All Questions
Tagged with optimization utility
63 questions
2
votes
2
answers
3k
views
Utility maximization question setting up.
Consider a consumer whose preferences can be represented by the following utility function: $$u(x_1,x_2)=\dfrac{x_2}{(1+x_1)^2}.$$
Assume the agent's income is $y=5$. The price of one unit ...
- 192
0
votes
1
answer
1k
views
Determining the elasticity of Hicksian Demands
If we have Hicksian (compensated) demand functions, how can we determine the income elasticity and own price elasticity?
Is the procedure the same as for Marshallian (uncompensated) demands?
- 1
1
vote
2
answers
692
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Reservation utility
I am self-studying contract theory using Bolton and Dewatripont (2005). It is meant for grad students, which might be why I am having a difficult time understanding basic terminology. Here is the ...
- 661
0
votes
2
answers
88
views
Optimal taxing in case of negative externalities
Suppose an individual $i$ has the utility function
$U= f(x(i)) - k$(sum of all $x$ with index not equal to $i$)
Where $x(i)$ denotes the miles driven by $i$, and $k$ is a positive constant.
The ...
- 169
3
votes
2
answers
439
views
Indirect changes in Marshallian Demand
Suppose we have a Cobb-Douglas utility function: $$U(x,y)=x^\alpha y^\beta$$ and a budget constraint: $$p_{x}x+p_{y}y=I$$ where $\alpha+\beta=1$.
It can be shown that the Marshallian demand for $x$ ...
- 448
7
votes
1
answer
164
views
Mythbusters - Determine optimal boarding strategy based on time and satisfaction score
Most airlines board passengers starting from the back of the plane and then working their way towards the front (after boarding priority classes and passengers).
In an episode of Mythbusters, Adam ...
- 370
1
vote
1
answer
227
views
Find Indifference curve/s and Marginal Rate/s of Substitution given only one point
Arka likes fries. She wants to consume as much as possible. She consumes either regular (1 oz) or large sizes (5 oz).
Draw her indifference curve through $(x_R, x_L) = (10,0)$ and her indifference ...
- 370
3
votes
0
answers
387
views
Constrained optimization for $u(x_1,x_2,x_3,x_4)=\alpha \min \{a x_1, b x_2\} + \beta \min \{c x_3, d x_4 \}$ [duplicate]
Suppose preferences are represented by the following utility function
\begin{equation}
u(x_1,x_2,x_3,x_4)=\alpha \min \{a x_1, b x_2\} + \beta \min \{c x_3, d x_4 \}
\end{equation}
Write the
...
- 189
8
votes
4
answers
2k
views
Why couldn't the Karush-Kuhn-Tucker optimization find the solution?
I have the following utility maximization problem:
$$\max (xy)$$
$$(x+y-2)^2 \leq 0$$
Conditions:
$$y-2\lambda (x+y-2) =0$$
$$x-2\lambda (x+y-2) =0$$
$$\lambda(x+y-2)^2=0$$
When I set $\lambda>0$, ...
- 1,044
3
votes
1
answer
148
views
Can be the duality theorem applied to not locally non-satiated utility functions?
I have the following not locally non-satiated utility function:
$$U(x,y)=-(x-1)^2-(y-2)^2$$
where $U(x,y): \, \!R^n_+ \rightarrow \!R $
The 3D plot of this function is an infinite paraboloid; ...
- 1,044
3
votes
0
answers
299
views
Optimizing Cobb-Douglas like functions
Economics isn't my home field, but I'm looking for references for a paper I'm working on and I'm hoping one of you can help. Are there many good references for optimizing a Cobb-Douglas like utility ...
- 31
8
votes
1
answer
6k
views
Leontief preferences
I can solve most utility maximization problems using my mathematical knowledge .... but not when it comes to Leontief preferences. I do not have a book to lean on (am self-studying), so would really ...
- 81
6
votes
1
answer
306
views
Optimization of Households' utility in " Rule-of-Thumb Consumers and the Design of Interest Rate Rules " (Gali et al., 2004)
I can't figure out how the calculation of first order conditions was carried out.
I can't figure out where the stochastic discount factor came from.
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