1. Consider a consumer who consumes two goods. The utility function is given by √√2x1 +1+√√x₂, U(X1, X₂) = where x ≥ 0 denotes the amount of good i 1,2 consumed. Unless stated otherwise, the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x1, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its
1. Consider a consumer who consumes two goods. The utility function is given by √√2x1 +1+√√x₂, U(X1, X₂) = where x ≥ 0 denotes the amount of good i 1,2 consumed. Unless stated otherwise, the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x1, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.2P
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Transcribed Image Text:1. Consider a consumer who consumes two goods. The utility function is given by
u(x1, x₂)
/2x1+1+√√√x₂,
-
where x > 0 denotes the amount of good i
=
the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12.
1,2 consumed. Unless stated otherwise,
(1) Calculate the marginal rate of substitution (measuring the value of good 1) at the
consumption plan (x₁, x₂) = (3, 4).
(2) Calculate the consumption plan that is optimal for the consumer.
(3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its
derivative with respect to p2, i.e., v'(P2), at p2 = 3.
(4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demand
for each good.
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