# 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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### 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 ...
• 191
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### 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 ...
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1 vote
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### 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 ...
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### 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 ...
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### 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?
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### 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
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### 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 ...
39 views

### Most Efficient Way Saving Money (Compound Interest)

If I have four children and I want to ensure each have £8,500 come there 18th birthday, assuming that I put money in each month, and gain 10% interest per year (taking into account compound interest). ...
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1 vote
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### Elasticity of scale from cost function

I have a problem that I just dont seem to figure out how to solve. Find the elasticity of scale when the following cost function is given: 3(n)^(2/3)(m)^(1/3)y^(4/3) Where n and m are input prices of ...
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### When differentiating $4x^2 + 3y^2 -3xy$ with respect to $x$, why does $3y^2$ 'disappear'?

When differentiating $4x^2 + 3y^2 -3xy$ with respect to $x$, why does $3y^2$ 'disappear'? Not too sure where this $3y^2$ goes, or why $3xy$ can turn into just $3y$. Would love an explanation behind ...
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### Annuity future value, getting extremely low value

The question states: Relative to your current age, the present value at age 67 found in question #1 becomes the future value you need to obtain given your current age now, How much money do you need ...
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### Suggested reading after course in game theory

I would like to hear some of your recommendations on books/papers or topics to research after having learned the basic vocabulary/mathematical framework of game theory. I would like to gain some ...
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### Dual Problems in Economics - Conceptual Question

Assume that I am solving a typical consumer problem in Economics in which I want to maximize the utility of an agent that consumes good $x$ and good $y$ and has a utility function $U=xy$ and a budget ...
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1 vote
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### Nash equilibrium in insurance pricing

The insurance market is considered to be a competitive market, so in order to study competition to determine a competitive premium, game theory seems to be a useful tool for studying those situations. ...
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### Profit Max Cartel

2 Companies both selling the same luxury good. Company A cost to produce < Company B cost to produce, price for the good is the same (P). How do I address the issue of profit maximization if the ...
1 vote
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### Price elasticity over years, semesters, quarters, etc - Midpoint method

I'm trying to calculate price elasticity using the midpoint formula over different years, semesters, quarters, etc. Taking in consideration the formula: Midpoint method Let's say we have this data: ...
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### Economic indexing, how to use relative index to compose a ranking method?

I want to rank regions based on the quantity and "quality" of the jobs. The following example will clarify mini research question: Suppose for this months there have been registered 5000 new ...
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### How to derive this optimality condition from Current value hamiltonian

I am reading a paper from https://academic.oup.com/ej/article-abstract/131/634/658/5876342 and don't know how to derive the optimality condition (7) from the current value hamiltonian. (p.663 in the ...
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### Proving that $\exp(-x^2-y^2)$ is a strictly quasi-concave function

Prove that $$f(x,y)=\exp(-x^2-y^2)$$ is a strictly quasi-concave function, that is,$\forall (x_i,y_i)\in \Re^2, (x_i,y_i)\neq (x_j,y_j), \lambda\in(0,1)$, f(\lambda x_1+(1-\lambda) x_2,\lambda y_1+(...
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1 vote
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### Rebalancing a stock portfolio with a given amount of extra cash

Suppose I have an investment portfolio made up of $n$ stocks each worth $p_i$, with the count of each being $c_i$, where $i \in [1, n]$. Let's say I've found that the optimal/target split of each ...
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### Writing down Bellman equation in recursive macroeconomics world.

Assume an infinite horizon representative agent economy with the following consumer preferences $u(c_t)$ The production technology of this economy uses capital and land, which is fixed amount in ...
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1 vote
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