2. A consumer spends her entire income on two goods, z and y. Her preferences are represented by the utility function u(z, y) = 4 In z + 6 In y. a) Find this consumer's demand for z and y, D.(Pz,Pe,I) and D,(Pz,Py; I), as functions of the price of I, Pz, the price of y, Py; and her income I. b) Suppose that the price of z is p, = $2 per unit, the price of y is p, = $3 per unit, and the consumer's income is I = $10. What bundle (z, y) maximizes the consumer's utility? c) Suppose that the price of z increases to $4 per unit. What bundle (z, y) does the consumer demand now? d) Given the price increase, how much extra income does this consumer need purchase the original bundle following the price change? e) What bundle (r, y) would the consumer choose to consume if she had that additional income, given the new prices? f) Decompose the total changes in the demand for r and y into their substitution and income effects.
2. A consumer spends her entire income on two goods, z and y. Her preferences are represented by the utility function u(z, y) = 4 In z + 6 In y. a) Find this consumer's demand for z and y, D.(Pz,Pe,I) and D,(Pz,Py; I), as functions of the price of I, Pz, the price of y, Py; and her income I. b) Suppose that the price of z is p, = $2 per unit, the price of y is p, = $3 per unit, and the consumer's income is I = $10. What bundle (z, y) maximizes the consumer's utility? c) Suppose that the price of z increases to $4 per unit. What bundle (z, y) does the consumer demand now? d) Given the price increase, how much extra income does this consumer need purchase the original bundle following the price change? e) What bundle (r, y) would the consumer choose to consume if she had that additional income, given the new prices? f) Decompose the total changes in the demand for r and y into their substitution and income effects.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
answer only d,e and f
Transcribed Image Text:2. A consumer spends her entire income on two goods, r and y. Her preferences are represented by the
utility function u(x, y) = 4 ln r + 6 In y.
a) Find this consumer's demand for z and y, D.(Pa;Pr,I) and D,(P., Py, I), as functions of the price of
2, Pz, the price of y, Py, and her income I.
b) Suppose that the price of r is p, = $2 per unit, the price of y is Py = $3 per unit, and the consumer's
income is I = $10. What bundle (r, y) maximizes the consumer's utility?
c) Suppose that the price of r increases to $4 per unit. What bundle (r, y) does the consumer demand
now?
d) Given the price increase, how much extra income does this consumer need purchase the original bundle
following the price change?
e) What bundle (r, y) would the consumer choose to consume if she had that additional income, given
the new prices?
f) Decompose the total changes in the demand for r and y into their substitution and income effects.
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