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Which of the following utility functions have the expected utility property? (a) $u\left(c_{1}, c_{2}, \pi_{1}, \pi_{2}\right)=a\left(\pi_{1} c_{1}+\pi_{2} c_{2}\ri...

Question

Which of the following utility functions have the expected utility property? (a) $u\left(c_{1}, c_{2}, \pi_{1}, \pi_{2}\right)=a\left(\pi_{1} c_{1}+\pi_{2} c_{2}\right)$ (b) $u\left(c_{1}, c_{2}, \pi_{1}, \pi_{2}\right)=\pi_{1} c_{1}+$ $\pi_{2} c_{2}^{2}$ (c) $u\left(c_{1}, c_{2}, \pi_{1}, \pi_{2}\right)=\pi_{1} \ln c_{1}+\pi_{2} \ln c_{2}+17$.

Which of the following utility functions have the expected utility property? (a) $u\left(c_{1}, c_{2}, \pi_{1}, \pi_{2}\right)=a\left(\pi_{1} c_{1}+\pi_{2} c_{2}\right)$ (b) $u\left(c_{1}, c_{2}, \pi_{1}, \pi_{2}\right)=\pi_{1} c_{1}+$ $\pi_{2} c_{2}^{2}$ (c) $u\left(c_{1}, c_{2}, \pi_{1}, \pi_{2}\right)=\pi_{1} \ln c_{1}+\pi_{2} \ln c_{2}+17$.



Answers

Which of the following functions $ f $ has a removable discontinuity at $ a $? If the discontinuity is removable, find a function $ g $ that agrees with $ f $ for $ x \neq a $ and is continuous at $ a $.

(a) $ f(x) = \dfrac{x^4 -1}{x - 1}$, $ a = 1 $
(b) $ f(x) = \dfrac{x^3 - x^2 - 2x}{x - 2} $, $ a = 2 $
(c) $ f(x) = [ \sin x ] $, $ a = \pi $


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