# Questions tagged [mathematical-economics]

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

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### Macroeconomics for Mathematicians

I'm coming from a math background (so my mind is set up for Definitions-Observation-Lemma-Proof frameworks) and looking for recommendations of a Macroeconomics textbook mainly devoted to growth models ...
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### Simple General Equilibrium Model of Public Goods: Intuition?

We assume a two person economy, denoted by person A and B. Good y is an ordinary private good, and each person begins with an allocation of this good given by $y^{A*}$ & $y^{B*}$ respectively. ...
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### Minimizing consumption in a single market( Partial Equilibrium)

Let there be a good X where the optimal consumption is 0; i.e the social costs for any unit provided would always be greater than the utility surplus of the market. We know that prohibiting it( ...
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### Calculating elasticity between log term and non-log term [duplicate]

Given the following, I am asked to calculate the elasticity of wages with respect to age: $$𝑙𝑛(𝑤_𝑖)=𝛽_1+𝛽_2𝑎𝑔𝑒_i+𝛽_3𝑎𝑔𝑒^2_𝑖+𝛽_4𝑌_𝑖+𝛽_5𝑇_𝑖+𝛽_6𝑀𝑎𝑟_𝑖+𝜖_𝑖$$ How does one ...
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### Calculating elasticity between terms in a regression equation

Given the following regression: $ln(w_i)=\beta_1+\beta_2age+\beta_3age_i^2+\beta_4Y_i+\beta_5T_i+\beta_6Mar_i+\epsilon_i$ I am asked to calculate the elasticity of wages with respect to age. Is the ...
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### Why can utility functions be continuous, and what does this imply for marginal utility?

I am studying microeconomics at the introductory undergraduate level and two related but distinct questions are puzzling me. First, my textbooks express utility functions as continuous functions by ...
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### When to use a lagrange multiplier?

I have a question in regards to the use of Lagrange multipliers in macro models. I have seen that when writing a Lagrange there are two ways to write the Lagrange multiplier: 1) Indexed or 2) ...
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### Notation? Inverse of demand function

I'm looking through The Investment Decisions of Firms by S.J. Nickell, and I've come across some notation that I don't quite understand. Any clarification would be very welcome. Nickell first assumes ...
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### Supply and Demand plotted on a three dimensional Cartesian coordinate system

Is it possible ? if it's possible can someone give me a reference ? Thanks !
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### Is there an index, parameter, ecuation, or anything to compare the tax pressure exercised by a country in relation to others countries?

In my country we are told often that the tax pressure over the companies and people is huge, making it unbearable and being a reason bankrupting the Economy, and one of the largests in the world. We ...
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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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### 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 ...
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### 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 ...
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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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### How do you calculate the intrinsic value or fair value of real estate?

How do you calculate the intrinsic value or fair value of real estate? I mean how do you determine that the house/commercial estate is undervalued or overvalued?
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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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### 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 ...
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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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### Why decreasing co-state variable (over time) is Compulsory?

I have a short question. In the continuous time infinite horizon optimal control maximization problem Like $$\max \int^{\infty}_0 u(c_t)e^{-pt}dt$$ I use current hamiltonian function and I obtain ...
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### What is the economic interpretation of the solution of this optimal control problem?

I have the following optimal control problem $$\max_{c_t} \int^{\infty}_0 e^{-p_it}\ln(c_t(i))dt$$ subject to $$\dot{w_t}(i)=rw_t(i) -n_ic_t(i)$$ $$w_0(i)=w_0>0$$ I have some wealthy and ...
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### Is it possible to have a preference relation that is complete but not transitive?

I've been doing my own reading on non-rational preference relations. I'm currently under the impression that transitivity follows as a direct result of completeness of preferences. However my (much ...