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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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9 views

Estimating multivariate random walk plus noise model using OLS

I'm currently working on replicating a scientific paper for practice in which they estimate a multivariate random walk plus noise model, apparently using OLS. I have no clue however how they would do ...
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2answers
38 views

How reasonable is the linearity assumption in regression analysis?

As someone who moved from physics to economics, there are some things about regression analysis that have always bothered me. One of the most basic assumptions in econometrics is that for studying the ...
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44 views

Is this Forex trading algorithm flawed?

I'll try to explain this the best I can, I'm sorry for my lack of economic concepts and terminology. There's a Foreign Exchange Market where a trader gets to make predictions about the currency ...
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1answer
12 views

Deriving a demand function from a specific utility function

Let's say I have a utility function of the form $Ax^b + Cx^d$. Now I would like to find the consumption depending on the price for one unit of good $x$. This means for any given $p$ I would maximize $...
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10 views

Recommended books about the problem of investment-consumption with a mathematical point of view

i looking for some material about this microeconomic problem with a numerical analysis point of view, so without stochastic processes. The core of the problem is maximize the utility funtion.
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Question based on cobweb differential equation [closed]

Solve the differential equation via cobweb theory $$ Y_t -0.5Y_{t-1}=20 \qquad \text{If}\qquad Y_0=10 $$
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6 views

The formula of CCI (Commodity Channel Index) indicator in stock market and the mathematical proof of it.

I am looking for the formula of CCI oscillator and the mathematical proof. If you can advise me some references, I am really thankful! Thank you so much!
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0answers
20 views

Brownian motion to model future asset values

https://quant.stackexchange.com/questions/45104/brownian-motion-for-modelling-future-asset-values Assume that an asset price $S$ is given by a Brownian motion. Argue from the definition why it is ...
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1answer
16 views

how to compute rating score based on votes

What is the formula to compute the rating score based on votes. Imagine each person can vote between 1 to 10. Now I have 20 votes from people. the results look like this: ...
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1answer
15 views

Derive short-run demand function?

Suppose a firm pays £500,000 in short-run costs for its capital and unskilled labour. Its only short-run decision, therefore, is to determine how many high-skilled workers, E, to hire. The wage ...
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1answer
32 views

log-transforming and finding partial derivatives

I trying to set up an economic model of trade, and i have a question regarding the partial effect of one of my variables that is logged along with my general function $X$. My model of bilateral ...
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1answer
21 views

Maximizing utility function

Consider a world where people live for up to three periods. In the first period each person earns 10. In the second period, each person earns 20. Earnings in the third period are 0. Assume that utility ...
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2answers
35 views

Construct portfolio given certain payoff function

My question is similar to https://quant.stackexchange.com/questions/37419/replicate-a-portfolio-with-given-payoff but I am not quite sure how to apply this to my problem. A portfolio of European ...
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1answer
27 views

How to calculate elasticity from a demand function? [closed]

PROBLEM PLEASE CLICK ---I've added a picture of the problem I am trying to solve, to make it easier to understand. With this sort of problem, I do not understand where the numbers needed for the ...
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0answers
26 views

Looking for a book about mathematical proof of technical analysis in trading stocks!

I am looking for a book which contents mathematical proof of technical analysis in trading stocks! I have read a lot about techniques in trading stocks, but never that they prove it. I am really ...
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1answer
25 views

Find profit from marginal profit

The marginal profit of a certain company is given by $$y ' (x) = \frac{100}{32-4x}$$ where $x$ represents the amount of money (in thousands of dollars) that the company spends in advertising. Find the ...
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if $x^*$ and $A^*$ maximize $px - c_x x - c_a A$, then are $p(A^*)x^* - c_xx^* - c_aA^*$ and $px^*(A) - c_xx^*(A) -c_aA^*$ equivalent

where $b$ and $c$ are strictly positive constants. Is the statement in the question correct, perhaps for some specific $x(A)$? The question is motivated by the following paragraph from an economics ...
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54 views

Nash equilibrium in Cournot competition

QUESTION: Assume there are two types of products, labelled $l$ and $n$. Firms compete in the market by choosing which product to sell and then choosing the quantities. Let $Q_n$ and $Q_l$ denote the ...
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1answer
35 views

How to find a Marshallian demand?

I have many doubts with this exercise of microeconomics. I do not know if anyone could help me please. Thanks in advance. Let $x$ be the food consumption of a household, and be $y$ the consumption of ...
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2answers
55 views

what does $\min()$ and $\max()$ mean in a function?

Could someone please explain to me what is the difference between these equations how it would affect the result and the way they are solved? $$Q2(K,L) = A\min(BK,CL)\text{ s.t. }A,B,C > 0$$ $$Q2(...
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0answers
31 views

Constrained Optimization: Abstract Problem

I could use some help with these problems. Suppose we have an objective function $f(x, y)$ and a constraint $y = h(x)$. Suppose the Lagrangian has a critical point at $(0, 0, \lambda^*)$. 1) Explain ...
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1answer
36 views

Market price Pt at any time

So I have this question and answer to it which one part i'm stuck understanding, here's the question. Given demand & supply functions as 𝑄𝑑𝑡 = 86 − 0.8 𝑃𝑡 and 𝑄𝑠𝑡 = −10 + 0.2 𝑃𝑡−1 Find: ...
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1answer
19 views

Optimization problem when demand curve is a power function

A monopolist faces a demand curve $q = p^{-b}, q>0$. The cost function is $c(q) = q^2$. What restrictions must be placed on $b$ for profit maximising solution to exist? Given the restrictions what ...
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0answers
24 views

N-dimensional definition of elasticity

The elasticity of a differentiable function $f(x)$ is defined as: $\varepsilon(x) = \frac{x}{f(x)}f'(x)$ What is the general form of this definition for N-dimensions, i.e., where $\vec{x}$ is a ...
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23 views

Supply and Demand Functions with Tax

I've been given the below supply and demand functions: $q^s(p)=50p~~~~~~q^d(p)=100(\frac{12}{p}-1)$ I've answered the first few questions, which include finding the equilibrium etc, and inverting ...
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25 views

Generalization to a continuum

Preamble, set-up: In economics, a well known optimization problem writes as follows: $$ \max_{\{x\}_{j=1}^n,y}U(x_1,y)+\sum_{i=2}^{n}\lambda_i\cdot U(x_i,y)+\mu\cdot(y-\sum_{j=1}^{n}(w_j-x_j)) $$ ...
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1answer
26 views

Computing the present value, compounded monthly

This is a problem from Ross's Elementary Mathematical Finance book: A five-year $\$10,000$ bond with a $10\%$ coupon rate costs $\$10,000$ and pays its holder $\$500$ every six months for five ...
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0answers
21 views

Bias-Variance OLS via eigendecomposition of projection matrix

I am struggeling to derive the squared-bias and variance based on an eigendecomposition for the OLS-procedure. The model Consider the univariate model $y_i = f(x_i) + \epsilon_i, \ i = 1, \dots, n$ ...
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1answer
23 views

Why can we replace dependent variable y with the residuals/error term e?

I don't understand why we can replace $y$ with $e$: As in the proof of the Gauss-Markov theorem, $$ \tilde{\beta} = [\,(W' W)^{-1}W' + C\,][\, W\beta + e\,] = \beta + (W' W)^{-1}W'e + CW\beta + ...
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0answers
74 views

Barrier Option pricing and valuation

Good day, A reverse knock-out barrier call option expires worthless if the asset price ever goes above a given barrier level. Calculate the value of this barrier option struck at $K = 3$ with ...
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44 views

Prove that every affine set that contains the origin is a subspace.

I need to solve this: Let V be a finite-dimensional vector space. Prove that every affine set that contains the origin of is a subspace of V. So I think I see why this is true, I'm just having ...
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0answers
78 views

Hedging Strategy for American Option

Good day, I was asked to devise a hedging strategy for an American Option given the following claims. Note, $r=0$ and the underlying stock pays a dividend of $1$ at time $t=1.5$ \begin{...
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1answer
45 views

Basic interest question

I have a really stupid question. I'm trying to figure out how long it will take someone to pay off their credit debt. So this is what I'm given: Someone owes $800 Have an annual interest rate of 12% ...
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2answers
29 views

Vector notation unclear step

In my econometrics textbook, I have this step which is not clear to me: \begin{align} S &= e'e \\ &= (y-W\beta)'(y-W\beta) \\ &= \underbrace{y'}_{1\times T} \ \underbrace{y}_{T\times 1} ...
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1answer
36 views

How to mathematically represent the stock market [closed]

I've been working a game based around the stock market and I've been trying to find a representation of the stock market as a 2 dimensional curve, where the x axis is the number of stocks that have ...
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1answer
25 views

Supply/Demand Shift (Find New Equilibrium)

Starting: supply curve $y=x+10$ and demand curve $y = -x+30$ with equilibrium at (10, 20). The problem states that DEMAND shifts leftwards by 3 units and to find the new equilibrium. My professor did ...
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1answer
36 views

“At what point does another year of age reduce the probability of smoking?”

Say I have something like: $$pSmoke = .656 - .069log(cigprice)+.012log(income)-.029educ + .02age - .00026age^2 - .101restaurn - .026white$$ where $pSmoke$ is the probability of smoking and $age$ is ...
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45 views

proof of conditional expectation given n i.i.d. random variables

This is another question from my self-study of Hayashi's Econometrics. How do we show in mathematical proof that given: $X = \begin{bmatrix}x_{1}' \\x_{2}' \\\vdots \\x_{n}'\end{bmatrix}$ where $x_{...
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2answers
61 views

Is an element of a vector a scalar or 1x1 vector or 1x1 matrix?

In econometrics, by Hayashi, they defined the error vector of n observations in a $ (n \times K)$ regression funcntion as: $\epsilon = \begin{bmatrix}\epsilon_{1} \\\epsilon_{2} \\\vdots \\\epsilon_{...
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0answers
44 views

Hicksian Demand Function

Derive Hicksian demand for - $$u(x,y) = ax+ b\ln(y)$$ Explain in words what they mean? I solved the problem with the Lagrange Multiplier Method and found Hicksian demand for $x$ only. Solution: ...
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1answer
41 views

Nash Equilibrium Grandfather Problem

A grandfather is writing his will and must decide how much money he will leave to his three children: Sean, Tom, and Brad. The grandfather comes up with the following plan. Each of his children is ...
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0answers
77 views

What is the difference between $\min(x_1,x_2)$ and $\min\{x_1,x_2\}$?

This question refers to microeconomic utility optimization where the utility function is Leontief. Are $\min(x_1,x_2)$ and $\min\{x_1,x_2\}$ interchangeable, or is there a difference? edit: I ...
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1answer
46 views

Price elasticity

If $P = 90 – 0.05Q$ is the demand function for calculators in an engineering college. (a) Derive expression for $\epsilon$ in terms of (i) $P$ only, (ii) $Q$ only. (b) Calculate the value $\epsilon$ ...
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56 views

Shadow price not covering costs

In (environmental) econ class we had to solve the following problem: ...
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1answer
38 views

What is the sum of the products of price times quantity divided by sum of quantities

I have a very simple question, what is the meaning, if any, of this? I.e. mathematically what does the following calculation mean? $$ \left(\frac{(Q1\cdot P1)+(Q2\cdot P2)+(Q3\cdot P3)}{Q1 + Q2 + Q3}...
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113 views

Digital Option risk neutral probability

In the $T$-period binomial model, if the asset price is $S$ at any time, the next period's price will be either $SU$ or $SD$. The interest rate per period is $r>0$ and $D^* < 1 < U^*$, ...
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1answer
153 views

Determine fair price of a digital option

A digital option pays one dollar at time $t = T$ if the asset price is above a fixed level (strike) $K$ and is worthless otherwise. Consider the following model, with $r = 0$: \begin{...
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0answers
17 views

Finding the max of profit

Is the following fourmula right when we have the MC and MR of a certain comodity ? $$P_{max}=\int_ 0^a (MR-MC)dx$$ where $a$ is the root of $MR(x)=MC(x)$ and $[MR-MC]'(a)<0$. I personally think ...
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1answer
36 views

Minimum Rate of Return

Question: A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average of 42%, what minimum rate of return, before the ...
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1answer
53 views

Exact Simple Interest Problem

Determine the exact simple interest on 1,000,000 invested for the period from October 24,1987 to January 7, 1990; if the rate of interest is 17%. What I've tried: October 24, 1987 to October 24, ...