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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
17 views

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 ...
-1 votes
0 answers
34 views

Economic Math involving the Cobb-Douglas function [closed]

Consider a Cobb-Douglas function $Q = L^\alpha K^{1-\alpha}$ where $0<\alpha<1$. Suppose that the inputs, $L$ and $K$, change with $x$ and $y$ such that $L=K=x^\beta y^{1-\beta}$ where $0<\...
  • 7
2 votes
1 answer
64 views

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 ...
0 votes
0 answers
13 views

Derivation of variance of AR(1) forecast residual formula.

The formula is written below. I'd appreciate it if anyone could provide me with the derivation for it or if they could provide me with a link to anywhere online or a textbook that covers it. The ...
-2 votes
1 answer
35 views

Engineering Economics Question: Uniform series present worth question

The cost of a fence that can detect poacher intrusion into a National Wildlife Preserve is $3.3 million per mile. If the effective life of the fence is 10 years, determine the equivalent annual cost ...
0 votes
1 answer
25 views

How do I normalize/standardize a data set to a certain set value (not average, not min, not max)?

I know the formulas for standardizing, normalizing, and mean normalizing (if we take the wikipedia's definition for these terms). What I want to do is to normalize to a set value. For example, if I ...
  • 1
0 votes
0 answers
9 views

Intuition behind the Compensating Variation!

In Economics, we can calculate the compensating variation (CV), which (to my understanding) is the amount of money we would need to give back to a consumer to keep them at the same level of Utility ...
  • 323
0 votes
0 answers
33 views

Minimization of the Pollution Problem

I study Economic Analysis.I came accross the following minimization problem I tried to show that M is quasiconcave but i failed. I tried using the definition of quasiconcavity or using the min ...
1 vote
1 answer
21 views

How can elasticity of $f(x)$ be expressed as a percentage change in $f(x)$ per $1$% change in $x$?

In answering the above question, we took the formula of elasticity: $El_xf(x) = (x/f(x))*(∂f(x)/∂x)$ We can transform it in the following way: $El_xf(x) = (∂f(x)/f(x))*(∂x/x)$ Now at this point, the ...
1 vote
1 answer
29 views

0.35 log points to percentage

What is 0.35 log points in percentages? I have no knowledge of this subject at all. From what I've gathered, it should be Percentage change = (e^log points - 1) * 100, so 42%. Is this correct?
  • 103
2 votes
1 answer
69 views

Need help identifying what sort of differential equation this is

I'm reading an economics paper, and have stumbled upon this differential equation system: $\dot x = -\beta xy^\alpha$ $\dot y = \beta xy^\alpha - \frac{1}{\sigma}y$ I haven't taken any classes on ...
  • 144
0 votes
1 answer
28 views

Equilibrium interest rate

There are two countries in the whole world: Bolivia and Peru. The aggregated investements in Bolivia is $I^B$ And in Peru they are $I^P$ (They are both exogenous). The savings for Bolivia, where $B,b &...
0 votes
1 answer
35 views

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 ...
0 votes
0 answers
23 views

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....
0 votes
1 answer
38 views

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....
  • 11
1 vote
1 answer
38 views

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?
0 votes
0 answers
24 views

Many questions about a loss distribution

Long question, but mostly set up: I'm trying to understand the capital requirements formulas of Basel III. They come from the Merton-Vasicek model for the value of a company's assets. Assume we have $...
  • 2,900
0 votes
0 answers
17 views

Definition of transition density

Sorry if this is a basic question but I have a hard time grasping the definition of transition density in a financial setting. From what I understand, transition density is the expected (future) value ...
1 vote
0 answers
53 views

Expected utility

The figure below describes John's preferences over lotteries for three prizes- $1, $2, and $3, where p1 is the probability of winning $1, and p3 is the probability of winning $3. Assume that John is ...
1 vote
0 answers
69 views

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 ...
4 votes
0 answers
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 ...
  • 5,520
0 votes
0 answers
31 views

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 ...
0 votes
1 answer
24 views

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 ...
-3 votes
1 answer
38 views

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 ...
0 votes
0 answers
29 views

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!...
0 votes
1 answer
36 views

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 ...
0 votes
0 answers
16 views

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 ...
0 votes
0 answers
18 views

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
1 vote
1 answer
39 views

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 ...
0 votes
0 answers
28 views

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
0 answers
38 views

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 ...
0 votes
0 answers
14 views

Economics Question - Days Forward Coverage Formula

I am trying to replicate a built-in function in our application that calculates Days Forward Coverage (How many days can your supply fulfill demands in a given horizon). I know how to arrive at the ...
0 votes
0 answers
11 views

Show that $c'(q) = c_1'(q_1) = c_2(q_2)$

This is originally an Economics problem but I hope I've rewritten it in a way that there's (very little to) no confusion. Assume that the functions are $\mathcal{C}^2$ and the maxima/minima exists ...
0 votes
0 answers
19 views

Are there characterizing theorems for veto and nomination?

We know that for some voting methods, there are characterizing theorems, for example, for majority vote we have May's theorem which states that: simple majority voting is the only anonymous, neutral, ...
1 vote
0 answers
75 views

Deriving Hamiltonian with Lagrange multiplier method

This is probably a basic concept, but I am having a hard time understanding why in deriving the Hamiltonian with the Lagrange multiplier method 1) we introduce a time-varying multiplier for ...
  • 181
0 votes
0 answers
21 views

ROR/IRR Analysis of mutually exclusive alternatives

I've got this homework problem, and I get two different answers solving it two different ways. I'd like to know which is the right answer and, if it's easy to explain, what is the flaw in the method ...
  • 195
1 vote
1 answer
96 views

Recursive economy in two islands

There are two economies A and B with infinitely many identical households. Since there are infinitely many identical households in each economy, they are all price taker. Maeasure of agents in A and B ...
  • 6,317
0 votes
0 answers
86 views

Show that the order of deletion doesn’t matter for the set of strategies surviving iterated elimination of strictly dominated strategies

Question from M.W.G-8B4 Show that the order of deletion doesn’t matter for the set of strategies surviving iterated elimination of strictly dominated strategies. My proof attempt I assume $G_n$ the ...
  • 6,317
0 votes
0 answers
19 views

Every Nash equilibrium is subgame perfect Nash equilibrium

Every Nash equilibrium is subgame perfect Nash equilibrium This statement is wrong. But i could not find a counter example What are your suggestions?
  • 6,317
0 votes
0 answers
17 views

Optimization of convex function - proof replication

Trying to solve: $$ \max_d \pi = \frac{(V^+ +2d_u + V^+\, d_u)^2}{16(V^+ - V^-)} \;\;\;\text{s.t.} \frac{4P_u}{1-d_u}>b-1 $$ And where $P_u = \frac{1}{8} (d_u-1) (V^+ d_u-V^++2 d_u)$ This is a ...
1 vote
1 answer
21 views

Cobweb recurrence relation

Consider the recurrence relation given by $2P_t + P_{t-1} = 3, P_0 = 0$. Does the graph of $(Q_t, P_t)$ look like a Cobweb where $Q_t = 4-2P_t$? My calculation tells me that $(Q_t, P_t) = (2 + 2(-0.5)^...
0 votes
0 answers
8 views

highly monotonic preferences and indifference curves

Show that if in $ R^2_{+} $ are continuous, highly monotonic preferences then indifference curves (i.e. classes of abstraction of relations ∼) are graphs of continuous, decreasing functions from the ...
0 votes
0 answers
32 views

What is my mistake here? I was trying to find F/G factor here

I was trying to derive an expression for F/G factor here for homework. I have attached my working in this picture. I always end up with a (1+i) in the numerator which is not in the actual formula. ...
0 votes
0 answers
21 views

Finding cost function

The production function is as follows $$f(z)=(z_1+z_2)(z_3+z_4)$$ Find the cost function? What I did is as follows. But I am not sure about my solution. How do you solve it?
  • 6,317
0 votes
0 answers
11 views

Walrasian equilibrium with quasi linear function

There is a two-person exchange economy Each agent has the following utility $u_i(x_i,y_i)=v(x_i)+y_i$ for agent $i=\{A,B\}$ Assume that $v$ is strictly concave and increasing function that has a ...
  • 6,317
1 vote
0 answers
15 views

Representation of an indicator variable conditional on means

I am just starting out with math in uni for my research so this is a really simple question. I calculated the fraction of number of school enrollments during a policy period from 1991 to 1993 over the ...
  • 11
0 votes
0 answers
25 views

The expectation of the product of an estimator with its transpose

I hope you are well. I have a problem that it seems to be really easy but I just don't know how to find the solution. So, this is the question ; I have to compute E(Ŷ'Ŷ). For that, I have some ...
0 votes
0 answers
47 views

Iterated elimination of dominated strategies

I have a simple question that I am struggling to think about, If a strategy survives IEDS does this it must be a best response? For example the following game: ...
  • 9
1 vote
1 answer
24 views

Asympotic Distribution

Question: Let $Y_1,\cdots,Y_n $ ~$_{i.i.d} N(\mu_0,\sigma^2_0)$, now consider following 3 estimators for $\theta_0 = \mu^2_0$: $\hat\theta_1 = \bar Y^2, \hat\theta_2 = \bar Y^2 - \frac{\sum_{i=1}^n(...
0 votes
1 answer
39 views

How do I substitute an expression into a summation term that includes a fraction?

I'm working on some economics homework and there is a problem I'm finding particularly difficult. The first question asks us to find the function that a firm will use to determine how much CO2 to emit ...

1
2 3 4 5
31