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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23 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 ...
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1answer
5 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 ? $$E_xf(x_0) = \frac{f'(x_0)·x_0} {f(x_0)} $$ ...
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1answer
46 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
20 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
23 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: $PROFIT(L,K) = 50 L^{0.2} K^{0.8}$, ...
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2answers
20 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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1answer
24 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 ...
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1answer
52 views

Help please mathematics [on hold]

Suppose that the dollar cost of producing q appliances is $c(q)=1000-0.05q+0.3q^2$ And the demand function is given by $p=20-0.025q$? Q1: compute the marginal cost when the quantity is equal to 1 ...
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1answer
19 views

In what way is ex post implementation important in robust mechanism design? [closed]

Can someone tell me the difference between ex post implementation and dominant strategy implementation. In what way is ex post implementation important in robust mechanism design?
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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 ...
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1answer
21 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 ...
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1answer
15 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 ...
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0answers
27 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, ...
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0answers
10 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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1answer
18 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 ...
4
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1answer
58 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
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1answer
25 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 ...
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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 ...
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0answers
12 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 ...
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0answers
15 views

economics partial derivative / consumer surplus question

Answer ALL parts of this question. (a) Explain what is meant by a „partial derivative‟, (you should include the definition of a partial derivative). For the function $z$ defined below, determine all ...
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0answers
48 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: ...
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0answers
38 views

Maximise the function with constraints

Is it possible to maximise this function algebraically $$f(x_{1},x_{2})=5\cdot \min\left(\frac{x_{1}}{6},\frac{x_{2}}{2}\right) + 2\cdot\min\left(\frac{1200-x_{1}}{3},\frac{300-x_{2}}{2}\right)$$ ...
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0answers
21 views

References for Duality Theory

I was wondering if anyone had any recommendations for Duality Theory. I've touched on Duality before in various courses but it's coming up quite a lot in my studies at the moment. I guess what I'm ...
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0answers
12 views

Infinite Horizon Transversality Condition

I am an economics student, and I have run into a question where I must apply a transversality condition in order to prove that we have a balanced growth path (all variables grow at the same constant ...
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1answer
23 views

Constrained maximization of …

I have to maximize $U(x,y)= Min(ax+y, by+x)$ s.a $p_{1}x +p_{2}y =m$. I try the traditional solution for a leontieff $(ax_{1}+y= by_{1}+x)$ function but I'm not sure.. beacause exist regions where one ...
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1answer
22 views

A Basic Question E-views

I ask a question about E-views. Is the P-value in the picture less than 0.05 or greater than 0.05? I'm confused because of the presence of the sign '<' in front of 0.10. Please help mee. Thank you. ...
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0answers
74 views

Advantages/disadvantages of a utiliarian social welfare function

If a planner obeys anonymity and strong Pareto principle (individual preferences carry over to the group), then the social utility function will be: $W(x)=\sum_{i=1, ..., n}U_i(x)$ i.e. summing ...
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1answer
30 views

Volatility of investment (/w currency hedging)

I´ve been trying to compute a volatility of invesment with currency hedging and I have a question. Let's take this example. We have our money in a fond copying the S&P500 index, which has 16% ...
0
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1answer
27 views

Prove that the core of this game is empty

A game (N, v) is simple if for every coalition S is a proper subset of N, either v(S) = 0 or v(S) = 1, In a simple game, a player, i, is said to be a veto player, if v(N \ {i}) = 0. Suppose (N,v) is ...
2
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1answer
32 views

Find Bayesian Nash Equilibria

A rich, honest, but mischievous father told his two sons that he had placed $10^n$ and $10^{n-1}$ in two envelopes respectively, where n ∈ $\{1,2,3,\ldots,10\}$. The father then randomly handed each ...
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0answers
12 views

Industry characterized by market power leads to deadweight loss

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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3answers
51 views

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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0answers
26 views

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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1answer
44 views

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 ...
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1answer
29 views

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 ? ...
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0answers
27 views

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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1answer
21 views

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 ...
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0answers
9 views

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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0answers
15 views

How to calculate the value added for the following question?

In $2012$ a store imported an iPad for $400$. In $2013$, the store sold the iPad for $600$. As a result of these transactions, the value added is: $A) 400$ in $2012$ and $600$ in $2013$ $B) 0$ in ...
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2answers
9 views

How to calculate the marginal cost of the following gasoline price?

A driver wants to buy gasoline and have her oil checked,too. The price of gasoline at the pump is 2 dollars per litre. The pricing for the oil check varies: it's 1 dollar when she buys 49 litres and ...
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0answers
12 views

Seanonal unit root test in gretl for seasonal period bigger than 12

I am working in GRETL with monthly sunspot number time series which is a seasonal time series with seasonal period 128 (11 year = 128 months). I am trying to perform the seasonal unit root test in ...
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0answers
19 views

Are these preferences rational according to utility theory?

I have this question about whether preferences satisfy the $6$ properties of utility, and am particularly stuck on the boundness, coherence and continuity conditions. Here is the problem: If one ...
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0answers
12 views

Does there exist a utility function for these gambles and preferences?

Suppose that you prefer a gamble which pays $£100$ with probability $0.5$ and $£10$ with probability $0.5$ to a gamble which pays $£200$ with probability $0.25$, $£50$ with probability $0.25$ and ...
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0answers
28 views

Show, by example, that we can find social welfare functions which satisfy any three of the four Arrow's axioms.

I want to show, by example, that we can find social welfare functions which satisfy any three of the four Arrow's axioms. Given at least three rewards, and at least two individuals, there is no ...
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1answer
28 views

Pairwise majority voting and Arrow's axioms

The following is a question on Arrow's theorem with a pairwise majority decision. The bits I was unsure about was (bi) (is the 4th condition satisfied?) and also is (bii) correct? Thanks for your help ...
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1answer
34 views

Arrow's theorem, strategic thinking and utilitarianism

I have this problem as part of a course on Decision Theory, and was not sure about question a (4th condition of Arrow's theorem) and question dii (utilitarianism). I have provided the whole question ...
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0answers
18 views

Sen's theorem on minimal liberalism

I want to solve the following question regarding Sen's theorem and preferences orderings. The bit I am having trouble with is 2b Question 1: Describe Sen's theorem ('paradox') There is no social ...
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0answers
34 views

Expected annual returns (financial maths)

An economy contains these three assets: Asset A has standard deviation of returns (per annum) of 25% and market capitalisation $600m Asset B has standard deviation of 20%, market capitalisation ...
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1answer
20 views

Give an example that the following condition does not imply WARP

I know how to prove that Weak Axiom of Revealed Preference (WARP) implies the following condition: if $a\in B_1, B_1 \subseteq B_2, a\in C(B_2)$, then $a\in C(B_1)$. $C$ here is a notation for choice ...