given that U= X2Y 2 , derive the Hicksian demand function for good Y.
- Given the utility function U = X0.5+Y0.5 and budget constraint I=Px X+ Py Y,(a) Is this utility function is homothetic?(b) Derive the consumer’s demand functions for goods X and Y.(c) Obtain the numerical values of the own-price elasticity, cross-price elasticity, and the income elasticity of demand for X and Y.(d) Derive the indirect utility function and the expenditure function for this consumer.e) Obtain the compensated demand functions for goods X and Y. (f) Prove that the Slutsky equation holds in this case.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 IdentitConsider an individual whose preferences are represented by the utility function U(x1,x2) = min {3x1+x2 , x1+3x2}. For this individual, Calculate her demand function X1* (P1, P2,m) Calculate her own price, cross price, and income elasticities at X1*(1, 2, 24) and at X1*(1, 4, 24). Based on these, can you say the goods 1 and 2 are (gross, or Marshallian) complements or substitutes?
