New answers tagged utility
6
votes
Accepted
Does Debreu's representation theorem of ordinal utility require Hausdorff topology?
No. However, the problem can be reduced to representing preferences on a Hausdorff space. Instead of trying to represent a complete preorder on a set, one can try to represent linear orders on the ...
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3
votes
Accepted
Constrained optimization to find utility maximizing allocation
I think you are trying to find a feasible allocation that maximises the sum of the utilities of the two individuals. So we can write the objective function as:
\begin{eqnarray*} \max_{x,y} & \ xy^...
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1
vote
Calculating price in a pure exchange economy
Let $\omega_1 = (\omega_{1}^X, \omega_{1}^Y)$, and $\omega_2 = (\omega_{2}^X, \omega_{2}^Y)$ be the endowment of the two consumers, respectively. Also, their utility functions are
$u_1(x_1, y_1) = x_1$...
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2
votes
What is the assumption behind "indifference curve does not cross"?
Consider any utility function $u: \mathbb{R}^2_+ \rightarrow\mathbb{R}$. Indifference curve for satisfaction level $\mu$ is defined as:
$\text{IC}(\mu) = \{(x, y)\in\mathbb{R}^2_+|u(x, y) = \mu\}$
I ...
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2
votes
Convex Preference but Convex Utility
Example given by Herr K. is perfect. Let me give another example of a dis-continuous utility function which is quasi-concave, but not concave.
Consider $u:\mathbb{R}^2_+ \rightarrow \mathbb{R}$ ...
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2
votes
Demand correspondence is both upper and lower hemi-continuous; is the preference continuous?
If the commodity space is $\mathbb{R}^2_+$ and the preference is Lexicographic, then with the standard budget sets $B=B(p_X, p_Y, M) = \{(x, y) \in \mathbb{R}^2 | p_Xx + p_Yy \leq M\}$ where $(p_X, ...
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3
votes
Accepted
Constant relative risk aversion for wealth spanning from negative to positive
I'm afraid the answer is no. Let's take any continuous and strictly increasing utility function $U(W)$ which is twice differentiable almost everywhere on the reals. Constant relative risk aversion (...
- 4,457
1
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What are some examples of goods/services whose utility functions have local maxima?
Such a point where utility is a local maxima is called a satiating point.
Think of a good that turns into a bad beyond a certain amount. Most non-tradable consumables goods are of such kind, where ...
0
votes
Reservation utility
It easier to understand this intuitively if one looks at μ as relative bargaining strength. Higher the bargaining strength, higher is the weight attached to their utility in the joint maximization ...
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5
votes
Accepted
How can I show convexity of this value function?
Suppose that $u(C,l)=\sqrt{C}-l^2$ and $f(l,A)=\big(l+g(A)\big)^2$, where $g$ is any function of $A$ that is not convex.
Then $$u\big(f(l,A),l\big)=l+g(A)-l^2.$$
The optimal labor supply is given by $...
- 9,190
2
votes
Accepted
risk aversion and the law of diminishing marginal utility
If your preferences over lotteries satisfy the vNM-axioms, i.e. if you are an expected utility maximizer, then you cannot be risk averse and at the same time not have diminishing marginal utility of ...
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0
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risk aversion and the law of diminishing marginal utility
I used to ask my students if they preferred getting \$4 with probability 1 or \$10 with probability 1/2 and \$0 otherwise. Most students went for the gamble. When I asked for their reasoning they said ...
- 26k
2
votes
risk aversion and the law of diminishing marginal utility
Risk aversion means that, when faced with a risky alternative and a sure alternative whose value is equal to the expected value of the risky one, the sure alternative is weakly preferred to the risky ...
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