Suppose a consumer has utility function U (x, y) = vx + /ya. Solve the utility maximization problem to find ordinary demand functions x*(Px, Py,I) andy*(Px, Py, I). Calculate the indirect utility function V(Pr, Py, I). Check what happens to thequantities demanded and indirect utility when prices and income all double.b. Does this utility function represent homothetic preferences? Calculate the income elasticity ofdemand for x and y. What will the income consumption curve and Engel curves look like? (no needto draw them)Is demand for these goods elastic, inelastic or unit-elastic? Find the own-price elasticity ofС.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 thecompensated demand functions x°(Px, Py,U)and y°(Px, Py, U), and the expenditure functionE(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 notcompensated demand is less elastic than ordinary demand, and is this consistent with the Slutskyequation?

We are going to use Consumer choice theory to answer these questions. Note: Since your question…

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?

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

100%

Suppose a consumer has utility function U (x, y) = vx + /y
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(Pr, 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
С.
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?

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