John considers oranges (R) and mandarins (M) as perfect substitutes. He gets the same utility from con- suming one orange or two mandarins and the marginal utility of each is constant. The price of oranges and mandarins is PR = 4 and PM = 1, and John has income Y = 40. 1.1 Write the utility function and derive the marginal rate of substitution. 1.2 Derive the optimal choice of oranges and mandarins. If the price of mandarins increases to PM = 3, what happens? Graph the optimal choice in both cases.
John considers oranges (R) and mandarins (M) as perfect substitutes. He gets the same utility from con- suming one orange or two mandarins and the marginal utility of each is constant. The price of oranges and mandarins is PR = 4 and PM = 1, and John has income Y = 40. 1.1 Write the utility function and derive the marginal rate of substitution. 1.2 Derive the optimal choice of oranges and mandarins. If the price of mandarins increases to PM = 3, what happens? Graph the optimal choice in both cases.
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.11P
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Transcribed Image Text:Question 1
John considers oranges (R) and mandarins (M) as perfect substitutes. He gets the same utility from con-
suming one orange or two mandarins and the marginal utility of each is constant. The price of oranges and
mandarins is PR = 4 and PM = 1, and John has income Y = 40.
1.1 Write the utility function and derive the marginal rate of substitution.
1.2 Derive the optimal choice of oranges and mandarins. If the price of mandarins increases to PM = 3,
what happens? Graph the optimal choice in both cases.
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