# Questions tagged [mathematical-economics]

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

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### homothetic functions in economics

Are there any results in economics that require function to be homothetic? The textbook I am using (Essential Mathematics for Economic Analysis) says that function is homothetic when " $f(x)=f(y)$...
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### Would some help me fill in missing steps from a textbook exercise left for the reader

Question: Suppose $C_t=(1-s)Y_t-\lambda G_t$ where $s>\sigma$ as in the basic Solow model. Out of the government expenditure , proportion $\phi$ is invested in public capital formation. Hence we ...
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### Can we model risk with only probability?

Sorry for the confusion! I am adding an example to see if it helps: For example, consider a gamble A, with payoffs {a,b,c,d}, whose probability of each payoff being realized is equal (so 25% each); ...
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### How to find $\phi$, that denotes the correlation of signals among informed traders?

Since I do not have an answer on Quantitative Finance in my question I cross-post here the problem to tag some other categories The following assumptions are part of the paper of Back, Chao and ...
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### Showing utility function gives preferences that are rational and convex

Consider a consumer with preferences relation $\succsim$ over non-negative commodities $x_1$ and $x_2$ such that their utility U = $x_1$ + $\ln(x_2)$ Are these preferences rational and are they convex/...
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### How can I model my problems with math?

I want to ask a question about mathematical economics. When I read an article about economics, I see lots of mathematical equations. I can solve them without any help. But I can't create my own ...
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### Leontief input output model with column sum greater than 1

In a linear algebra textbook I came across the following question (not included in the answer key): Consider an open economy with a consumption matrix \begin{equation} C = \begin{...
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### Auction with one buyer and multiple sellers

In the standard auction model, there are one seller and multiple buyers, the bidders are the buyers. Consider now an auction with one buyer and multiple sellers, where the bidders are the sellers. ...
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### How can I know whether a good is inferior or normal? I can't determine elasticity with this?

I just need to make sense out of elasticities and how to determine if a good is normal or inferior. I have determined by $X_1$ which is in the form $m/p_1 - p_1/p_2$, that I should just take the ...
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### When do prices not exist?

Often we employ the use of the separating hyperplane theorem to prove existence of price vectors, when discussing infinite economies this proof is substituted for proving existence of linear ...
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### Derivative of definite integrals - how did MWG arrived at this result? Microeconomics

For a wage as a function of profit: $w(\pi)$ and profit $\pi \in [\pi_{min},\pi_{max}]$, the owner of a company sets the minimum wage to satisfy the following condition: obs $e = \{e_l, e_h\}$ but in ...
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### Bothersome Mean/Variance Analysis

I'm currently writing my thesis in which I compare a series of ESG General Equilibrium models. I fell over this proof in Pastor, Stambaugh, Taylor Sustainable Investing in Equilibrium (2019) page 42. ...
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### HARA preferences details

I am searching for some exntensive details about HARA preferences. Where could I find some extensive details for HARA preferences? Something like a textbook or notes
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### Lorenz curve extension to 3d?

While thinking about Lorenz curves and economic inequality I wondered if you can extend Lorenz curves to Lorenz surfaces by revolving a Lorenz curve about the line of perfect equality. Would such a ...
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### Tax multiplier in IS-LM model

I should consider a following modification of IS-LM model: IS curve is standard: Y = C(Y-T) + I(r) + G In LM curve the demand for money depends now on after tax income: M/P = L(r, Y-T) Price level is ...
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### Nash in demand functions!

I am searching for some types of games that are played in linear demand functions. Altough I hear that there is a vast literatrure for games that are played in the intercept or the slope of the demand ...
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### What are the mathematical prerequisites to understand Whinston and Green's “Microeconomic Thoery”?

I've completed my under graduation in economics where I used micro books like Nicholson and Snyder's Microeconomic Theory and Hal Varian's Intermediate Microeconomics. I am comfortable with topics ...
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### What is the difference in estimation between A, B, and C? They seem very similar [closed]

This is a question in our econometrics class, and we're unsure of how to deal with the additional z2 and z3 in part B and part C.
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### How was the Cobb Douglas function derived?

In economics and econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the ...
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### What is the math behind the coefficient of Absolute Risk aversion? [duplicate]

I have a good grasp of Calculus but I have never used the ratio of second and first derivatives. So, I am having a hard time understanding what it does and how?
Given the marginal rate of substitution of $x$ for $y$ : $\frac{u'(x)}{u'(y)}$ I know one can interpret this as the amount of $y$ one is willing to give up for an additional unit of $x$, or the ...