# 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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### Solution to a system of nonlinear equations with certain conditions

I am working in a model and I found a problem relating a nonlinear system of equations. Let $\mathbf{D}(\mathbf{Q})\in \mathbb{R}^N$ for $\mathbf{Q}\in \mathbb{R}^N$ be a continously differentiable ...
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### Characterize the mixed strategy Bayesian Nash equilibria for this game. [closed]

A two-player game where Player 1 can choose either U or D and Player 2 can choose either L or R. Player 1 is either cooperative with probability $P$ or uncooperative with probability $1−P$. Player 1 ...
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### Max-min and min-Max relationship in ZeroSum Games

In the attached Zero Sum Game, I have solved for two Mixed Nash Equilibrium, $(l,m)$ and $(m,r.)$ In $(l,m)$, the payoff is $8/5$ to $P_1$, and $-8/5$ to $P_2$. Here, $P_1$ mixes between Top and ...
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### Bolzano-Weierstrass theorem in the neoclassical growth model

I have a doubt regarding the use of the Bolzano-Weierstrass theorem in a dynamic optimization problem. Exactly, the problem is the neoclassical growth model (or Ramsey model). In the website that I ...
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### Estimate the current elasticity and the current value

Consider the statemen A manufacturer of aluminum doors is currently selling 500 doors per week at a price of \$85 each. If the price were lowered to \$80 each, an additional 70 doors per week could be ...
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### Maximizing a function with binary indicators

I am an econ undergrad trying to understand how to maximize this payoff function, which includes binary components. I want to solve this equation using backwards induction, so I want to maximize the ...
1 vote
71 views

### Attempt at creating a formula relating debt, payments and interest

I tried writing down a formula relating a given debt and interest to the periodic payments and number of payments. So let's say someone starts off with a debt of $D$. The periodic interest is $r$ (for ...
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### Suppose $A$ is a $2x2$ matrix and ${\bf x}=(x_1, x_2)$. What does "$f(Ax)$ is supermodular" mean?

Suppose $A$ is a $2x2$ matrix, e.g., $A=\begin{vmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \\ \end{vmatrix}$, and ${\bf x}=(x_1, x_2)$. Suppose $f()$ is continuous and twice differentiable. ...
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### Closed-form solution for polynomial recurrence relation.

Is there a closed-form solution for the recurrence relation $x_{t+1} = x_{t}^\alpha + 1$, where $\alpha \in (0,1)$? If it were $x_{t+1} = x_{t}^\alpha$, then taking the Log of both sides would make it ...
1 vote
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### Discrepancy between the average annual return and the actual stock price

I would really appreciate it if somebody can help me with the math on this one. I feel the need to apologize in advance if this errs on the dumb side. If somebody could walk me through this and make ...
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1 vote
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### Exercises on Edgeworth Box

I don't know if this is the right forum to ask these questions (if so, tell me where to ask them). I have my microeconomics exam soon and I would like to know if I solved a couple of exercises ...
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### Quasi-Concave Function $u(x,y)$ has Decreasing Marginal Rate of Substitution

Let $u:\mathbb{R}^2 \to \mathbb{R}$ be $C^2$, strictly increasing in both arguments, and strictly quasi-concave: $\{(x,y)\vert u(x,y) \leq \bar{u}\}$ is strictly convex for all $\bar{u}$. By the ...
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### Why does the Paraeto Principle actually work? (The 80-20 Rule) [closed]

So, in economics, (and now expanding to other fields too, most significantly marketing tho I suppose commerce is but an extension of economical thoughts), there is a very widely held principle that 80%...
1 vote
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### Finding optimal economy path with best value [closed]

This problem is based on Warcraft 3 Legion Tower Defence custom map. First level problem: Let we say that from the beggining of the game we have infinite gold. We have 1 builder from the start. He ...
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### How can I apply the Hamiltonian function and Pontryagin's maximum principle in the context of Optimal Control Theory?

I am really struggling to grasp how the Hamiltonian Function and Pontryagin's Maximum Principle work in the context of Optimal Control Theory (Maths for Economics) course. I am given the following ...
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### Is my Hamiltonian correct?

To solve the following optimization problem, $$\max _{\left\{\ell_t\right\}} \int_0^{\infty} e^{-\rho t} u\left(c_t, N_t\right) d t$$ subject to  \dot{N}_t =\left(\bar{b}\ell_t-\delta\right) N_t, ...
1 vote
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### Derivative w.r.t exogenous variables

Suppose $f(x_{1}, x_{2})$ defined on a compact set, which guarantee the existence of extrema, $x_1*, x_2*$, and also given the Hessian matrix of $f$ is strictly concave. Suppose there is also a ...
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### Calculating the value of this asset

calculate the cash value of a financed asset that is paid in the following way: an initial payment of 500,000, in month 2 a payment equal to half its value, in month 7 a payment equal to a third of ...
I have this model without intercept $y_i = \beta x_i + u_i$ where $\widehat{\beta} = \frac{\sum x_i y_i}{\sum x_i^2} = \beta + \frac{\sum x_i u_i}{\sum x_i^2}$ I want to verify the consistency of \$\...