As usual, goods 1 and 2 are perfectly divisible, meaning that ₁ and 22 can take on any nonnegative real values and need not be integers. Good 3 is indivisible and unique, meaning that 23 must be either 0 or 1 (for example, good 3 could be an original painting). (a) Show that this consumer's preferences are monotone. Solution: The derivatives du/day and du/da2 are positive for x1, x2 > 0. Increasing 23 from 0 to 1 increases utility by 1/2. Therefore, if the quantity of all three goods increases, utility (strictly) increases. (b) Find this consumer's Marshallian demand. Solution: If x3 = 0, the optimal choice is (#₁, #2,83) = (25₁, 252,0). If x3 = 1, the optimal choice is (#1, #2, #3) = W 2p1 1 w - P3 2p2
As usual, goods 1 and 2 are perfectly divisible, meaning that ₁ and 22 can take on any nonnegative real values and need not be integers. Good 3 is indivisible and unique, meaning that 23 must be either 0 or 1 (for example, good 3 could be an original painting). (a) Show that this consumer's preferences are monotone. Solution: The derivatives du/day and du/da2 are positive for x1, x2 > 0. Increasing 23 from 0 to 1 increases utility by 1/2. Therefore, if the quantity of all three goods increases, utility (strictly) increases. (b) Find this consumer's Marshallian demand. Solution: If x3 = 0, the optimal choice is (#₁, #2,83) = (25₁, 252,0). If x3 = 1, the optimal choice is (#1, #2, #3) = W 2p1 1 w - P3 2p2
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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