For questions regarding the mathematical analysis of economic models and problems. This includes questions about the formulation or solution of models from microeconomics or macroeconomics.
Questions tagged [economics]
1602 questions
14
votes
3 answers
Can someone explain Cremer-Mclean's astonishing result in auction theory?
In mechanism design/auction theory, there is a famous result by Cremer and Mclean that if agents'/bidders' valuations are even slightly correlated, then all the surplus can be extracted by the principal/auctioneer. This is what makes auction theory…
Zermelo
10
votes
1 answer
How to minimize game night transactions?
Me and a number of friends occasionally met up and play some game (often pool or some card game) and play for small stakes to give the game a little extra spice. After each round we jot down the results of the round to keep tally of who owes who how…
erikxiv
- 201
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4
votes
1 answer
Sanity check: Is my teacher wrong about this word problem?
I'm taking Engineering Economy this semester. I'm actually liking it so far!
My teacher posted solutions to homework problems (picture 3), one of which was this one:
My answer is this:
$$P = \$4000, i=10\% $$
$$F = P + P(1 + i)$$
$$= \$4000 +…
Werewoof
- 325
4
votes
1 answer
What's the most straight-forward way to prove Walras's Law?
Walras' Law states that summation of pi Ei(p) = 0 for all pi.
We define Ei(p) = xi(p) - qi(p) - Ri.
What are the next steps that I should take?
user7087
3
votes
1 answer
Euler Equation and Marginal Rate of Substitution
I was wondering if someone could help me clarify a result from my lecture notes. I have put them as a picture. It concerns the result on the last slide (the other three slides are included as well because it may be useful).
The problem is, I do…
user133993
- 651
3
votes
1 answer
distinguish homogenous and homothetic
I am not sure how to distinguish whether a function is homothetic.
For example,
Q1.
$$
U(x,y) = a\log(x) + b\log(y),
$$
Q2.
$$
U(x,y) = \exp[(x^a+by^a)^3 +r]
$$
I can understand that these two functions are not homogenous.
But i don't know why…
ssandi
- 91
3
votes
0 answers
A question about "welfare independence"
I am working on some applications of measures of inequality (economic inequality). Upon reading a paper by Kolm (Kolm, S. C., Unequal Inequalities I, Journal of Economic Theory, 12 pp 416-442, 1976) I found a result that I found intriguing and for…
Mittens
- 39,145
3
votes
0 answers
Determine Capacity for Airline Membership Model
I am trying to determine a simple calculation for capacity for one single 747 plane -- there are 200 seats on the plane and the plane flies twice per day, every day of the year.
If there was a membership model where each person had a an allotment…
zkidd
- 131
3
votes
0 answers
A car is to be purchased in monthly payments of $19500$ for five years starting at the end of three months. How much...
I was helping my comrade answer some questions when we found this question. It goes like this:
A car is to be purchased in monthly payments of $19500$ for five years starting at the end of three months. How much is the cash value of the
car if…
fitzmerl duron
- 1,495
3
votes
2 answers
From which areas of mathematics does consumer theory in microeconomics spawn?
In my intermediate microeconomics class last year, I was rather surprised by the math involved in building consumer theory. In consumer theory you do things like define a binary relation $\succsim_a$ over a set of outcomes $X$ where $x\succsim_ay$…
crf
- 5,551
3
votes
1 answer
How to find Pareto-improvements with maths?
I hope this is not off topic.
I've got two utility functions for two different kinds of agents, A and B, and their endowments ($w_1$ and $w_2$) of the (2) goods ($x_1$ and $x_2$).
The utility functions are:
$U^A={x_1}^{1/2} {x_2}^{1/2}$
$U^B=2log…
Luigi
- 305
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- 14
2
votes
1 answer
No theft model of corruption
Consider the model of corruption explored by Shleifer and Vishni’s where there is one
government-produced good $X$. There is a demand for that good described by the inverse
demand equation
$$Q_d = 10 – P.$$
The official government price for the good…
2
votes
1 answer
Use Roy's Theorem to prove that ...
I have an advanced microeconomics theory related question:
Use Roy's theorem to prove that $s_i(p,y)= -\frac{\partial v(p,y)}{\partial lnp_i}/\frac{\partial v(p,y)}{\partial lny}$.
This question has been bothering me for quite sometime now and so I…
user87274
2
votes
0 answers
Fair apportionment of a single resource over time
Suppose there is a single, indivisible resource that can be used or enjoyed by just one of two parties at a time. You can imagine a field of crops that can be plowed by just one of two farmers in any year. My question concerns the equitable…
David G. Stork
- 29,774
2
votes
0 answers
Proving local non-satiation in arbitrary metric space
I have a pure exchange economy where every consumption set $X_i$ is non-empty and convex and every preference relation $\succeq_{i}$ is strictly convex. I am asked to show that preferences are locally non-satiated at any consumption bundle different…
Charles
- 705