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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0answers
15 views

Determine the system of difference equations for $(k_t,p_t)$

Let $f:\mathbf{R}_+\rightarrow\mathbf{R}$ be defined as $f(k_t)=\frac{k_t}{\alpha+(1-\alpha)k_t}$ $p_{t+1}=\frac{r}{n}p_{t}+\frac{\beta}{n}k_t+\frac{e+s-1}{n}f(k_t)$ $k_{t+1}=\frac{\delta}{n}k_t+\...
0
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2answers
432 views

Using Lagrange for finding Marshallian Demand

I want to find the marshallian demand function for the user function $u(x_1,x_2) = x_1^ax_2^{1-a}$ where $a \in (0,1)$. This is what I have so far: $$L = x_1^ax_2^{1-a} - \lambda(p_1x_1 + p_2x_2 - y)$...
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1answer
40 views

Arrow's impossibility theorem implications [on hold]

If we knew that in an unfair voting system (ie: it is known that IIA does not hold) then if (1) holds, how would we go about inferring that (2) holds and then is it possible to show that if (1) and (2)...
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0answers
25 views

(Order Relation) Monotone Continuous Complete Preorder on $\mathbb{R^L_+}$ has $y\geq x\rightarrow y\succsim x$

I am trying to show a monotone continuous complete preorder on $\mathbb{R^L_+}$ has $y\geq x\rightarrow y\succsim x$. Can you please share your 2cent on the below proof? Thank you! Point of ...
-2
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3answers
62 views

economics using differential equations [on hold]

I need help with this calculus problem The producer of a certain commodity determines that to protect profits, the price p should decrease at a rate equal to half the inventory surplus $S−D$, where $...
0
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1answer
39 views

$\succsim$ preorder on X being continuous imply lower contour set closed

$\succsim$ is preorder (i.e. preference relation) on X that is continuous. This implies the lower contour set is closed. Would you please share your 2 cent on my parenthesis explanation (e.g. line ...
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0answers
22 views

Applying Slutsky's Equation

Note: I asked in the Mathematics Meta regarding if it is permitted to ask Mathematics questions of economic nature. I also posted this question in the Economics Stackexchange but have not got any ...
0
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1answer
42 views

(Proof) Representing preorder $\succsim$ as a real-valued function.

I am reading a proof and having a hard time understanding on some parts. In math language, the proof is trying to show the existence of continuous preorder $\succsim$ (i.e. preserved under limits, ...
-1
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2answers
29 views

Marginal revenue of a monopolist [closed]

A monopolist faces a demand function $Q=4000(p+7)^{-2}$. If she charges a price of p, her marginal revenue will be: (a) $p/2+ 7$ (b) $2p+ 3.50$ (c) $p/2-7/2$ (d) $-2(p+7)^{-3}$ Correct answer is ...
-1
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0answers
9 views

Calculate the yield curve spread to forward rates [closed]

First, using the table below I found the yield cure spread to spot curve is 0.88% using the following formula: $$100 = \frac{CF_1}{(1+\text{Spot}_1+SPD)^n} +\cdots+ \frac{CF_n}{(1+\text{Spot}_n+SPD)^...
1
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1answer
23 views

Production functions total cost

Production function is: $f(L,M)=L^{1/2}M^{1/2}$. L is the number of units of labour, M of machines used. Cost of labour is 9 per unit, whereas the cost of machine is 81 per unit. Total cost of ...
1
vote
1answer
668 views

What is my unit of observation for this time series data set?

My professor gave us a data set to run a regression and I have a data set which lists years from 1959-2007, gross private investments (in billions of dollars), and gross private savings (in billions ...
1
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0answers
38 views

Which derivative is correct?

Consider the following expressions: $$C_{i}=\sum_{j=1}^{N_i}v_{j}, \quad v_j \in \mathbb{R}, \quad N_i \in \mathbb{N} $$ \begin{equation} x_{i}=\frac{C_{i}}{N_i} \end{equation} I want to obtain an ...
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0answers
18 views

Binary choice models

a) Suppose you have a sample of $600$ females and we are interested in their labor force participation decisions. What kind of econometric model would you use if you wanted to empirically estimate ...
2
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2answers
351 views

Good economics textbooks.

I would like a suggestion for the most mathematically fun/interesting mathematical economics textbook, preferably using abstract math. I want to prove theorems to complete my economics minor. I have ...
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0answers
14 views

Two variable integral arising from an application of myersons lemma

We have the following equation. $f:[0,1] \times[0,1]\to [0,1]$ f is monotone. $$(x+y-1)f(x,y)=\int_{0}^{x} f(t,y) dt +\int_{0}^{y} f(x,t) dt$$ further we have the symmetry condition that. $$\...
0
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1answer
36 views

Calculate future price with continuous compounding

A forward contract for 4 months is entered into when a stock index is at 1000. If the risk free interest rate is 3% per year (with continuous compounding) and the dividend yield on the index is 2% ...
0
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0answers
34 views

Normalization in Economics (relative price)

I am reading a textbook in Economics and realized normalization of price is extremely common. (Reference: Microeconomic Theory (MWG, p 24)) Can somebody please help me understand two things: (1) ...
2
votes
1answer
439 views

Euler Equation and Marginal Rate of Substitution

I was wondering if someone could help me clarify a result from my lecture notes. I have put them as a picture. It concerns the result on the last slide (the other three slides are included as well ...
0
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1answer
44 views

For which values of $\gamma$ does this inequality hold?

Edited: Just realised my first post was somewhat misleading and not precise. Thanks to the two commetators that pointed it out. I am working on an article and ended up wondering for which values of $\...
1
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1answer
39 views

Complementarity and Substitutability

I am reading a paper in the international journal of game theory entitled Unequal Connections by Goyal and Joshi (2006) and it has the following sentences: "If strategic complementarity obtains... In ...
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1answer
28 views

Profit after price increase and volume drop

What happens with profit if prices increase by 10 pct and volume decrease by 10 pct? I guess the sales are determined as $$ TR = P \cdot Q, $$ so the changes results in $$ TR' = (1.1 \cdot P) \cdot (...
0
votes
1answer
35 views

Average cost and the level of output

A firm's average cost function is: $$AC = x^2 - 2x + 50 , \ 0 \leq x$$ a) Find the level of output to minimalize average cost (AC) function b) Find the level of output when average cost equals ...
0
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1answer
35 views

Discrete Uniform Probability: isn't my textbook just wrong?

My textbook is showing me examples of discrete probability distributions, one of them is in the picture: I learned in Calculus that the summation of the series $1/n$ where $n\to \infty$ is ...
1
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1answer
75 views

Does this inequality hold?

I am currently writting a paper and ended up with an expression that looks like the following: $$\frac{\sum_{i=1}C_{i}}{\sum_{i=1} {N_i}^\gamma {C_{i}}^{1-\gamma}}$$ for $i=1...K$, $C_i>0$, $N_i ...
0
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0answers
12 views

Econometrics, forecast, in sample and out of sample regression

Is there anyone who can explain me the difference between an in sample regresion, out of sample expansion regression and an out of sample rolling regressions? I have time series data from 1990 to 2016/...
0
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0answers
30 views

The simplest, advanced optimal pricing problem

Consider an arbitrary distribution, $F(x)$, with density $f(x)$ and the property of increasing hazard rate: ${f(x)\over1 - F(x)}$ increasing in $x$. Let $p^*$ maximize $p(1-F(p))$. Show that $p^*$ ...
0
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1answer
12 views

Elasticity of the function

Please find the elasticity of the function f(x) in x0: $$f(x) = \frac{ax^2} {1+ x^2} $$ $$ x0=10$$ Could you please check is done correct ? $$E_xf(x_0) = \frac{f'(x_0)·x_0} {f(x_0)} $$ $$f'(x)=\...
0
votes
1answer
50 views

Maximalize profit

Please advise on how to solve this exercise A firm’s profit is given by the function: $$\text{Profit} = 1200 - 6x^2 - 8x + 4xy - 10y^2 + 96y$$ where $x$ denotes output and $y$ advertising ...
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1answer
27 views

The level of output to maximize profit

Could you please give me any advices how to solve this exercise? Would be grateful for any help:) A firm's market demand function is $AR = 150-3x$ , and its total cost function is $TC= 0.1x^3 - 3x^2 +...
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2answers
29 views

Maximize firm's profit

Please give me any advices how to solve this. I'm good in maths, but I just don't understand these economical issues A firm's profit is given by the function: $PROFIT(L,K) = 50 L^{0.2} K^{0.8}$, ...
0
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1answer
25 views

Find change in gross profit after price change

How do you solve this question? A company has 3 products. They contribute to 30%, 30% and 40% of sales respectively. They have profit margins of 15%, 30%, and 50% respectively. If the ...
0
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2answers
22 views

Replication a options portfolio

I'm not too sure I'm going about answering this question correctly. I have used the following to derive my answer. I see that the portfolio above is a combination of a short-call(strike price 20) ...
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2answers
65 views

help for an integral

I need help calculating this integral: $$\int_0^x \frac{2(e^{\gamma u}-1)}{(\gamma+\kappa)(e^{\gamma u}-1)+2\gamma} du$$ I tried with the integration by parts but the situation seems to get ...
2
votes
1answer
161 views

What is this subclass of the class of monotonic transformations?

Let $u$ be a continuous function from $\mathbb{R}$ to $\mathbb{R}$. Then $v$ is called a positive monotonic transformation of $u$ if $u(x) < u(y)$ if and only if $v(x)<v(y)$ and similarly for ...
0
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1answer
27 views

Counterexample to each Arrow's axiom

I am trying to find ways that combine group preferences which hold for 3 out of the 4 Arrow's axioms. Here is what I have come up with so far: Unrestricted Domain Not sure what scheme would ...
-1
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1answer
32 views

Population and production in a dynamic system [closed]

I' trying to solve this problem but would need some help: Let $N=N(t)$ denote the size of a certain population, $X=x(t)$ the total product and $y(t)=X(t)/N(t)$ the product per capita at time $t$. ...
1
vote
1answer
16 views

cost minimization knowing the cost of labor and capital

The production function is $f(L,M)=4L^{0.5}M^{0.5}$ , where L is the number of units of labor and M is the number of machines used . If the cost of labor is \$100 per unit and the cost of ...
0
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0answers
29 views

Why is maximising expected monetary value not plausible for large amounts of money?

My teacher asked us which of these gambles do you prefer: $g_1=£500,000$ $g_2=0.1£2,500,000 \oplus 0.89£500,000 \oplus 0.01£0$ The EMV for each gamble is £500,000 and £695,000 respectively, ...
0
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1answer
20 views

Depletion Engineering Economy

An engineer sold his machine for $17,000$, after using it for 5 years. He bought a new machine worth $75,000$ with an expected life of 12 years, and a salvage value of $2,000$. The operating cost ...
0
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0answers
13 views

Which of these influence diagrams are not valid?

Which of these are valid influence diagrams? For those that are not, state the exact reasons why The squares, circle and diamonds represent decision, chance and value nodes respectively. (1) - ...
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0answers
24 views

Decision tree probabilities

I am solving the following decision problem. I formulated the problem into the tree OK but am unsure of what the probabilities along the branches are. i.e. how do I go from, for example, $P(H_1 \cap ...
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3answers
160 views

My brothers share from income.

My brother is driving a limo with his partner who told him that they will go $50-50$ on income and also $50-50$ on gas. So if my brother earns $\$1000$ by spending $\$200$ on gas, what will be my ...
4
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1answer
59 views

Analyse the US presidential election from the perspective of Arrow's theory

I want to consider the voting system against the 4 Arrow's axioms. So first the voting system simplifies to first-past-the post system where the highest polling candidate wins the election. How does ...
2
votes
1answer
27 views

What model should I use for judging a dimension given only composed data with another?

I am attempting to upgrade a modeling system using a limited type of statistical information, but with the sample covering the entire system. The problem is how to use the additional information in ...
-1
votes
1answer
29 views

I need a formula to find this value.

So, I need a formula to help me find out profitable ventures. I am buying items for X and selling them for Y. However, there are fees involved. Everytime I buy an item, an additional 1% of my money ...
0
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0answers
13 views

Arrow-Debreu Equilibrium pricing

I have this problem in asset pricing that I don't know how to solve. Here it is: Consider an economy with a complete set of Securities and $N$ states of the world Tomorrow. Assume that there are two ...
0
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0answers
52 views

Utility maximization problem

I tried to search through the site and couldn't find a similar example. The task is to solve the utility maximization problem to identify the inverse demand for e(electricity). The utility function: $...
11
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6answers
4k views

Motivating linear algebra for economics students?

I'm a tutor for the introductory linear algebra course at my school; this course is required for most upper division economics classes, so a lot of my tutees are economics majors. This is a typical ...
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0answers
39 views

Maximise the function with constraints

Is it possible to maximise this function algebraically $$f(x_{1},x_{2})=5\cdot \min\left(\frac{x_{1}}{6},\frac{x_{2}}{2}\right) + 2\cdot\min\left(\frac{1200-x_{1}}{3},\frac{300-x_{2}}{2}\right)$$ ...