2. If h(y) denotes an individual's happiness (called “utility" in economics) when having income Y, then yh" (y) h'(y) R(y) is called the coefficient of relative risk aversion, which measures how much an indi- vidual is willing to take risks. Compute R for the following utility functions, where a, b, c, d are constants ay + 6 h(y) = (ay + b)°, h(y) cy +d° In the computations, you can assume that no denominator is 0. Simplify as much as possible.
2. If h(y) denotes an individual's happiness (called “utility" in economics) when having income Y, then yh" (y) h'(y) R(y) is called the coefficient of relative risk aversion, which measures how much an indi- vidual is willing to take risks. Compute R for the following utility functions, where a, b, c, d are constants ay + 6 h(y) = (ay + b)°, h(y) cy +d° In the computations, you can assume that no denominator is 0. Simplify as much as possible.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Relative Risk Aversion in Economics
If \( h(y) \) denotes an individual's happiness (referred to as "utility" in economics) when having income \( y \), then the coefficient of relative risk aversion \( R(y) \) is given by:
\[
R(y) = -\frac{yh''(y)}{h'(y)}
\]
This coefficient measures how much an individual is willing to take risks. To compute \( R \) for the following utility functions, assume that \( a, b, c, d \) are constants:
1. \( h(y) = (ay + b)^c \)
2. \( h(y) = \frac{ay + b}{cy + d} \)
In the computations, you can assume that no denominator is zero. Simplify as much as possible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e4673fd-fa1f-499f-888d-6c0ef020d982%2Fa1a61a56-f7fe-4c50-af7c-d39cc36eb93a%2Fdgmshien_processed.png&w=3840&q=75)
Transcribed Image Text:### Relative Risk Aversion in Economics
If \( h(y) \) denotes an individual's happiness (referred to as "utility" in economics) when having income \( y \), then the coefficient of relative risk aversion \( R(y) \) is given by:
\[
R(y) = -\frac{yh''(y)}{h'(y)}
\]
This coefficient measures how much an individual is willing to take risks. To compute \( R \) for the following utility functions, assume that \( a, b, c, d \) are constants:
1. \( h(y) = (ay + b)^c \)
2. \( h(y) = \frac{ay + b}{cy + d} \)
In the computations, you can assume that no denominator is zero. Simplify as much as possible.
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