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Questions tagged [economics]

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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How to model a simple market equilibrium with linear programming?

I want to model the following problem. The problem is well-known in economics. demand-supply curve equilibrium. Is there any straight forward technique to solve the equilibrium point obtained by an ...
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16 views

Derivatives/Optimization, Macroeconomics-New Keynesian economy-from Heijdra book

So I get the process shown till (e). What I do not understand is how they get from (f) to (g), and unfortunately, also from there till (j). If anyone could show me how they did the derivatives + ...
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48 views

I'ts true that this sum is equal to this integral?

I need to know how that sum $$\sum_{k=1}^n \frac{1}{(1+i)^{T_k}}*({T_k}-{T_{k-1}})$$ Can be equal to the integal $\displaystyle \int^{{T}}_{0} {\frac{1}{(1+i)^{s}}}ds$ Where $T_0=0$ and $T_n=T$ and ...
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1answer
22 views

Monthly change formula logic.

I need an explanation of the formula: monthlyChange=(newValue-oldValue)/oldValue Why to divide by old value? Apparently the difference is described well just via subtracktion "newValue-oldValue".
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15 views

Integration by parts (proposition in Bontemps et al (2000) “Equilbrium Search with Continuous Productivity Dispersion”)

I am struggling to understand a step in a proof of existence of equilibrium in the following paper: Bontemps, Robin, Berg (2000) "Equilbrium Search with Continuous Productivity Dispersion" (starts at ...
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1answer
36 views

How to improve general mathematical literacy?

Hi I'm a Sophomore in economics attempting to read published economics papers. I often encounter models such as the one below: I've taken several lower-level mathematics courses but have difficulty ...
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13 views

I don,t know how to derive labor augmented growth accounting [closed]

Using $Y=F(K,AL)$, I want to know how to derive $$\frac{dY}{dt}/Y = \frac{dF}{dK} × \frac{K}{Y} × \frac{dK}{dt}/K + \frac{dF}{dL} × \frac{L}{Y} × \left[ \frac{dA}{dt}/A +\frac{dL}{dt}/L\right]$$
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1answer
25 views

Can someone explain the derivation for this profit function

So, how come the derivative ends up as f'-q/l Some other identities are qi/q=Li/L, qi=Li/L * f(L) and L=sumLi enter image description here
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0answers
37 views

Prove that $\min_{\mu}\sum_{i=1}^n|y_i-\mu|=\text{median}\{y_1,\cdots,y_n\}$ [duplicate]

How to prove the equation below in a simple way? $$\min_{\mu}\sum_{i=1}^n|y_i-\mu|=\text{median}\{y_1,\cdots,y_n\}$$
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1answer
37 views

Why does this integral hold?

Given that $h_i(p,u) = \frac{de(p,u)}{p_i}$, why does this equality hold? $p^0$ is a vector $(p^0_1, p^0_2, p^0_3....)$ and $p^1$ is a vector $(p^1_1, p^1_2,....)$ . Shouldn't the upper bound and the ...
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1answer
34 views

Why does this equality hold (integrals)?

Could someone explain the last equality for me? Source: MWG Microeconomic Theory
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1answer
53 views

Demonstrate that (1) and (2) are equal

$$DR_t= \frac{B_t}{P_t}-\frac{B_{t-1}}{P_{t-1}}\tag{1}$$ $$DR_t=\frac{NB_t}{P_t}- \pi_t\frac{B_{t-1}}{P_t}\tag{2}$$ Knowing that $\pi_t=\frac{P_t}{P_{t-1}}-1$ and $NB_t=B_t - B_{t-1}$, demonstrate ...
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1answer
18 views

First Order Conditions for Maximization Problem

Could someone explain why the second maximization problem follows from the first? And how did we get the FOC in that form? For $max_{p' \in R^L} py(p')$ are we holding p fixed? Thank you!
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Ordered Choice Model. Checking accuracy/forecasting

I am using an Ordered probit model. When forecasting with the model, i.e. adding new data points to estimate a probability of an event occurring my question is can I use the same data points that I ...
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0answers
28 views

Why is this matrix negative definite?

This is from the textbook "Microeconomic Theory" by MWG. On one page they said: For information, the Slutsky matrix is negative semidefinite, and x is a vector of only non-negative entries. I don'...
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15 views

Comparative statics question with an application

In the state of Mexas, two politicians (Mr. BO, or "Politician 1" and Mr. TC, or "Politician 2") are competing intensely for a senate seat. The two politicians spend on advertising to increase the ...
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1answer
15 views

If equivalent variation is 0, can compensating variation be positive?

I'm solving a problem where wealth changes and I got that $EV=0$ and $CV=1$. This seems impossible to me; is it? I'm given $e(p,u)=u/(p_1^{-1}+p_2^{-1})$. I'm also given $(p_1^0,p_2^0,w^0)=(1,1,1), ...
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1answer
41 views

Solve this particular optimisation problem

Can anyone help answer the below? I know I'm supposed to use the envelope theorem i.e. find the value function then differentiate wrt $p$$x$ and $p$$y$, but I'm struggling to get the right answer. ...
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1answer
22 views

PPF comparative advantage

Ive been looking all over the place for an answer to this question. I'm sure its simple and its driving me nuts. The answer is b. but i dont know why. $W10 = C10 \implies 1W = 1C$ $7W = 2C \...
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2answers
38 views

Is compound interest better than simple interest at all times????

I was recently calculating compound interest for one of my questions and I came to one quite intruiging problem so from what I understand simple interest is! when you have the same amount of interest ...
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1answer
17 views

I need help with a Business math markdown problem

Company x uses a markup on cost of 55% to establish its retail prices.This pricing rule builds on a profit of 22% of cost. What rate of markdown can Company X offer to break even on the reduced price? ...
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0answers
17 views

Calculate yield on weekly saving account that pays a set deposit bonus not an interest rate

If a weekly saving account paying in £100 every week for 15 weeks, paid a £25 bonus every time you deposit the £100 (Instead of a interest %), then matures at the end of the 15th week, how do I ...
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1answer
18 views

Linear Transformations of Data (Econometrics) [closed]

If $Z=XA$ and $A$ is a non-singular matrix, what is the dimension of $A$?
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1answer
71 views

Proving with calculus Cobb Douglas Production Function's Returns to Scale

Background and Trivial Proof by "Example" The way the Rate of Return for the Cobb Douglas production function is proven in the new definition of my textbook is as follows. The Cobb Douglas function ...
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1answer
16 views

Finding no. of items in the observation, when mean is given? [closed]

The mean of certain number of observations is 40. If two more items with values 50 and 64 are added to this data, the mean increases to 42. Find the number of items in the original data?
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1answer
19 views

Logarithmic derivative confusion with Elasticity of Substitution

I've been reading an economics text book ( advanced micro by Jehle) and I found this definition for the elasticity of substitution. But I don't understand what $dlnr$ would be given that $r=x_j/x_i$....
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1answer
15 views

Examples of Covariance Stationary Time Series

I seem to be having trouble in comprehending what it means for a time series to be covariance stationary. Specifically, with the third condition of for any $t$ and $h$, $ cov(x_t,x_{t+h})$ only ...
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0answers
36 views

Using kuhn tucker to solve non negativity constraints

George likes breakfast tacos and milk. His utility is given by $u(t, m) = t + 5 \ln(m)$. Suppose tacos and milk both cost 1 dollar a piece. How should George spend the $\$4$ he has set aside for ...
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2answers
38 views

inequality between entropy measure and Herfindahl index

I am considering the entropy measure and the Herfindahl-Hirschmann- (or Hirschmann-Herfindahl)-Index to measure diversification of firms. A firm is perfectly focused if it generates all sales in one ...
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1answer
20 views

Show preference relation continuity.

We have preference relation $\succeq $ on $X = \mathbb{R}^n$ represented by u(x) = $\sum_{i=1}^{n} x_i$. Show that $\succeq $ is rational, continuous and strong monotonic. So I think I have ...
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1answer
42 views

demand function from utility

thanks in advance. I’m looking to find a way (apart from Lagrange and MUx/MUy=Px/Py) to derive demand function for x, not y. You see, whenever I try solving the problem, I get y’s Demand instead of x....
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23 views

Reverse engineer maximization problem:

I am looking for a function $u(x) : R^+ \to R$, such that $\frac{w}{1+p}$ is a solution to $\max_x u(x) \text{ s.t. } px \leq w$. Is there some continuous function for which this is the case? I ...
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0answers
32 views

Lagrange multipliers and derivative of Lagrangian

I have an optimisation problem $\min f(x)$ s.t. $g(x) = E$, with Lagrangian $L = f(x) + \lambda(g - E)$, and I know that $g$ is binding. Can I argue that the shadow price can be locally approximated ...
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0answers
26 views

Micro-Econ Question | Price Elasticity and demand changes

You sell car insurance to low-income consumers. You have the cheapest rates in Texas—just $30 per month—and you have 100,000 identical customers. You estimate that the price elasticity of demand for ...
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1answer
84 views

Is “Real Analysis with Economic Applications”, by Efe A. Ok, a good book for a self-teaching beginner in real analysis? [duplicate]

I'm interested in self teaching myself Real Analysis with the primary purpose of using it for economics, for this I decided to use Real analysis with economic applications by Efe A. Ok Now what I was ...
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0answers
14 views

Find government budget at the equilibrium level of income and there is a surplus or deficit

Consider an economy in which taxes are autonomous and the following values of autonomous consumption, planned investment, government expenditure, autonomous taxes, and the marginal propensity to ...
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1answer
20 views

Finding the Minimum Price | Supply, Demand Equation [closed]

Suppose that Kodak supplies its “Instamatic” film cameras according to the equation Qs = -47,400 + 5,000*PK , where PK is the Kodak camera’s price. Consumer demand for Kodak’s instamatic cameras is ...
3
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1answer
91 views

Sanity check: Is my teacher wrong about this word problem?

I'm taking Engineering Economy this semester. I'm actually liking it so far! My teacher posted solutions to homework problems (picture 3), one of which was this one: My answer is this: $$P = \$4000,...
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0answers
36 views

expected utility, St Petersburg Paradox, effect of initial wealth on limit price

I have a question about the St-Petersburg paradox. In the case of expected utility with log utility function, how can we show analytically that, for $w > 2$, $c$ (limit price) is increasing in $w$ (...
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0answers
59 views

Finding the Dictator in Arrow's Impossibility Theorem

Arrow's Impossibility Theorem states that if we have at least three different social states and a finite number of individuals (voters), any social welfare function that satisfies the conditions of ...
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0answers
24 views

Choquet Integral - literature and papers

I'm currently looking for some books, articles and lectures about Choquet integral, it's applications (mainly in actuarial office) and everything connected to this (rather something practical than ...
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3answers
45 views

Percentage Plateau

We're trying to figure out something, and things aren't adding up. The senario is that you make $\$ 50,000$ a year. Every year you get a $15\%$ bonus of that income, which then gets added to your next ...
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2answers
103 views

Can you solve this stolen money riddle?

So, a basic word problem has gone viral on FaceBook quite a few times now and many people remain convinced of their own incorrect answers. Suppose a man walks into a store to steal a $\$100$ bill ...
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2answers
80 views

Explaining Why the Zero Conditional Mean Assumption is Important

I am currently relearning econometrics in more depth than I had before. One thing I am trying to make sense of currently is why it is necessary for the assumption of: $$E(u\mid x)=E(u) $$ to be true (...
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1answer
75 views

Players A and B repeatedly flip a (possibly unfair) coin until one loses everything. Each starting with a different amount of money

There are two players $A$ and $B$. At the beginning $A$ has $a_0 ∈ [0,1]$ amount of money and $B$ has $b_0 = 1 - a_0$ amount of money. They have one possibly unfair coin which they flip repeatedly. $A$...
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2answers
56 views

Solution to a problem of equilibrium

I am not sure how to write this problem. But here it goes. I have a fixed amount of money. I want to distribute it in three different jackpots. Each one with a unique way of payout. Jackpot1 pays the ...
2
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1answer
40 views

First-Order Stochastic Dominance

Consider two cumulative distribution functions $F(x)$ and $G(x)$ for $x\in[a,b]$ where $G(x)$ has the first-order stochastic dominance over $F(x)$. That is, $F(x)>G(x)$ for all $x\in(a,b)$. We ...
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2answers
55 views

Intermediate Economics

This question refers to a market in which quantity demanded is given by $q = a - bp$ and quantity supplied by $q = c + dp$. In this market, an increase in the parameter $a$ would: a. increase ...
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2answers
134 views

Demand Function

A consumer has the utility function over goods X and Y, $U(X; Y) = X^{1/3}\cdot Y^{1/2}$ Let the price of good x be given by $P_x$, let the price of good $y$ be given by $P_y$, and let income be ...
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1answer
26 views

What is an example of a situation that uses the kinematic equations that isn't motion through space?

The kinematic equations describe the relationship between a variable $x$ and its first $\frac{dx}{dt}$ and second $\frac{d^2x}{dt^2}$ derivatives, assuming its second derivative is constant. This does ...