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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110 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
22 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
19 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
18 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 ...
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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 ...
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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
33 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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0answers
29 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 ...
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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 ...
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1answer
234 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 ...
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1answer
42 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) }{ ...
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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
34 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 ...
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0answers
26 views

Time derivative of a production function

Given the production function is $$Y=F(K,AL) = \left [ \alpha (AK)^{\rho} + (1-\alpha) L^{\rho} \right ]^{\frac{1}{\rho}},$$ and that capital $K$ evolves at time $t$ as expressed by this equation ...
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0answers
20 views

Envelope theorem for Conditional value at risk

Let $X$ be a Gaussian random variable and suppose $f(p,X)$ is a strictly increasing and continuous function in $p \in \mathbb R$. Conditional value at risk is defined in the following way ...
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1answer
44 views

For which values of $\rho$ does the CES production function satisfy the Inada conditions

Given $F$ is a constant elasticity of substitution (CES) production function: $$F(K,AL) = \left [ \alpha K^{\rho} + (1-\alpha) (AL)^{\rho} \right ]^{\frac{1}{\rho}},$$ where $\alpha \in \left ( 0,1 ...
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1answer
25 views

Mixed portfolio [closed]

Suppose that Ms Lynch can make up her portfolio using a risk-free asset that offers a surefire rate of return of 15% and a risky asset with an expected rate of return of 25% with standard deviation 5. ...
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1answer
43 views

price and quantity after taxation

Given that demand for a good X is equal to $q_D=393-2p$ and market supply is $q_S=p/4-12$. Find equilibrium price and quantity, consumer and producer surplus and draw a diagram illustrating the ...
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1answer
24 views

Penalty and minimization of a social cost

It is part of broader question in economics however it is about minimizing the expression (which depicts social cost of a crime): the expression is $$\min ...
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1answer
63 views

Public goods - 2 people buying something

Bob and Ray are thinking of buying a sofa. Bob's utility function is $U_B(S,M_B)=(1+S)M_B$ and Ray's utility function is $U_R(S,M_R)=(3+S)M_R$ where $S=0$ where S=0 if they do not get the sofa and S=1 ...
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1answer
31 views

Government's intervention - price and quantity after taxation

Given that demand for a good X is equal to $q_D=393-2p$ and market supply is $q_S=p/4-12$. Find equilibrium price and quantity, consumer and producer surplus and draw a diagram illustrating the ...
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0answers
22 views

Change in variables that depend on each other in a system of equations

This is an economics question, but I have been referred to math stack exchange: We have the following equations: \begin{align}Z &= C + a + b \\ C &= cY, \\ Y &= Z.\end{align} Easily ...
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0answers
47 views

how to calculate expected utility for probability decision problem?

consider a decision problem: classifying $x$ as belonging to one of two classes $C_1, C_2$. there are prior probabilities for each class, $p(C_1), p(C_2)$ and likelihood probabilities for data given ...
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2answers
44 views

Maths for economics: finding the level of production that minimises marginal cost [closed]

Let the total cost function of a firm be given by: $$TC(Q)= 16Q^3 - 72Q^2 + 446Q + 90$$ Find the level of production that minimises the marginal cost of production. (This is basically taking the ...
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2answers
120 views

First mover advantage in a Stackelberg game

I am considering a simple game with two firms. Each firm faces the following demand function \begin{equation*} q_i(p_i,p_j)= a- b p_i + cp_j, \end{equation*} where $i,j\in \{1,2 \}$ and $i\neq j.$ ...
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0answers
18 views

Difference between Sequential and Weak Sequential Equilbria

This is in reference to the Game theoretic concepts as Nash equilibrium refinements. Sequential equilibrium are often defined as satisfying two conditions: consistency and sequential rationality. ...
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1answer
26 views

Recursive utilities in a repeated game

I am trying to set up utilities for an infinitely repeated game and I am having some trouble figuring out how to write the correct functional form. This game has a stochastic component where a ...
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0answers
38 views

Kuhn Tucker condition is sufficient for a global optimum?

$L$ is the variable and $s,r$ are parameters. The question asks to solve $max_{L\geq0}rf(L)-wL$ where $f(L)$ is twice continuously differentiable, strictly increasing and strictly concave. Then how ...
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2answers
35 views

Max price of a share

Company is planning to pay a dividend of 5\$ per share (dividend for previous year). Investor that wants to buy a shares of this company assumes that dividend will be stable (Thus will not change in ...
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0answers
12 views

Are distributed lag (DL) models with i.i.d. error always stable?

I am currently doing an econometrics course for which there is no textbook available, and cannot find the answer for the above question. I understand that a distributed lag model DL(q) can also be ...
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1answer
52 views

Application of Integration on Investments

A small business expects an income stream of $\$300$ per month for a period of $9$ years. The income will be invested at an annual interest rate of $17\%$, compounded continuously. How much interest ...
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1answer
18 views

How to determine loan payment and total price of a loan

Let's say, that we have borrowed a $100,000 for a 5 years, with 6% p.a. interest rate. How can one determine the value of a loan payment, if we are making payments every quarter and at the beginning ...
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4answers
57 views

What are the restrictions such that $f'(x) = f(x)/x$?

Let $C(y) \geq 0$ denote some cost function. Let $MC(y) = C'(y)$. Let $AC(y) = \frac{C(y)}{y}$. I am considering the economic case where $$MC (y)= AC(y)$$ This boils down to a simple math problem as ...
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1answer
19 views

Microeconomics competitive equilibrium interest rate determination

I've got a microeconomics question that involves rearranging an equation with summation, where the only constant are $1$ and $r$. Firstly this is the equation stating that across individuals $i=1$ to ...
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0answers
10 views

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

Now I have $ 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 + ...
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1answer
51 views

Tail driven inequality [closed]

In this empirical model, Lj is a measure of left-tail driven inequality and Rj a measure of right-tail driven inequality. It represents what in this article? What exactly is the meaning of ...
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0answers
16 views

R squared conceptual question with respect to number of observations.

The following statement is true. However, I have difficulties to understand why. I would appreciate if someone could explain it conceptually or perhaps with or without reference to any formula. In a ...