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.
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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
b. Calculate the own price elasticity using the "share elasticity" of any good. Let us assume that the prices of both goods are equal.
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- Derive demand functions for x and y for the general class of Cobb-Douglas preferences represented by the utility function u(x, y) = x α y β . As functions of px, py, I, α, and β, calculate price elasticities, cross-price elasticities, income elasticities, and expenditure shares for x and 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 Identit
- Suppose that an agent has utility function u(x,y)=x+2y. What information is necessary to calculate the agent’s optimal consumption of x? price of y only price of x only income only price of x, price of y, and income price of x and y onlySuppose the market demand curve for pizza can be expressed as QD = 100 - 2P + 3Pb, where QD is the quantity of pizza demanded, P is the price of a pizza, and Pb is the price of a burrito. What is the slope of this demand function, and what information does the slope provide?..Assume 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.
- For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x and x2 are p₁ and p₂ respectively and income is m. i) U(x1x2) = ln(x1+ x2) ii) U(x1x2) = (x1+ x2)Consider the utility function u(x) =√x1+ √x2 ; and a standard budget constraint: p1x1+p2x2=I. a.Are the preferences convex? b. Are the preferences represented by this function homothetic? c. Verify that the demand function is homogeneous of degree 0 in prices and income.For each of the following utility functions, find the Marshallian demand function, the indirect utility function and the expenditure function. Assume that prices of x1 and x2 are p1 and p2 respectively and income is m. U(x1 x2) = In (x1 + x2) U(x1 x2) = x1 + x2
- Suppose a consumer’s utility from consuming the two goods x and y is given by: PHOTO a) Calculate the uncompensated (Marshallian) demand functions for x and y respectively. b) Calculate the consumer’s indirect utility function for x and y c) Compute the compensated (Hicksian) demand functions for x and y d) Determine the uncompensated own- and cross-price elasticities. e) Determine the compensated own- and cross-price elasticities.A consumer is willing to trade 4 units of x for 1 unit of y when she is consuming bundle(8, 1). She is also willing to trade in 1 unit of x for 2 units of y when she is consumingbundle (4, 4). She is indifferent between these two bundles. Assuming that the utilityfunction is Cobb-Douglas of the form U(x,y)=xα yβ, where α and β are positiveconstants, what is the utility function for this consumer?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. (A) Set up a Lagrangian optimisation function for the consumer and compute the optimal consumption bundle for the consumer B)the solution in (a) represents the mashallian demand function for x1and x2. using the solution in (a) compute the indirect utility function
