Question 1: Suppose that Samantha has Cobb-Douglas preferences over tomatoes (good 1) and potatoes (good 2) U(q1, q2) 1/2 1/2 91' 92 (1) Calculate Samantha's optimal choice (qi, q5) if pi = 2, p2 = 2 and Y = 64. (2) Calculate Samantha's optimal choice (q*, q**) if the price of tomatoes in- creases to Pi = 8. (3) On a clearly labeled graph: plot both budget constraints, both of Samantha's optimal choices, and sketch indifference curves through each optimal choice. Then, sketch how the total effect of the price change can be broken into the substitution effect and the income effect.

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Chapter1: Making Economics Decisions
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Question 1: Suppose that Samantha has Cobb-Douglas preferences over tomatoes
(good 1) and potatoes (good 2)
1/2 1/2
U(q1, 92) = q q
(1) Calculate Samantha's optimal choice (qi, a5) if p1 = 2, p2 = 2 and Y = 64.
(2) Calculate Samantha's optimal choice (q*, q**) if the price of tomatoes in-
creases to P1 = 8.
(3) On a clearly labeled graph: plot both budget constraints, both of Samantha's
optimal choices, and sketch indifference curves through each optimal choice.
Then, sketch how the total effect of the price change can be broken into the
substitution effect and the income effect.
(4) Calculate the choice (q1, q2) that splits the price change into its two effects.
(5) You should have found in parts (1) and (2) that q = q**. Does changing the
price of tomatoes have no effect on the demand for potatoes or does it have
two effects that cancel each other out?
Transcribed Image Text:Question 1: Suppose that Samantha has Cobb-Douglas preferences over tomatoes (good 1) and potatoes (good 2) 1/2 1/2 U(q1, 92) = q q (1) Calculate Samantha's optimal choice (qi, a5) if p1 = 2, p2 = 2 and Y = 64. (2) Calculate Samantha's optimal choice (q*, q**) if the price of tomatoes in- creases to P1 = 8. (3) On a clearly labeled graph: plot both budget constraints, both of Samantha's optimal choices, and sketch indifference curves through each optimal choice. Then, sketch how the total effect of the price change can be broken into the substitution effect and the income effect. (4) Calculate the choice (q1, q2) that splits the price change into its two effects. (5) You should have found in parts (1) and (2) that q = q**. Does changing the price of tomatoes have no effect on the demand for potatoes or does it have two effects that cancel each other out?
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