# Questions tagged [economics]

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.

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1 vote
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### A Basic Question of Continuous Time Macroeconomic Model (Variation of Constant to Solve an ODE)

I am going through the continuous time macro slides by Ben Moll (link is: https://benjaminmoll.com/wp-content/uploads/2019/07/Lecture2_ECO521.pdf), when deriving New keynesian model in continuous time,...
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### Inflation Calculations Skewed by low prices.

I am currently calculating inflation metrics for a retail store. I am simply using their POS data, to calculate the Year-Over-Year price change of each item. I then weight this on the sales, sum it up,...
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### What are some common distributions assumed for approximating a demand curve?

A demand curve is a function $d(p)$ such that at price $p$ the demand for the good is given by $d(p)$. This means that you are making a sales of $p\cdot d(p)$ at price $p$. For typical goods, demand ...
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### A put option and a call option with identical exercise price are both marketable or neither is.

I am doing Exercise 1.13 in Introduction to Mathematical Finance: Discrete Time Models by Pliska. Exercise 1.13 Suppose the interest rate $r$ is a scalar, and let $c$ and $p$ denote the prices of a ...
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### Is there any book "economics for mathematicians"? [closed]

If you search economics book there are plenty of them on the market. We may say the say about "mathematics for economists" or "application of mathematics in economics". But I've ...
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### Trying to find why solutions to both maximization and minimization problems exist before even solving it [closed]

There is a problem which I have been thinking about but can't come to a conclusion. And Final exam is tomorrow: enter image description here My attempt: To find solutions to both maximization and ...
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### Why is the GST for the wholesaler based on the marked price? We don't know if that is the cost price.

The price of a sewing machine is Rs.40000.The wholesaler allows a discount of 10% on it to the shopkeeper. The shopkeeper sells the sewing machine to a customer at a discount of 5% on the marked price....
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### Taylor Expansion for the Return averaged over k periods? [closed]

this is my first question here. I need help to understand the Taylor Expansion which gives the (2.2.5) equation (see the pictures). Thanks (pictures from: Schmidt - Quantitative Finance for Physicists....
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1 vote
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### Regression relation to casual relationship

If the correlation coefficient of two variables is 0, can there still be a causal effect between them? And can the causal relationship between these two variables be studied by regression analysis?
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1 vote
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### What does it mean to "solve forward/backward" a differential equation?

I know what it means to solve forward/backward difference equations. What I have not been able to wrap my head around is how that formally makes sense in continuous time. To make things concrete, here ...
116 views

### Derivation of index decomposition analysis

I’m currently reading a paper on index decomposition. The paper is here for reference : https://www.sciencedirect.com/science/article/pii/S0140988315001772 The paper is setting out how it has gone ...
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### How do you allocate based on historical outcomes when these can be both positive and negative?

I would like to allocate an expected yearly return based on the monthly outcomes of last year. However, these monthly outcomes can be both positive and negative. For example (year 3 in the image), the ...
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### Combining Math and Reading Test Scores presented in standard deviation units from the mean (mean not given)

I am working with a large dataset for regression purposes and am attempting to predict test scores using various societal / demographic factors. There are two scores, math and reading, that I am ...
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### How to prove $\{(x_1,x_2)\in\mathbb{R}^2\mid u(x_1,x_2)\geq u^*\}$ is closed? [closed]

I have the following problem: (continuous function) Suppose that we consume non-negative amounts of a good $1$ and good $2$, namely, $x_1$ and $x_2$. The utility from consuming $(x_1,x_2)$ is defined ...
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### Basic log-linearization

In the first equation I can't figure out where the $1/x$ part comes from... When using first-order taylor approximation arount $x_t = x$, I just get $ln(1)*(x_t-x) = (x_t-x)$ Thank you for your help!...
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### How to prove that any preference relation on (countable) X has a utility representation with a range (0,1)?

Theorem: If $X$ is countable, then any preference on $X$ has a utility representation with a range $(0,1)$. The stated proof in Rubinstein's lecture notes: Proof: Let $\{x_n\}$ be an enumeration of ...
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### Pair Matching Algorithm Ideas?

I am trying to work out a small task where I need to match up a sequence of events that have offsetting scores and see if there is a better theoretical framework to solve this in a more efficient way ...
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### How to represent probability in the matrix payoff?

I need to build a 2x2 matrix of the game payoff. There are 2 players A and B that can play 1 or 0 simultaneously. I have a rule that in the case of both players playing 1, the award equal to X may be ...
1 vote
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### First order condition (consumer problem) [closed]

Can you help me find the first-order condition of the following problem with respect to α: $max[u(C_t) + δ *E_t[u(C_{t+1})]]$, such that: $C_t=e_t-αp_t$, and $C_{t+1}=e_{t+1}+αX_{t+1}$ For context ...
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### Solve optimization problem using KKT method

Question: Solve the UMP $${Max} \quad u(x,y) = ln(x+1) + ln(y+1)$$ $${s.t.}\quad p_1x + p_2y \leq w$$ $$x,y \geq 0$$ Then the Lagrangean function is L = ln(x+1) + ln(y+1) +\lambda(w - p_1x - ...
1 vote
### Prove that the stochastic process $s_t$ follows a normal distribution where the mean and the variance are functions of time in each case.
The two basic models of finance are the following: $\textbf{The Samuelson SDE (aka Black - Scholes - Merton model):}$ Suppose that $Z=\left(Z_t, t\in\mathbb{R}^{+}\right)$ is a Wiener process (aka ...