Carefully write down the consumer's utility maximization proble and find Marshallian demand functions using the Lagrange metho Be especially careful listing all the consumer's constraints. Show that the demand functions you found in (a) are indeed the s lutions of the utility maximization problem for the utility functi (1). Derive the indirect utility function of the consumer. Derive the expenditure function of the consumer.
Carefully write down the consumer's utility maximization proble and find Marshallian demand functions using the Lagrange metho Be especially careful listing all the consumer's constraints. Show that the demand functions you found in (a) are indeed the s lutions of the utility maximization problem for the utility functi (1). Derive the indirect utility function of the consumer. Derive the expenditure function of the consumer.
Chapter21: Demand: Consumer Choic
Section: Chapter Questions
Problem 1E
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part B C D
urgently
Transcribed Image Text:Consider a consumer whose preferences over
two consumption goods are represented by
the utility function
u(x, y) = ye-¯ª,
(1)
where x denotes the quantity of the first good, and y denotes the quan-
tity of the second good consumed by the consumer.
Let I> 0 denote the consumer's income, and let the market prices
for a unit of each good be, respectively, px = p, and py = 1. Assume
that 0 < p < 1.
(a) Carefully write down the consumer's utility maximization problem
and find Marshallian demand functions using the Lagrange method.
Be especially careful listing all the consumer's constraints.
(b) Show that the demand functions you found in (a) are indeed the so-
lutions of the utility maximization problem for the utility function
(1).
(c) Derive the indirect utility function of the consumer.
(d) Derive the expenditure function of the consumer.
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