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Questions tagged [mathematical-economics]

The application of mathematical methods to represent theories and analyze problems in economics.

2
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1answer
126 views

Showing marginal product of capital is independent of the scale of production

The image is pretty much self-explanatory. To add some context, I'm learning Solow-Swan Growth Theory and my professor said that the marginal product will not change if both capital and labor increase ...
-1
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0answers
7 views

Solve consumer’s problem [on hold]

Suppose a consumer consumes three goods, his utility function is given by $$u=min\{x+y,x+z\}$$ Solve the consumer’s problem i.e. find the optimal consumption bundle. No other information is given in ...
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0answers
26 views

how to relate prices to demand [on hold]

I have two markets 1 and 2 and two firms A and B,The demand is related as demand for firm A in market 1 is equal to demand for firm B in market 2 and demand for firm A in market 2 is higher than ...
-2
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0answers
13 views

Finding Nash equilibrium [on hold]

$n\geq 2$ individuals have to decide how much capital($y$) to put into their firm, they use the following method. Simultaneously each partner $i$ submits a real number $s_i \geq 0$, the amount of ...
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0answers
24 views

Optimation using the Lagrange method [on hold]

How do I solve this problem? Thanks on beforehand.
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0answers
17 views

Maximin from expected utility maximization and common knowledge?

My conjecture is that if 2 agents are in a zero sum game, and they have both agents are Bayesian rational expected utility maximizers. common knowledge of Bayesian rationality and of the structure ...
0
votes
0answers
14 views

how could productvity be measured in oil sector?

the activity in an oil company is composed of 3 parts administrative laboratories (geological search) concessions( workover,drilling) How could productivity of workers be measured in this case ? ...
0
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0answers
35 views

Kink versus a jump in a line passing through origin [closed]

Suppose I have a function defined as follows $n(r) = \begin{cases} n_h \quad \text{if} \quad r< \hat{r} \\ n_l \quad \text{if} \quad r \ge \hat{r}\end{cases}$. Where $n_h > n_l$ and $r \in [0,\...
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0answers
32 views

I don't know how to drive Growth accounting of Labor augmented cobb

Using $Y=F(K,AL)$, I want to know how to derive $$\frac{dY}{dt}/Y = \frac{dF}{dK} × \frac{K}{Y} × \frac{dK}{dt}/K + \frac{dF}{dL} × \frac{L}{Y} × \left[ \frac{dA}{dt}/A +\frac{dL}{dt}/L\right]$$
0
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0answers
17 views

Optimal trajectory of consumption/leisure/work and path integral (variational calculus) approach to total lifetime utility maximization?

Is there connection between the total lifetime (discounted) utility maximization and path integral (functional integral, Feynman integral, variational calculus) approach to the selection of optimal ...
0
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1answer
47 views

Can there be a sample such that SRF and PRF do not intersect?

I am confused if it is possible for to randomly select a sample such that SRF and PRF do not intersect. I have thought of the concept of parallel lines, which allows for such a case but I am unsure if ...
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0answers
12 views

help: basic eoq with perishable items

Consider the following modi cation of the basic EOQ model. When the inventory is at positive level X(t), in addition to demand draining inventory at rate gamma, the inventory perishes (due to e.g. ...
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0answers
13 views

help: eoq model with backlogging with different demand rates

Consider the following modification of the EOQ model with backlogging. When the inventory is positive, demand arrives at rate lamda1; when the inventory is negative, demand arrives at rate lamda2. ...
0
votes
1answer
71 views

Income effect $-\frac{\partial x_i}{\partial m} x_i$ or $\frac{\partial x_i}{\partial m}x_i$?

Recall that the slutsky equation is: $$\frac{\partial x_i}{\partial p_i}=\frac{\partial h_i}{\partial p_i}-\frac{\partial x_i}{\partial m}x_i$$ I know $\frac{\partial h_i}{\partial p_i}$ defined as ...
1
vote
1answer
40 views

What is the concept of ordinal utility?

I have read in many books that since utility cannot be measured - so ordinal concept or comparison concept is used. If that is so, how can one define a mathematical function for utility which gives a ...
1
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0answers
25 views

Anscombe and Auman Expected Utility

I would like to hopefully get some insights on the Anscombe and Aumann Expected utility. I've read some proofs and understood the Expected Utility Theorem (VNM) which allows us to approach consumers ...
2
votes
1answer
45 views

Proving the existence of Nash Equilibrium using alternate approaches

Most of the standard books/papers/reading materials prove/state the existence of a Nash Equilibrium by appealing to Sperner's Lemma, or to Brouwer's/Kakutani's FPT. However, I've recently come to know ...
4
votes
1answer
66 views

Deriving average productivity from a CES production function

Following the work of Raurich et al. (2012) I got stuck trying to derive the average productivity starting from the following CES production function: $$Y=A\left [ \alpha K^{\frac{\sigma -1}{\sigma }}...
0
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0answers
22 views

How to find cross price elasticity of demand in case of two perfect substitutes? Please give a mathematical intuition

I saw somewhere that Cross price elasticity of demand in case of perfect substitutes is $\infty$. I do not think that this is right in all the cases. Even if it is, please give a mathematical ...
0
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0answers
16 views

Showing continuity and strictly increasing U for Indirect Utility and Expenditure Function?

Hey I'm having trouble with this question from my problem set. I think intuitively I understand why the underlying utility has to be strictly increasing and continuous but I'm not sure how to show it ...
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0answers
36 views

Applications of Pure Mathematics in Economics

Are there any applications of number theory and abstract algebra in economics? An economist had told me that number theory had an application to a theorem in economics, however he did not remember ...
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0answers
31 views

Mean Field/Differential Game and Measurability

Consider the following scenario. There is a continuum of players in a population, with population measure normalized to $1$. Each player has a type $\theta \in [0,1]$ and we suppose that $\theta$ is ...
2
votes
1answer
88 views

Is this Cost function concave or convex?

Given the following cost function, where t is the quantity of some product. $$C(t) = 1/3t^3 - 7t^2 +11t + 50$$ here is a graph between $t= 0$ and $t = 25$ We are asked if this function is convex or ...
8
votes
1answer
61 views

How likely are the Sonnenschein-Mantel-Debreu results?

I have been reading about the SMD results and it's "damning" nature for GET. My understanding of the result is as follows: price changes not only cause a substitution effect but also change the wealth ...
2
votes
1answer
72 views

Help needed to understand proof in Myerson and Satterthwaite (1983)

The following image is an excerpt taken from Myerson and Satterthwaite's 1983 paper Efficient Mechanisms for Bilateral Trading: I know what the theorem is all about, all I need is some help with the ...
0
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0answers
32 views

Help me solve this?

Suppose the market for railing is competitive. The demand function is given by Q=120-2P, FVF projecting is active in the market and faces a cost function C(Q)=200+2Q+0,5Q^2. a) What is the optimal ...
1
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0answers
14 views

Value of companies with circular ownership [duplicate]

Given two companies, total assets of $100 million each. Company 'A' owns \$50M of company 'B'. Company 'B' owns \$50M of company 'A'. If you look at the value of both companies do you ...
3
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0answers
16 views

How should I calculate bulk selling price for a small business?

Some friends of mine run a small business, in a small garage-like space, with a few employees, making and selling "plumbuses". The typical customer orders about 5 plumbuses at a time. When I heard ...
1
vote
1answer
32 views

Purpose of Semidefinite Integral

I want to know the meaning of Semidefinite Integral. I am used to read definite and indefinite integral but I want to know the meaning of such equation : $\pi(e)\left(1-F\left[-\frac{a}{\pi(e)}\...
1
vote
1answer
44 views

Simplest model of an economy exhibiting (hyper)inflation

I would like to find a minimal mathematical model for describing financial crises of the type that produces hyperinflation. Here's a naive attempt, just to give the idea of what I'm thinking of. ...
2
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0answers
36 views

Open Foundational Problems in Mathematical Economics

What are some open problems in mathematical economics which are treated as if they have been solved in economics papers? As an example, one of my teachers has previously pointed out to me that there ...
2
votes
1answer
103 views

Euler's Theorem

Can anyone give me connection and intuition behind each of the following euler's equation- Euler's equation in production function represents that total factor payment equals degree of homogeneity ...
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0answers
29 views

Including definite integrals inside definite integrals - Crossposted from MathSE

This question is cross-posted from MathSE: link I have the following differential equation from a journal article: $\dot{g}(t) - \delta(t)g(t) = -H(t) --- (1) $, which is integrated between t and T. ...
0
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0answers
18 views

Is delivery-capability (in economics) a probability?

A dealer with a large, but finite stock counts for 1 year a = the number of all purchase inquiries that reach him this year and b = the number of purchase inquiries that he can deliver on the ...
0
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0answers
204 views

Is Gaussian distribution the proper choice for step in financial time series? E.g. DJIA ROI suggests Laplace instead

Data compression uses Laplace distribution ($\rho=\exp(-|x-\mu|/b)/2b$) for probability distribution of differences, while I see it seems economy uses Gaussian distribution everywhere (?), e.g. in ...
0
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2answers
38 views

How do I calculate the amount of money I get from an investor and the percentage I give him in return?

Let's say I owe a company. At the final state I want to be left with 1M cash for myself and 50 percent of the company. The investor is not willing to buy shares and give me the money but only invest ...
0
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0answers
31 views

Is this way of modeling undisclosed debt correct?

I am woking with a model like the one in Alfaro and Kanczuk (2006), that is in turn based in Arellano (2008), where sovereign´s preferences are given by: that in case of not defaulting is subject to: ...
0
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1answer
17 views

Devising a model for inflation for a closed points system

I am working on a project that involves points. The idea is that users will earn points and redeem them for certain rewards. The means via which the users earn are fairly limited (They can attend a ...
2
votes
1answer
34 views

How does this demand function satisfy the Weak axiom if it doesnt satisfy the necessary and sufficient conditions?

Let $x_k = \frac{w}{\sum{p_l}}$ for $k = 1...L$ be the demand function. This demand function does satisfy the weak axiom and this can be shown simply. The slutsky matrix is an $L \times L$ matrix ...
1
vote
1answer
111 views

Did I calculate the expected value and the variance correctly?

I have the following assignment to solve but I'm not sure if I solved it correctly. Questions Let the stochastic process $(Y_t)_t$ be defined by $Y_t = \mu + Y_{t-1} + \varepsilon _t$ with $(\...
41
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21answers
10k views

Criticism of Math in Economics

I've been reading and speaking to a number of educated economists and economics PhDs who are against the use of intense mathematics and mathematical proof in economic theory. Specifically I've been ...
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0answers
184 views

How can I determine if a token economic is viable?

Given a system where you incentivize people to do actions in a system, we might have good and bad actors. I would like to know if there is a software or framework where I could put the different <...
1
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0answers
26 views

Deriving Single Good Demand Curve

came across a problem set that I had no clue how to tackle, but looks painfully simple. It's a market for electricity where households utility is represented by: U(E) = aE - 2mL2 (Household Utility) ...
1
vote
1answer
181 views

Prove all cost functions are concave in input prices and demand for inputs is downward

I've seen proofs that cost functions are concave of the form $C(\lambda w + (1-\lambda)w',q) \ge \lambda c(w,q) + (1-\lambda)c(w',q)$ although this neither feels convincing nor does it seem like a ...
1
vote
1answer
33 views

Simple Regression With Dummy Variable

Consider a simple linear model: $Y = \beta_1 + \beta_2 MALE + u$ where $MALE$ is a dummy variable. $MALE = 0$ if female, $MALE = 1$ if male. A model is fitted: $\hat{Y} = \hat{\beta_1} + \hat{\...
1
vote
2answers
63 views

Demand curve confusion

My economics textbook says that demand curves slope downward - but then goes on to say that when demand increases, prices go up! Does anyone else find this confusing? Edit: from the small number of ...
4
votes
1answer
51 views

Interpretation of the Cross Partials of the Cobb-Douglas

Consider a Cobb-Douglas Prod. Function $$Y=AL^{a}K^{1-\alpha}$$ This has the cross-partial: $$\frac{\partial^2 Y}{\partial K\partial L}=(1-\alpha)\alpha AL^{\alpha-1}K^{-\alpha}$$ Is the ...
2
votes
1answer
57 views

Proof of DCF model by mathematical induction

I am confident with the concept of DCF. However, I wanted to check the following proof given that if investors hold a share in $ t $, sell it at $t+1$, receive dividend $\ D_{t+1} $ and the price at $...
1
vote
0answers
117 views

Firm's profit max problem, in present value terms

So I am kinda stuck on this question. The question goes as follows: Consider a multiperiod firm, selling q1 units of a product in period t=1 at spot price P1 and q2 units in period t=2 at spot price ...
4
votes
2answers
80 views

General model of economics, economics as mathematical structure

Contrary to the common view, the physics is all about models, there are no such thing as law of nature, because every physical law has its applicability range and therefore all of laws as models. But ...