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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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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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 \end{...
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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 ? I'...
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33 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
22 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 days? ...
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0answers
11 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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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
10 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 0....
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13 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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20 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 $£10$...
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0answers
31 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
30 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
36 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
19 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
38 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 ...
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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
32 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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2answers
27 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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0answers
111 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
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 ...
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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
26 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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22 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
20 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
22 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 $$\frac{...
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1answer
21 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 market,...
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1answer
19 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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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 ...
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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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1answer
35 views

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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30 views

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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0answers
23 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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0answers
24 views

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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1answer
29 views

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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2answers
22 views

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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1answer
311 views

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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0answers
40 views

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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0answers
16 views

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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0answers
31 views

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)...
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1answer
43 views

Solving for n in Present Value and Annuity formula

I derived the formula for n=.... of the following formula P = $\ 525 $ A = $\ 15 $ i = $\ 0.015 $ Answer: $\ 50 $ P = $\ A [\frac{((1+i)^n - 1) }{ (i*(1+i)...
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0answers
15 views

Engineering Economics

Suppose that a college graduate earns about 78% more money per hour than a high- school graduate. If the lifetime earnings of a high-school graduate average $1,200,000, what is the expected value of ...
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1answer
37 views

Profit and loss question.

A person bought two bicycles for Rs.1600 and sold the first at 10% profit and the second at 20% profit. If he sold the first at 20% profit and the seconds at 10% profit .He would get Rs.5 more.The ...