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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1answer
19 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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3answers
46 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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1answer
18 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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1answer
25 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% ...
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0answers
8 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
19 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
28 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
8 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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1answer
37 views

Cost minimisation calculus

(Note: I'm a beginner at calculus): I'm solving a calculus problem in microeconomics intermediate course. The question is: Determine the factor demand functions, 𝑥∗(𝑤 , 𝑤 , 𝑦), by using the cost ...
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0answers
25 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
43 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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1answer
18 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 ...
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0answers
23 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
6 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
89 views

Utility maximization of n goods

I have a question that involves finding the optimal demand of $n$ goods for a consumer. However, I haven't anything like this before and I'm not sure how to proceed. The consumer has a utility ...
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1answer
634 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 ...
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0answers
12 views

Seasonal time series

I am working with yearly sunspot number time series, which is clearly seasonal (period of 11 years). I have tried to model it with SARIMA (so that is a seasonal time series), but the best model was a ...
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2answers
8 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
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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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
17 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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1answer
32 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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1answer
22 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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0answers
23 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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0answers
15 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
32 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
39 views

Exchange Rate Dynamics

Due to my project in mathematics I am trying to understand the dynamics of exchange rate. Consider the following: $$\dot{p}= \pi \ln (D/Y)= \pi[u+\delta(e-p)+(\gamma -1) y-\sigma r] \ \ \ \ \ \ \ \ ...
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1answer
23 views

About Linear Regression

Let the regression model of $y_i$ over $x_i$, $i=1,2...,N$$$y_i=\beta x_i+u_i$$, then $$\beta=\frac{\sum y_ix_i }{\sum x_i^2}=\frac{\sum y_i }{N}=\bar{y}$$ The problem is that I can't see how to ...
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1answer
15 views

Overlaping jurisdictions Model: Proof of Lemma 1; The Size of Nations

I've been reading the book 'The Size of Nations' by Alberto Alesina and Enrico Spolaore (can be found on the net if you know where to look) and I'm having trouble following their "proof" of the first ...
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3answers
30 views

Use the given rate of inflation to calculate the value of $100 in 1910, now.

problem: You have been told that the average rate of inflation between 1910 and 2016 is $3.8\%$. Using this information, calculate how much $100 in 1910 would be worth today. What I tried: This one ...
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0answers
109 views

Question on economics (monopolist) (will involve simple calculus)

QUESTION: Consider the problem of a monopolist that sells its product on two different markets $m$, with $m=1,2$. Each market has an aggregate demand function given by $1200−α_mp_m$, where $p_m$ ...
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1answer
18 views

Need to find annual payment in 2 halfs of the payment period [closed]

A loan of $4000 is to be repaid over a period of 8 years. During the first years, exactly half of the loan principal is to be repaid (along with accumulated compound interest) by a uniform series of ...
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2answers
24 views

Rearranging economics equation - steady state of capital

In my textbook, there are two formulas that follow on from each other, which I can't seem to be able to recreate. These are equations from the Solow-Swan model of growth in economics which state, that ...
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2answers
122 views

Break Even Point

Suppose that x thousand units of a product will be sold when the price is p(x) = 50 - 1.25x dollars per unit and the cost of producing x thousand units is C(x) = 20x + 100 thousand dollars. a) What ...
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1answer
41 views

Solving $(1.0025^N - 1 )/1.005^N = 0.4$ without linear interpolation

How can I solve an equation in this form without using linear interpolation? $$ \frac{1.0025^N - 1 }{1.005^N} = 0.4 $$ Usually I would have to guess two values that I know $N$ is between and then ...
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1answer
31 views

Find the Nash equilibria

A law is passed requiring a monopolistic soft-drink manufacturer to separate the production department and the marketing department. The marketing department chooses the price $P > 0$ to charge for ...
0
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1answer
11 views

Find all Nash equilibria in pure strategies

We consider the following public good provision game. There are 2 players, each choosing the amount of money $x_i$ ($i$ denotes 1 or 2) they will give to build a public good. We assume that each ...
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2answers
38 views

Generate two negatively correlated data in excel

Let's say that we have two prices that are negatively correlated to each other, for instance we have price $p_1$ and we want to generate negatively correlated price $p_2$ with the following ...
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1answer
16 views

Find subgame Nash equilibrium

Two players, A and B play the following game. First A must choose IN or OUT. If A chooses OUT, then the game ends, and the payoffs are: A gets 2 and B gets 0. If A chooses IN, then B observes this and ...
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0answers
18 views

What can you conclude from this correlogram?

You have 100 observations of a time series, y. You run a regression of y on the first ten lags of itself. You examine the results, which show that the coefficient on the tenth lag is 0.35 and it is ...
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1answer
17 views

Annuity and future equivalent values

I need some clarification on the formulas to use for these questions. Q1. If $\$30,000$ is deposited now into a savings account that earns $7\%$ per year, what uniform annual amount could be ...
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1answer
21 views

Basic question about algebra for relative demand.

Suppose I have two markets, Home and Foreign. Suppose that $$\frac{p_1}{p_2} = \frac{c_2^F}{c_1^F}$$ $$\frac{p_1}{p_2} = \frac{c_2^H}{c_1^H}$$ Supposedly I am supposed to be able to show ...
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1answer
20 views

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 ...
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1answer
30 views

Economics Application of Rates of Change

The Consumer Price Index ($CPI$) is a statistical estimate of the change of prices of goods and services bought for consumption. It is generally calculated by collecting the prices of a sample of ...
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0answers
21 views

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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2answers
23 views

Are these results consistent with expected utility thoery?

Results show people prefer gamble A over B. The same group of people prefer gamble C over D. A: $2400 for sure B: 0.33% chance of $2500, 0.66% chance of 2400, and 1% chance of 0 C: 33% change of ...
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0answers
15 views

Confidence Intervals for Elasticities using Conversion Rate

I am looking at elasticities for price changes in e-commerce data. The different prices have very different quantities because of the different number of page views, so I'm using Conversion Rate ...