Suppose a consumer has utility function U(x, y) = vx + Jy a. Solve the utility maximization problem to find ordinary demand functions x*(Px, Py,I) and y*(Px, Py, I). Calculate the indirect utility function V(P, Py, I). Check what happens to the quantities demanded and indirect utility when prices and income all double. b. Does this utility function represent homothetic preferences? Calculate the income elasticity of demand for x and y. What will the income consumption curve and Engel curves look like? (no need to draw them) Is demand for these goods elastic, inelastic or unit-elastic? Find the own-price elasticity of C. demand for x. d. Can you tell whether x and y are (gross) complements or substitutes without calculating cross- price elasticity? Explain how you know. e. Using the same utility function, solve the expenditure minimization problem, to find the compensated demand functions x°(Px, Py,U)and y°(Px, Py,U), and the expenditure function E(Px, Py, U). Check what happens to expenditure if both prices double. f. Calculate the own-price elasticity of compensated demand for x. Can you confirm whether or not compensated demand is less elastic than ordinary demand, and is this consistent with the Slutsky equation?
Suppose a consumer has utility function U(x, y) = vx + Jy a. Solve the utility maximization problem to find ordinary demand functions x*(Px, Py,I) and y*(Px, Py, I). Calculate the indirect utility function V(P, Py, I). Check what happens to the quantities demanded and indirect utility when prices and income all double. b. Does this utility function represent homothetic preferences? Calculate the income elasticity of demand for x and y. What will the income consumption curve and Engel curves look like? (no need to draw them) Is demand for these goods elastic, inelastic or unit-elastic? Find the own-price elasticity of C. demand for x. d. Can you tell whether x and y are (gross) complements or substitutes without calculating cross- price elasticity? Explain how you know. e. Using the same utility function, solve the expenditure minimization problem, to find the compensated demand functions x°(Px, Py,U)and y°(Px, Py,U), and the expenditure function E(Px, Py, U). Check what happens to expenditure if both prices double. f. Calculate the own-price elasticity of compensated demand for x. Can you confirm whether or not compensated demand is less elastic than ordinary demand, and is this consistent with the Slutsky equation?
Chapter5: Income And Substitution Effects
Section: Chapter Questions
Problem 5.3P
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ISBN:
9781337617383
Author:
Roger A. Arnold
Publisher:
Cengage Learning