# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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:$$dh_{t}=\frac{\partial s}{\partial w_{... 2answers 47 views ### Lagrange multiplier with line constraint So I am attempting to minimize the 2-dimensional plane equation$$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\...
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 ...