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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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12 views

Finding the Bayes-Nash Equilibrium for First-Price Auction with 2 bidders

Let $\sigma_i$ be the strategy profile for bidder $i$ that indicates how they should bid based on their value. As we know, if there are 2 bidders both with their values $v_1,v_2$ on $U[0,1]$ in a ...
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15 views

Exchange rate, interest rate problem

I am supposed to solve this: czech investor has 1 000 000 Czech crowns available. Exchange rate is 27 Czech crowns / 1€. Interest rate in a czech bank is 3% and 6% in a German bank. Investor expects, ...
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1answer
29 views

Prove $(b-a) \cdot \int_a^b \alpha(x) \beta(x) dx \ge \int_a^b \alpha(x) dx \cdot \int_a^b \beta(x) dx$.

Suppose $\alpha: [a, b] \to (-\infty, \infty)$ and $\beta:[a,b] \to (-\infty, \infty)$ are both nondecreasing. Then, $$(b-a) \cdot \int_a^b \alpha(x) \beta(x) dx \ge \int_a^b \alpha(x) dx \cdot \...
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1answer
21 views

Interest rate problem

I am supposed to solve this problem: mexican interest rate is 28%, interest rate in the US is 7% and exchange rate is 7.5 Mexican pesos for 1 US dollar. If interest rate parity applies and we don't ...
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1answer
15 views

Percentage change of a quotient

This was line in my Econ notes that was "by definition". If anyone can clarify this I would really appreciate. We have a relationship: $APL = \frac{Y}{L}$ Now, define $\Delta x$ as "percentage ...
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1answer
36 views

Looking for economics research article that applies concepts from real analysis.

As a final project for my real analysis/advanced calculus I am being asked to write a discussion/critique of a paper in my field that applies concepts from real analysis. This could include anything ...
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1answer
37 views

Transform a non-linear differential equation into a linear equation

Following the work of Yaoji Lu - 1967 (here's a link to the full paper) I got stuck at the step when the author transform a non-linear differential equation into a linear equation (eq. 3.9 pag. 19). ...
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7 views

Plotting phase diagram in system of first order difference equation.

Let's suppose we have we have two system of difference equations. I need to ask one thing. When we plot phase diagrams in difference equations, do we assume particular solution and then plot it in y ...
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0answers
8 views

How can you test whether a fixed effects (FE) or correlated random effects (CRE) model is more appropriate?

I know that the Hausman test can be used to compare FE and RE. Is there a similar test to evaluate FE vs. CRE?
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0answers
14 views

New Keynesian Model

Short-term multiplier process with respect to consumption (dC/dG). What happens if lerner index (1/theta) is zero. PricesConsumption=Alpha(Full income) Full income= Wages+Profit-Taxes Taxes=...
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0answers
17 views

Currency Conversion - Getting an equivalent % of currency outside of z/y pair

I am working with 3 currencies. I am trying to get a value (price of Y per Z) that is less 39X. Let me elaborate with an example. 3% of 1300X = (39 X). I want to take 39X away from the Z/Y pair. ...
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1answer
142 views

Correlation matrix with same pairwise correlation coefficient

Question Correlation matrix. Consider 𝑛 random variables with the same pairwise correlation coefficient $\rho_n$. Find the highest possible value of $\rho_n$ for a) n=3 b) n=4 c) general, n $\geq$...
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1answer
26 views

How to derive the equation $\text{Present value} = \text{profit} \times \dfrac {1-e^{-\text{interest rate}\times \text{time}}}{\text{interest rate}}$

How can I derive this equation: $\text{Present value} = \text{profit} \times \dfrac {1-e^{-\text{interest rate}\times \text{time}}}{\text{interest rate}}$
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2answers
22 views

Cannot reconcile simple algebra problem

I'm having trouble with a reconciling two statements. Suppose a merchant has a price he normally charges for goods ($P_{original}$). Recently he's decided to transition onto Amazon which charges 11....
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1answer
19 views

Intertemporal choice, Microeconomics

I am struggling with this basic example. I understand how to calculate everything else but when I get to the point where I should take the equation together with the budget equation to solve for $c_1$ ...
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1answer
10 views

Calculating Percentage of Tax Revenue

So the question asks me to find the % tax revenue but I can't seem to get the right answer, can anyone help? The demand and supply functions for pens with a tax imposed on the buyers is given by: $Q^...
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1answer
122 views

Deriving three points from a curve

I've got a following graphic, where green line is sale. From economics classes, I think marginal return from media advertising can be specified as a first derivative (actually, partial derivative but ...
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1answer
37 views

Business mathematics

The demand function for a good is given as $$P = 50 - 2Q$$ Write down expressions for the TR and MR functions. Find and classify the type of the point price elasticity at price $P = 10$ ...
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0answers
24 views

Utility Function - Calculating consumer surplus

Consider the utility function $U(X_1, X_2) = X_1X_2$. Assume that the consumer has budget $M=18$, that the prices are $p1 = p2 = 1$ to start, and that the price of good $1$ rises to $p1 = 2.25$. Find ...
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1answer
22 views

Answer to Price to charge to maximize revenue?

Looking for an answer to this problem: I understand total revenue calculations, and have tried to find the calculation needed but don't understand. Question: Currently, the demand equation for a ...
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0answers
23 views

Cost-Beneft-Time Analysis

Suppose you want to maximize money per hour, and there are two ratios that you can look at: (money per hour) / (cost) (money per hour) / (time waited in hours) Suppose there are two different ...
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1answer
42 views

Elasticity of Demand:How to Calculate Maximum Revenue

A company has determined that demand for its newest netbook model is given by $\ln q−4\ln p+0.002p=7$, where $q$ is the number of netbooks they can sell at a price of p dollars per unit. They have ...
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0answers
36 views

How to model a simple market equilibrium with linear programming?

I want to model the following problem. The problem is well-known in economics. demand-supply curve equilibrium. Is there any straight forward technique to solve the equilibrium point obtained by an ...
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0answers
20 views

Derivatives/Optimization, Macroeconomics-New Keynesian economy-from Heijdra book

So I get the process shown till (e). What I do not understand is how they get from (f) to (g), and unfortunately, also from there till (j). If anyone could show me how they did the derivatives + ...
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0answers
54 views

I'ts true that this sum is equal to this integral?

I need to know how that sum $$\sum_{k=1}^n \frac{1}{(1+i)^{T_k}}*({T_k}-{T_{k-1}})$$ Can be equal to the integal $\displaystyle \int^{{T}}_{0} {\frac{1}{(1+i)^{s}}}ds$ Where $T_0=0$ and $T_n=T$ and ...
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1answer
23 views

Monthly change formula logic.

I need an explanation of the formula: monthlyChange=(newValue-oldValue)/oldValue Why to divide by old value? Apparently the difference is described well just via subtracktion "newValue-oldValue".
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0answers
18 views

Integration by parts (proposition in Bontemps et al (2000) “Equilbrium Search with Continuous Productivity Dispersion”)

I am struggling to understand a step in a proof of existence of equilibrium in the following paper: Bontemps, Robin, Berg (2000) "Equilbrium Search with Continuous Productivity Dispersion" (starts at ...
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1answer
41 views

How to improve general mathematical literacy?

Hi I'm a Sophomore in economics attempting to read published economics papers. I often encounter models such as the one below: I've taken several lower-level mathematics courses but have difficulty ...
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1answer
28 views

Can someone explain the derivation for this profit function

So, how come the derivative ends up as f'-q/l Some other identities are qi/q=Li/L, qi=Li/L * f(L) and L=sumLi enter image description here
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0answers
46 views

Prove that $\min_{\mu}\sum_{i=1}^n|y_i-\mu|=\text{median}\{y_1,\cdots,y_n\}$ [duplicate]

How to prove the equation below in a simple way? $$\min_{\mu}\sum_{i=1}^n|y_i-\mu|=\text{median}\{y_1,\cdots,y_n\}$$
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1answer
41 views

Why does this integral hold?

Given that $h_i(p,u) = \frac{de(p,u)}{p_i}$, why does this equality hold? $p^0$ is a vector $(p^0_1, p^0_2, p^0_3....)$ and $p^1$ is a vector $(p^1_1, p^1_2,....)$ . Shouldn't the upper bound and the ...
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1answer
34 views

Why does this equality hold (integrals)?

Could someone explain the last equality for me? Source: MWG Microeconomic Theory
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1answer
56 views

Demonstrate that (1) and (2) are equal

$$DR_t= \frac{B_t}{P_t}-\frac{B_{t-1}}{P_{t-1}}\tag{1}$$ $$DR_t=\frac{NB_t}{P_t}- \pi_t\frac{B_{t-1}}{P_t}\tag{2}$$ Knowing that $\pi_t=\frac{P_t}{P_{t-1}}-1$ and $NB_t=B_t - B_{t-1}$, demonstrate ...
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1answer
21 views

First Order Conditions for Maximization Problem

Could someone explain why the second maximization problem follows from the first? And how did we get the FOC in that form? For $max_{p' \in R^L} py(p')$ are we holding p fixed? Thank you!
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7 views

Ordered Choice Model. Checking accuracy/forecasting

I am using an Ordered probit model. When forecasting with the model, i.e. adding new data points to estimate a probability of an event occurring my question is can I use the same data points that I ...
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0answers
32 views

Why is this matrix negative definite?

This is from the textbook "Microeconomic Theory" by MWG. On one page they said: For information, the Slutsky matrix is negative semidefinite, and x is a vector of only non-negative entries. I don'...
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17 views

Comparative statics question with an application

In the state of Mexas, two politicians (Mr. BO, or "Politician 1" and Mr. TC, or "Politician 2") are competing intensely for a senate seat. The two politicians spend on advertising to increase the ...
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1answer
19 views

If equivalent variation is 0, can compensating variation be positive?

I'm solving a problem where wealth changes and I got that $EV=0$ and $CV=1$. This seems impossible to me; is it? I'm given $e(p,u)=u/(p_1^{-1}+p_2^{-1})$. I'm also given $(p_1^0,p_2^0,w^0)=(1,1,1), ...
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1answer
42 views

Solve this particular optimisation problem

Can anyone help answer the below? I know I'm supposed to use the envelope theorem i.e. find the value function then differentiate wrt $p$$x$ and $p$$y$, but I'm struggling to get the right answer. ...
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1answer
23 views

PPF comparative advantage

Ive been looking all over the place for an answer to this question. I'm sure its simple and its driving me nuts. The answer is b. but i dont know why. $W10 = C10 \implies 1W = 1C$ $7W = 2C \...
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2answers
41 views

Is compound interest better than simple interest at all times????

I was recently calculating compound interest for one of my questions and I came to one quite intruiging problem so from what I understand simple interest is! when you have the same amount of interest ...
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1answer
17 views

I need help with a Business math markdown problem

Company x uses a markup on cost of 55% to establish its retail prices.This pricing rule builds on a profit of 22% of cost. What rate of markdown can Company X offer to break even on the reduced price? ...
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0answers
17 views

Calculate yield on weekly saving account that pays a set deposit bonus not an interest rate

If a weekly saving account paying in £100 every week for 15 weeks, paid a £25 bonus every time you deposit the £100 (Instead of a interest %), then matures at the end of the 15th week, how do I ...
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1answer
19 views

Linear Transformations of Data (Econometrics) [closed]

If $Z=XA$ and $A$ is a non-singular matrix, what is the dimension of $A$?
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1answer
166 views

Proving with calculus Cobb Douglas Production Function's Returns to Scale

Background and Trivial Proof by "Example" The way the Rate of Return for the Cobb Douglas production function is proven in the new definition of my textbook is as follows. The Cobb Douglas function ...
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1answer
19 views

Finding no. of items in the observation, when mean is given? [closed]

The mean of certain number of observations is 40. If two more items with values 50 and 64 are added to this data, the mean increases to 42. Find the number of items in the original data?
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1answer
22 views

Logarithmic derivative confusion with Elasticity of Substitution

I've been reading an economics text book ( advanced micro by Jehle) and I found this definition for the elasticity of substitution. But I don't understand what $dlnr$ would be given that $r=x_j/x_i$....
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1answer
19 views

Examples of Covariance Stationary Time Series

I seem to be having trouble in comprehending what it means for a time series to be covariance stationary. Specifically, with the third condition of for any $t$ and $h$, $ cov(x_t,x_{t+h})$ only ...
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0answers
45 views

Using kuhn tucker to solve non negativity constraints

George likes breakfast tacos and milk. His utility is given by $u(t, m) = t + 5 \ln(m)$. Suppose tacos and milk both cost 1 dollar a piece. How should George spend the $\$4$ he has set aside for ...
3
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2answers
55 views

inequality between entropy measure and Herfindahl index

I am considering the entropy measure and the Herfindahl-Hirschmann- (or Hirschmann-Herfindahl)-Index to measure diversification of firms. A firm is perfectly focused if it generates all sales in one ...