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$$\sigma_{ij} = \frac{d\ln(x_j/x_i)}{d \ln \text{MRTS}_{ij}(x)} = \frac{d\ln (x_j/x_i)}{d \ln(f_i(x)/f_j(x))}$$ | $$\sigma_{ij} = \frac{d\ln(x_j/x_i)}{d \ln MRTS_{ij}(x)} = \frac{d\ln (x_j/x_i)}{d \ln(f_i(x)/f_j(x))}$$ |
Unit |
ECC5650 |
Topics |
Gambles, Returns to scale |
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latex error! exitcode was 2 (signal 0), transscript follows:
[JR 2.23] Consider the utility function,
latex error! exitcode was 2 (signal 0), transscript follows:
What restrictions must be placed on parameters, a, b, and c for this function to display risk aversion?
- Over what domain of wealth can a quadratic VNM utility function be defined?
Given the gamble
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show that
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and thatlatex error! exitcode was 2 (signal 0), transscript follows:
.Show that this function, satisfying the restrictions in part (a), cannot represent preferences that display decreasing absolute risk aversion.
Provide a proof that the CES utility function
latex error! exitcode was 2 (signal 0), transscript follows:
actually exhibits constant elasticity of substitution and thus deserves its name.
[JR p.125] Consider the production function
latex error! exitcode was 2 (signal 0), transscript follows:
Show that this function exhibts variable returns to scale;
Find the output level
latex error! exitcode was 2 (signal 0), transscript follows:
for which this function exhibits constant returns to scale.