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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5 views

how to find the greatest profit and a charge for a maximum profit?

the demand function for fiesta memory sticks is p=1000/q^0.3 where q is the amount of memory sticks that can be sold in a week at the price p. the total manufacturing and shipping costs amount to R100 ...
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Determine a total cost of producing x units

marginal cost is $C'(x) = 5 + \frac{10}{\sqrt{x}}$, it is known that producing 100 units costs 950$, how much would it be to produce 400 units? from that I can calculate total cost function which is $...
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What kinds of mathematics are used to explain the theories of valuation?

Using economics as example, Marx "explained" to us "philosophically" what happens when capital is "created" from an initial value: D -> M -> D' (with D' > D) but even though „das Kapital“ is ...
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Farmer and owner Bayesian game

A farmer has talent $\theta$ uniformly distributed on $[0,1]$. His payoff from farming his land is $\theta.$ Before setting up his farm, he chooses some $w\geq0$, which a plant owner can either accept ...
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1answer
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How to convert 3 variable quadratic form into a sum of squares?

How do I convert the 3-variable quadratic form q(x₁ x₂ x₃) = row vector [x₁ x₂ x₃] multiplied by [a₁₁ a₁₂ a₁₃ a₂₁ a₂₂ a₂₃ a₃₁ a₃₂ a₃₃]₃ₓ₃ matrix multiplied by column vector [x₁ x₂ x₃] into the ...
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Stackelberg model of oligopoly [closed]

doing some econ revision and this is one question I'm struggling to find information on, it's: "Does first-mover advantage depend on the assumption of complete information?" Can anyone please help ...
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1answer
33 views

Minimization problem using Lagrange multiplier

This is a microeconomics question, however, as it is the calculations that cause problems I hope you can help me anyways. I have to minimize the following using Lagrange: $$ \min p_1x_1+p_2x_2 $$ ...
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Optimal liquidation Pairs Trading how to plot threshold?

I have been reading this paper http://www2.math.uu.se/~johant/pairs-perp.pdf and at the end they plot the optimal threshold $b$ as a function of $\alpha$ for different values of $\beta$. I have been ...
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29 views

Dimensional analysis of a very simple utility function

Suppose we have a utility function $u:\mathbb{R}_+\rightarrow\mathbb{R}$ defined by $u(x)=x$, where $x$ stands for quantity of apples. Suppose we measure the quantity of apples in kg. How can we ...
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Arrow's impossibility theorem simple proof and explanation

I am trying to prove the Arrow's Impossibility Theorem. I was searching on the internet but there is lots of different versions. I want to prove it for this statement: Arrow's Theorem: ...
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Log linearisation without linearising: formal correctness

For the Real Business Cycle model in macroeconomics we want to derive an equation for the deviation of an endogenous variable from steady state dependent on the changes of other variables from steady ...
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how to solve the Bayesian Nash equilibrium when there is payoff unknown

in this situation, I don’t know how to solve this. Is it correct that the answer of (a) is ε E [0,1]? I cannot even solve the problem a.
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Symbolic computation software for macroeconomic model

I am looking for software that is capable of symbolically solving a typical macroeconomic model. The rest of my question gives an example of a small model. A country maximises: $$\mathbb{E}_0\sum_{t=...
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Compare the least square estimators and the residuals of two Linear Regression with an alternative regressor

So I have been given this as an assignment for my econometrics course and I seriously can't understand where to begin here: Consider the least square regression $ y ∈ R^n $ on $ X ∈ R^{n*k} $, and the ...
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Cointegration of the xt and yt and the distribution of the test statistic

So I'm trying to solve the following question: I've managed to answer the first part of the question (which involved explaining the whole process) and I know that the test isn't following a standard ...
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48 views

Probability Theory in Economics

I'm looking for a topic in probability theory to do some summer research in (for my own learning, nothing too fancy). What are some areas within probability theory that find applications in modern ...
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45 views

Engineering Economics Excel Issue

So I have a problem that I am facing some difficulties in solving the excel part. The problem is: Consider an investment of 10 units of money. For a given interest rate “i” the annual worth is 𝐴(𝑖)...
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Bank Interest in Terms of Convolution

Example 4 from an old set of MIT notes asks: Bank interest. On a savings account, a bank pays the continuous interest rate $r$, meaning that a sum $A_0$ deposited at time $u = 0$ will by time $...
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can anyone explain this regression equation in econometrics?

The observed outcome, $Y_i$, can be written in terms of potential outcomes as if $D_i=1$, then $Y_i=Y_{1i}$; if $D_i=0$, then $Y_i=Y_{0i}$ . Thus, $Y_i=Y_{0i}+(Y_{1i}-Y_{0i})D_i$. We know $Y_{1i}-Y_{...
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Regression Analysis of Time Series Data

My model is in the form of: $Y_t=\beta_0+\beta_1 Y_{t-1} + \beta_2 X_t + \beta_3Z_t$. I have only learned regression analysis of cross-section data. I'm wondering which function in R should I use to ...
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1answer
28 views

Am I solving price elasticity of demand correctly?

Quantity demand is given by the equation 50 - 10p + .5y where p is price and y is income. ...
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Meaning of $(\textbf{x}_i,\epsilon_i)$, $i=1,\dots,n$ is a sequence of independent observations

In William Greene's Econometric Analysis book (7th edition), page 64 states (right above equation 4-20) assumption A5a: $$\tag{A5a} (\textbf{x}_i,\epsilon_i)\quad i=1,\dots,n \quad \text{ is a ...
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Derivation of the elasticity of substitution of a general production function with labor-augmenting technological progress

I am following and trying to fully understand a famous and interesting work of Bentolila and Saint-paul (2003). They try to explain movements of the factor's share in terms of a relationship between ...
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What are the topics in Linear Algebra that model Identification Strategy in Econometrics (or Identifiability in Statistics)?

I just would like to know what concepts one should know before talking about identification strategies in econometrics. I see people studying such concepts but I'm not sure they realize (or even know) ...
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What are some two variable functions with applications in economics?

Functions that are used for anything finance/economy related. I've been researching for quite a while and just can't find two variable functions.
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1answer
31 views

How can I prove this about Nash equilibrium

Show that in each Nash equilibrium of the game, each player receives the same (and maximum) payo↵ from any two strategies that are played with positive probabilities (under, of course, the assumption ...
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Need some intuition on terms used in solving dynamic systems: explosive, bounded, stable, stochastic equilibrium, …

E.g. What is an explosive equilibrium? In what sense it it an equilibrium, as it is, I guess, not stable? What is a bounded equilibrium? Is it the same as a stable equilibrium? What is a non-bounded (...
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1answer
23 views

What does it mean to close a model?

What does it mean to close a model (dynamic system)? Some context from a paper by Farmer, Solving and Estimating Indeterminate DSGE Models: " It is well known that linear rational expectations (LRE) ...
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1answer
28 views

Total Differential of Aggregate Supply

Our macroeconomics professor took the total differential on Equation #1 and the result was Equation #2. After multiple attempts using the knowledge I have in calculus, I can't find a way to get from ...
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2answers
32 views

Change (discontinuity) in Nash Equilibrium with change in parameter

I am solving for duopoly competition between two firms who decide a product characteristic and price. I find that I get two different types of equilibria based on a parameter 'a' - with a ...
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1answer
29 views

Why Walrasian budget set is not compact for p=0?

I know that budget set is defined as $B(p,b) = \{x \in R_+^n: p.x \leq b \}$. If $p \geq 0$ and $b \geq 0$, this budget set is called Walrasian budget set or the competitive budget set. I also ...
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Bounded rationality: Least-squares learning: understanding the technique

This method is presented in Evans and Honkapohja (2001) I don't understand the formula used by the least squares learning technique to form expectations in economic models. This formula is given by, ...
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31 views

Difference between 2SLS and OLS

Consider a instrumental variables model with stochastic regressors,target and instruments: $x\in \mathbb{R}^{d}, y\in\mathbb{R},z\in \mathbb{R}^{q}$,$q\geq d$ , satisfying the relation $$ y = x\alpha +...
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Write down an interpretation of the function $M(G, i, t, y) = G+\frac{(i)^{\alpha}(t)^{\beta}}{y^{\delta}}$

Suppose that the marks $(M)$ you get on an university exam is predicted by the following function: $M(G, i, t, y) = G+\frac{(i)^{\alpha}(t)^{\beta}}{y^{\delta}}$, where: $G$ is your current university ...
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1answer
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Calculate new percentages of the member of a society when one member died.

I have a question that may seem easy to solve but for me it is not so easy. Suppose I have a society with $4$ members:$A,B$ and $C$. $A$ owns the $50\%$ of the society, $B$ the $20\%$, $C$ the $20\%$ ...
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19 views

production function that takes time and quality as inputs

I am unsure if Math StackExchange is the proper website to post a question related to economics or management. I apologize if it's not. My question is ... For a manufacturer, he needs to decide how ...
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1answer
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maximizing using lagrangian

So I have a question from my quiz. I don't want a specific answer but a help or guidence. My objective function is F(x,y)=x+4y and my subject is I-Pxx-Pyy=0 where I,Px and Py are both positive ...
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1answer
23 views

Expectation Notation Difference

I have a very short question regarding the notation of an expectation term. So in macroeconomics there is the Euler equation: $$C^{-\sigma}_t=E_t\beta C^{-\sigma}_{t+1}(1+i_t)/(1+\pi_{t+1})$$ My ...
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Derive the condition that a country is a net exporter.

I'm having trouble solving the following question. There exists only two countries in the world: Albania and Bulgaria. There is complete free trade between the two. The aggregate investment in ...
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Loan Mortgage Problem: Fully Amortizing Loans vs Interest Only Loans

There is some mortgage balance L with a periodic interest rate r for n periods. Monthly ...
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Integral as an average and normalisation

There are some mathematical aspects I do not really understand from my macroeconomics course. For labour $N_t$ and capital $K_t$ following equations are given: $$N_t=\int_{0}^1 N_{jt} dj=1 \qquad (1)...
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35 views

Dynamic Programming and Hamiltonian problem

Consider the following infinite-horizon optimal control problem for a firm in continuous time. At any moment $t \geq 0$, let $s(t) \in [0, 1]$ be the relative size of the market for the firm’s product....
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Level sets and Concave function

in my Calculus textbook about Concave functions the following is derived from this expression: Let $f$ be a function defined in a convex set which is subset of $\mathbb R^n$ and $Df(x)$ the first ...
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1answer
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Economics: a question about investment and rate

I have a question about Investments/Economics that needs answering: Gary invested some money at $3\%$ and $\$1200$ more than that at $5\%$. His total annual interest was $\$340$. How much did ...
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2answers
43 views

How to transform a m-th order difference equation into a first order system of difference equations?

I have a problem that asks for following: Consider the in-homogenous linear difference equation $y_t-4y_t+2y_{t-3}=4^t$. Write the LDE as a system of first-order LDEs. The solution is given: define $...
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1answer
22 views

Algebra problem about sale and regular price [closed]

Can you please help me solve this problem? The sale price on a new natural gas furnace is $\$2750$. This represents $12\%$ off the regular price. What is the regular price?
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how to calculate effective annual rate if it's calculated once in 3 years?

Interest rate is $9\%$ a year, but it's calculated once every $3$ years. How to calculate the effective annual rate? The formula I know is: $$r = \left(1 + \dfrac in\right)^n - 1,$$ where $n$ is ...
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18 views

Help with a simple total differentiation

I have the following equation: $$H_{t}=S(W_{t}P_{t})W_{t}(E_{t})E_{t}(Y_{t})$$ Letting lower-case letters denote logs, I have totally differentiated to obtain:$$dh_{t}=\frac{\partial s}{\partial w_{...
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2answers
47 views

Lagrange multiplier with line constraint

So I am attempting to minimize the 2-dimensional plane equation $$p(x,y)=ax+by$$ with the constraint $$g(x,y)=x+y=c.$$ By the method of Lagrange multipliers I get $$\nabla p=\lambda\nabla g\iff\...
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1answer
51 views

Calculation of CPI

My class was canceled due to the coronavirus and I am supposed to solve the following problem: Assume that the consumer consumes only two goods, and his utility function is $u=x_{1}x_{2}$. Last year ...

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