# Tagged Questions

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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An industry characterized by market power (that is, a non competitive industry) always leads to deadweight loss- Is this statement true or false If true, how to explain ?
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### Savings question: How long will savings last if I withdraw a certain amount every year?

Let's say that for $30$ years I insert $.20$ dollars every year into a bank account for with interest rate $5\%$. After 30 years, I stop inserting money, and start withdrawing 0.70 dollars every year. ...
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### Find linear price function from a point

I have to do a simple managerial economics exercise. I know that a firm sells $Q=16000$ units at a price of $P=1672$. Moreover, I know that it will sell 18% more units if the firm decrease the ...
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### Solving optimization with Lagrange multipliers

I am fairly new to Lagrange multipliers. Can someone please show me how to maximize the following function: \begin{align} f(x,y)=240\sqrt{x}+y \end{align} Subject to: \begin{align} 30x+y=720 \end{...
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### Number of firms in the market

Suppose market for corn is in long-run equilibrium. All suppliers face same cost curve $AC=300-q+0.02q^2$. The demand curve is given by: $D(P)=642,000-36P$. How many firms are there in the market ? I'...
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### Mathematics of a Real 3-Commodity Market Model

Ok, the mathematics for this problem may not be too straightforward, but I hope someone can help. I’m looking at a different approach to how an economic market is modelled today, and am looking for ...
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### Solve for the interest rate while we are not told if it is simple or compound.

You are offered to have a discount of \$20 if you pay cash now for \$1500 due in 120 days. If you pay cash now, at what rate may you consider your money to be earning interest for the next 120 days? ...
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### Bayes risk and Bayes decision

We are considering a sample of size $n$ from an exponential distribution, with parameter $w >0$. We wish to produce an estimate for $d$, for $w$ , with loss function: $L(w, d)=w(w-d)^2$ The prior ...
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### True market value

Given n elements, which are all traded against each other, is it possible to assign a single value to each one that reflects how much it's worth compared to all other elements? i.e.: the Forex market,...
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### Microeconomics. How to solve mathematically Exchange/Edgeworth Box models.

Problems Hey guys. First post here. So im an econ student and these are the questions i am faced with VS the answers that i am supposed to have. I understand Edgeworth Box models from the lecture ...
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### Formula from New Keynesian model $\min_{C(j)} \int_0^1 p(j) C(j) dj = p(j)$

Please help. I am trying to sort out some mathematics in the economics literature. One troubling mathematical operation is the following: $$\min_{C(j)} \int_0^1 p(j) C(j) dj = p(j)$$ Is that ...
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### Showing that the elasticity of arrival rate for workers wrt $\theta$ is between $0$and $1$

Let $L=E+U$ where $L$ is labour force, $E$ is number of employed, and $U$ is unemployed people. Let $u = \frac{U}{L}$ and $v = \frac{V}{L}$. Given $m(u,v)$ as a matching function that determines ...
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### OLS IA & IB Estimator Proof/Simplification

My Econometrics professor included this slide in his "Properties of the OLS Estimators" presentation, and I have to admit, I don't see what he's done. I would sincerely appreciate an expanded (step-by-...
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### ODE: Expected life time of an investment

I was thinking on the following problem about ordinary differential equations applied in economics: Compute the expected life time $u(S)$ of an investment on an asset at current price $S_0$ if it will ...
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### Interpreting Indirect Utility Function

Given the utility function $u(x_1,y_2)=2\sqrt{x_1}+\sqrt{x_2}$ maximize it with the given constraint $p_1 x_1+p_2 x_2=m$. Having solved the problem, using the standard Lagrangian multiplier method, ...
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### Inflation Index

The inflation index of a country $A$ in $1995$ relative to $1990$ was $5$. Meaning that the ratio of dollars spent during $1990$ for goods compared to dollars spent for same goods is $1:5$. In country ...
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### Basic optimization question

A teacher put this problem up the other day and I'm confused about how he got to the answer. Can you explain it to me? Job $X$ provides $20$ vacation days and $143,000$ euro annual salary. Job $Y$ ...
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### Limits: Show derivative approaches 0 and infinity.

Consider: $F(K,L) = A[\alpha K^\psi+(1-\alpha)L^\psi]^{1/\psi}$ with $0 \lt \psi \lt 1$ The questions asks to find whether the following two conditions hold: $Lim_{K \to 0}F_k(K,L) = \infty$ and ...
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### Calculating the equilibrium price. ( Theory- whith no smooth supply and demands curves)

I was looking for a theory wich explain the following problem: I have the next , demand, supply curve: The book didn't explain how to compute the equilibrium price with this market (only was named)...