# Questions tagged [mathematical-economics]

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

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### Shortcuts for elasticity of substitution

How can I find the elasticity of substitution (I know the definition) if I know the utility function $u(x,y)$? I know its increasing in $x$ and $y$, etcetera, and has everything else you want from a ...
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### Definition of covered market

I do Industrial Organization course, and I've seen the phrase "market is covered" several times in my lecture slides, however, I'm struggling to find the formal definition of "covered market" and the ...
26 views

### Equations of “rational mechanics” and general equilibrium

Vilfredo Pareto, referring to the equations that determine equilibrium, wrote: These equations do not seem new to me, they are old friends. They are the equations of rational mechanics. This ...
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### Annual Fraud Recovery Over Time: Should I adjust for inflation?

I have a dataset of the total amount the U.S. Department of Justice obtained annually in settlements/judgments of government fraud cases from fiscal years 1988-2019. There's a lot of variation, but ...
25 views

### For the case of two goods, give an example of preferences that are represnted by a continuous utility function that allows for fat indifference curves

The question in the title sounds like a trick question, due to the monotonicity property that indifference curves have, such that for two goods x and y, strong monotonicity implies y > x. Possible ...
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### How are low/middle/high classes defined mathematicaly?

I am only looking for mathematical references. I think this belongs to econometrics but am not sure nor where to look at it specifically. I suspect the definition is given with some kind of weighted ...
14 views

### dynamical system of consumption nontrivial steady state [closed]

Consider the following dynamical system of consumption (ct) and wealth (wt). ct+1/ct = 1 − β(ct/wt − α) wt+1 + ct = θwt + γ Here, all Greek letters denote fixed structural parameters that are ...
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### Linearization of the dynamic system (I did it, but I have a mistake that I cannot catch. Help me please)

I have the following dynamic system in discrete time For p is price, d is demand and s is supply. $$p_{t+1}-p_t= a(d_t-s_t)$$ $$s_{t+1}-s_t=bp_ts_t-ws_t$$ $$d_t= k-gp_t$$ I have to linearize this ...
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### Determine lot size with extra constraints and EOQ formula

Given a fixed price of 250,00 dollars for the warehouse and the price of the product is 5,00 dollars per product. The order cost is 500,00 dollars but if more than 1000 products are ordered then it ...
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### Mathematical framework for modelling the relationship between price and sales of a product

In my job as a data scientist, I am required to model the relationship between the price of a product and the sales or number of unit sold. I am trying to build a simplistic model, the assumptions of ...
40 views

### What guarantees that endowed agents have non-zero prices in an Arrow-Debreu Economy

In my research I am trying to find minimal conditions to guarantee a quasi-equilibrium must always be a typical Arrow-Debreu equilibria in a rather specific production setting. This may be rather ...
63 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 ...
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### A question on the accuracy of economic forecasts

I apologise if thi's question appears dumb or boring, but I am asking it as a lay person. The context is that I am always arguing with friends that they should trust the economists view that Bexit (...
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### How do we define an efficient tax in microeconomics?

I am currently working through problems to study for an upcoming exam. I am not seeking a solution per se. I am looking at the intertemporal choice model. I am looking at two periods where consumption ...
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### How to test if the effect of one regressor entirely comes from other regressors?

I have a regression model that includes IQ test scores as the dependent variable; my own education, my father's education and my mother's education as independent variables. Suppose I want to know ...
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### Karush-Kuhn-Tucker in infinite dimension

Does the Karush-Kuhn-Tucker theorem on sufficient conditions for optimality of a convex program apply in countable dimension? For precisions, see Definition 4.1.1 and Theorem 4.1.4 of this course. ...
44 views

### Regarding the Expenditure Function Underlying a Bliss Point

I've been looking at expenditure systems and have been really interested in the behaviour of the demand system that underlies bliss points: Consider the bliss point utility function of the following ...
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### Interpretation of dummy variable : Random Effects Model

I am running a RE regression and I have export similarity index between two countries as the dependent variable and have a dummy variable such as share a border(=1 if countries share border, 0 ...
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### Existing metric for personal productivity hours needed per life hour?

With about 50 hours of productivity a week, including work, cooking, etc. I can complete the tasks and pay the expenses necessary to live about a week. Subtract maybe 5 hours of labor that goes into ...
51 views