1. A consumer has 16 dollars. The price of x₁ is p₁ dollars, and the price of x2 is p2 dollars. The consumer has a utility function, u(x1, x2) = x1x2. (a) Write down the demand function of x1, and calculate the con- sumption of x1 when p₁ = 4. (b) Suppose the price of x₁ decreases from p₁ = 4 to p₁ = 2, what is the change in the consumption of x₁? (c) Calculate the substitution effect. Hint: You need to calculate an interim income m' such that the purchasing power is constant after the price change, then calculate Ax₁ = x₁(m', p₁) - x1 (16, p₁) (see p141-142, Varian).
1. A consumer has 16 dollars. The price of x₁ is p₁ dollars, and the price of x2 is p2 dollars. The consumer has a utility function, u(x1, x2) = x1x2. (a) Write down the demand function of x1, and calculate the con- sumption of x1 when p₁ = 4. (b) Suppose the price of x₁ decreases from p₁ = 4 to p₁ = 2, what is the change in the consumption of x₁? (c) Calculate the substitution effect. Hint: You need to calculate an interim income m' such that the purchasing power is constant after the price change, then calculate Ax₁ = x₁(m', p₁) - x1 (16, p₁) (see p141-142, Varian).
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1. A consumer has 16 dollars. The price of x₁ is p₁ dollars, and the price of
x2 is p2 dollars. The consumer has a utility function, u(x1, x2) = x1x2.
(a)
Write down the demand function of x1, and calculate the con-
sumption of x₁ when p₁ = 4.
(b)
Suppose the price of x₁ decreases from p₁ = 4 to p₁ = 2, what is
the change in the consumption of x₁?
(c)
Calculate the substitution effect. Hint: You need to calculate
an interim income m' such that the purchasing power is constant after
the price change, then calculate Ar₁ = x₁(m', p₁) - x₁(16, p₁) (see p141-142,
Varian).
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