Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility functionz; u(x, y) =
Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility functionz; u(x, y) =
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Reese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is
represented by the utility functionz;
u(x, y) = xy + x + y
Suppose now that Reese’s income is high relative to the prices of peanut butter and
chocolate (more concretely, imagine I > px and I > py). What is Reese’s Marshallian
demand for peanut butter, x^∗(Px, Py, I)?
Transcribed Image Text:The image contains a series of equations labeled (a) through (e). Each equation expresses the variable \( x^*(p_x, p_y, I) \) in terms of the variables \( p_x \), \( p_y \), and \( I \). These variables are typically used in economic models where \( p_x \) and \( p_y \) are prices of goods, and \( I \) is income. Here is the transcription of the equations:
(a) \( x^*(p_x, p_y, I) = \frac{I - p_x + p_y}{2p_x} \)
(b) \( x^*(p_x, p_y, I) = \frac{I}{2(p_x - p_y)} \)
(c) \( x^*(p_x, p_y, I) = \frac{I}{2p_x} - \frac{p_x}{p_y} \)
(d) \( x^*(p_x, p_y, I) = \frac{I + p_y}{2p_x} \)
(e) \( x^*(p_x, p_y, I) = \frac{I}{p_x} + \frac{p_y}{2} \)
Each equation depicts a different functional form, likely evaluating the optimal choices given the specified constraints and parameters.
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