Question

5. Suppose that, for a certain consumer, whenever the price of $x$ is twice the price of $y$ (ie, $P_x = 2p_y$), the consumer optimally consumes twice as much $y$ as $x$ (ie, $y = 2x^*$). Which of the following utility functions represent preferences consistent with this behavior? (a) $U(x, y) = 2\ln(x) + y$ (b) $U(x, y) = 3x + y$ (c) $U(x, y) = \min\{4x, 5y\}$ (d) $U(x, y) = \ln(x) + 2\ln(y)$ (e) $U(x, y) = xy$

Name: 5 suppose that for a certain consumer whenever the price of x is twice the price of y ie px 2py the consumer optimally consumes twice as much y as x ie y 2x which of the following utility 60384
Uploaded: 2023-06-13T09:38:55-08:00
Duration: 2 min 49 s
Channel: Sri K
Description: 5 suppose that for a certain consumer whenever the price of x is twice the price of y ie px 2py the consumer optimally consumes twice as much y as x ie y 2x which of the following utility 60384

          5. Suppose that, for a certain consumer, whenever the price of $x$ is twice the price of $y$ (ie, $P_x = 2p_y$), the consumer optimally consumes twice as much $y$ as $x$ (ie, $y = 2x^*$). Which of the following utility functions represent preferences consistent with this behavior?
(a) $U(x, y) = 2\ln(x) + y$
(b) $U(x, y) = 3x + y$
(c) $U(x, y) = \min\{4x, 5y\}$
(d) $U(x, y) = \ln(x) + 2\ln(y)$
(e) $U(x, y) = xy$

5 suppose that for a certain consumer whenever the price of x is twice the price of y ie px 2py the consumer optimally consumes twice as much y as x ie y 2x which of the following utility 60384

Added by Esperanza C.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Sri K

06/13/2023

Step 1

This means that the ratio of the quantities consumed is equal to the inverse ratio of the prices. This is a characteristic of Cobb-Douglas utility functions. Show more…

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5. Suppose that, for a certain consumer, whenever the price of $x$ is twice the price of $y$ (ie, $P_x = 2p_y$), the consumer optimally consumes twice as much $y$ as $x$ (ie, $y = 2x^*$). Which of the following utility functions represent preferences consistent with this behavior? (a) $U(x, y) = 2\ln(x) + y$ (b) $U(x, y) = 3x + y$ (c) $U(x, y) = \min\{4x, 5y\}$ (d) $U(x, y) = \ln(x) + 2\ln(y)$ (e) $U(x, y) = xy$