Questions tagged [elasticity]

Elasticity is the measurement of how responsive an economic variable is to a change in another.

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23
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4answers
2k views

What are Giffen Goods?

What exactly are Giffen goods and are they of purely theoretical interest or has there been empirical evidence of their existence?
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2answers
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How is price elasticity determined in practice?

Price elasticity of demand and Price elasticity of supply are two of the most important concepts of microeconomics, but they're generally explained from a hypothetical standpoint, and little effort is ...
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1answer
11k views

How does one derive the elasticity of substitution?

For two goods $x$ and $y$, the elasticity of substitution is defined as $$\sigma \equiv \frac{d\log\left(\frac{y}{x}\right)}{ d\log\left(\frac{U_x}{U_y}\right) }= \frac{\frac{d\left(\frac{y}{x}\right)}...
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5answers
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Econometrics: Is elasticity meaningful in my, or any, regression?

A few months ago I interned at this organization; and, as a going away present, I decided to spend my last week, with whatever off time I had, to investigate the factors that affect teacher salaries. ...
12
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1answer
730 views

What are estimates of the elasticity of demand for credit with respect to interest rates?

When interest rates go up one percent (not one percentage point), what happens to demand for credit? I've only been able to find two papers in this area: Gross and Souleles (2001) study credit cards ...
11
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1answer
443 views

Is elasticity of substitution between goods empirically constant?

In New Keynesian models, we use a lot of CES assumption, usually Dixit-Stiglitz, to develop an economic model. Is CES, constant elasticity of substitution between goods, empirically (approximately) ...
9
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3answers
3k views

Why absolute value in elasticities and marginal rate of substitution?

This is a point I find very confusing and very hard to justify to students. Depending on the books, one finds many different conventions regarding the sign of elasticities and marginal rate of ...
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3answers
12k views

Intuition - Why does elasticity vary along a curve?

Source: p 96, Principles of Microeconomics, 7 Ed, 2014, by N Gregory Mankiw Even though the slope of a linear demand curve is constant, the elasticity is not. This is true because the slope is ...
7
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2answers
896 views

Constant Elasticity of Substitution: Special Cases

Take an $n$-commodity constant elasticity of substitution utility function, $$U = \left[\sum^n_{i=1} \alpha_i x^\rho_i \right]^\frac{1}{\rho}$$ How do we show the following: Show that as $\rho \...
7
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2answers
473 views

Is elasticity purely an aggregate concept or can it be individualized

First question here. I am not an economist by training, but I do quite a bit of econometric analysis in my job (my background is maths). I often get asked about elasticity, and I am familiar with ...
7
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2answers
1k views

What determines the outcome of a price war, and why isn't that outcome reached instantaneously?

Mary is making a hefty profit manufacturing and selling widgets. Jim has some money laying around and he is trying to figure out if he shouldn't start manufacturing some widgets too. In this example ...
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Calibration of utility function parameters controlling labor disutility

Consider the very basic utility function $$ u(c, n) = \log (c) - \alpha \frac{n^{1 + \frac{1}{\nu}}}{1 + \frac{1}{\nu}}$$ Where $c$ is consumption and $n$ is working hours. As the Frisch elasticity ...
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2answers
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Elasticity of demand equals -1 but income decreases!

In my textbook, it's stated that: When $\epsilon < -1$, demand is elastic and raising price will result in smaller income, while lowering price will result in bigger income. When $\epsilon =...
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567 views

Help with Income Elasticity Exercise in Becker's Economic Theory

On page 18 of his book Economic Theory, Gary Becker provides the reader with the following exercise (no answers given): Exercise Statement: Write the formula $\sum_j K_jN_j = 1$ where $N_j$ is the ...
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1answer
1k views

If the Engel Curve of a Cobb-Douglas utility function is positive and linear, than does that mean it is neither a necessity nor a luxury good?

Since the concavity of the Engel Curve determines whether it is a necessity or luxury (i.e. how fast quantity demand changes in relation to changes in income), and since the second derivative of a ...
6
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1answer
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How do I calculate price elasticity of demand using historical price and quantity data?

I work for a company that produces retail items and I am tasked with calculating the price elasticity of demand for a subcategory that shall remain unnamed. I have 5 years of monthly market data that ...
6
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1answer
427 views

Estimating Price Elasticity from sales

I'm looking at data for an online shop with clothing items listed at different prices. I'd like to use this information to do some kind of profit maximization (i.e. I'd like to have some understanding ...
5
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2answers
318 views

Proof coefficient in log-log model is equal to coefficient of elasticity

I am trying to see how we treat $\varepsilon$ in the following proof: Suppose we have a log-log single variable regression model $$ \ln(y) = \alpha + \beta \ln(x) + \varepsilon $$ then take partial ...
5
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2answers
665 views

Horizontal demand curve

If it is assumed that every consumer within a particular region has the same 'valuation' for a certain product, and consumers will purchase no more than one unit of the product, is the market demand ...
5
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2answers
760 views

Calculate the elasticity of substitution of Epstein-Zin preferences

$$ \newcommand{\E}{\mathbb{E}} $$ Let a consumption sequence be given $C=(C_0, C_1,...)$ and let $C_t^+ = (C_t, C_{t+1}, ...)$. Now, suppose I have Epstein-Zin preferences, \begin{align*} U_t(C_t^+) &...
5
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1answer
104 views

Using an elasticity to evaluate changes in a dependent variable

Often in textbooks and online I see thte definition of an elasticity to be as follows: 1) $\epsilon = \frac{\frac{\Delta Y}{Y}}{\frac{\Delta X}{X}}= \frac{\partial \log Y}{\partial \log X}$ Thus, ...
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2answers
154 views

Can Linear Supply-Demand Equilibria Be Understood as a Feedback-Control Process?

I'm not an economist, but rather an applied mathematician working in control theory. I've recently been watching Berkeley's intro to econ course in a personal project to better understand economics ...
5
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1answer
330 views

Housing Supply Elasticity: Proxy for Exogenous House Price Movements

Mian and Sufi (2014) say We use individual and zip code level data, and exploit cross-sectional variation in house price growth to estimate the impact of rising home values on borrowing and ...
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3answers
1k views

Price Elasticity of Demand for Positive Price Increases

What does it mean when the price elasticity of demand %Qd/%P is greater than one? Typically I hear that it means the demand is elastic since if, say, the price decreases by 1% the demand for the ...
5
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1answer
63 views

Why do money markets fluctuate so much?

Compared to commodity markets, money markets move a lot. My guess is that commodity markets are less elastic due to fixed production costs. But I don't know if that is the correct explanation.
5
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1answer
201 views

Generalized KPR: Frisch Elasticity

Consider the following version of KPR preferences (with $l$ being leisure): $$ U(c,l) = \left(\left(c\right)^\gamma l^\omega\right)^{1-\sigma}$$ I'm after the Frisch elasticity: $$ \frac{\partial(1-...
5
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1answer
555 views

Estimating elasticity of substitution in nested CES functions

I have aggregate data on $L_t, K_t$ and $X_t$, and want to estimate elasticity of substitution parameters, $\gamma$ and $\sigma$ for these factors. Assuming the production function takes the following ...
5
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1answer
177 views

About intertemporal elasticity of substitution

The inter temporal elasticity of substitution between two periods of time is $$\sigma=-\frac{d[\ln(c(s)/c(t))]}{d[\ln(U'(c(s))/U'(c(t)))]}$$ I need to prove that $$\lim_{s \to t}\sigma = -\frac{U'(c(t)...
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2answers
561 views

Estimating price elasticity of demand

I have 25 quarterly observations and I want to estimate price elasticity of demand. I intented to use GMM-IV estimator. However, I read that it is not good for small samples. What can you suggest me? ...
5
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2answers
3k views

Elasticity of Durable Goods vs Non-Durable Goods

Does anyone know any seminal reference (either a paper in a top economics journal or a book) that compares own-price elasticities of demand for durable vs non-durable goods? My intuition tells me ...
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4answers
10k views

Why are elasticities defined as logarithmic derivatives?

In my economics class, we often compute the elasticity of $Y$ with respect to $X$, $$\eta = \frac{\partial \log Y}{\partial \log X}.$$ You can compute this from the slope of a line fit to a log-log ...
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4answers
9k views

Intuition: Why does perfectly elastic supply imply no producer surplus?

Foreword: I ask NOT about the whole question; so I quote only the following part of the answer. Source: p 153, Question 7c, Principles of Microeconomics, 7 Ed, 2014, by NG Mankiw = Chapter 7, Question ...
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3answers
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Why is the Market-Clearing Price also an Equilibrium Price?

When the price is such that supply equals demand for e.g. bicycles, everybody who wants to buy a bike at that price gets one, and every bike gets sold. Everybody goes home happy and the marketplace ...
4
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1answer
135 views

Question on significance of different ways of measuring Price Elasticity of Demand

I'm a pre college student, self studying economics, I have a question regarding the different forms of measurement of Price Elasticity of Demand. The basic equation for PED with respect to a point $(...
4
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1answer
519 views

Demand Curves for Stocks

i am currently working on a paper on demand curves for stocks and have some questions. I've read that many models (CAPM, APT, Modigliani-Miller theorem) assume demand curves for stocks to be flat. Can ...
4
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2answers
3k views

Monopoly pricing under constant elasticity of demand

While reading Ch. 24-Monopoly from Intermediate Microeconomics by Hal Varian (8 th edition), on pg. 441, he writes that a monopolist will never choose to operate where the demand curve is inelastic. I ...
4
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1answer
83 views

Demand function estimation

The model specification is: $$D_{ij} = A + aP_{ij} + bY_{ij} + cN_{ij} + e_{ij}$$ where: $i, j$ = $i$-th year, $j$-th month, $D$= demand (outgoing minutes) $P$ = average price of call, $Y$ = ...
4
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1answer
257 views

Elasticity of substitution in Jehle and Reny Advanced Micro (3rd ed) exercise 3.8

Letting $f_i(\mathbf{x})=\partial f(\mathbf{x})/\partial x_i$, ($\mathbf{x}$ is a vector, a commodity bundle, and $x_i$ is a scalar, commodity $i$ in the bundle) show that, $\sigma_{ij}(\mathbf{x})\...
3
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2answers
420 views

How exactly does elasticity relate to slope?

My book (Goodwin's Microeconomics in Context, pg. 117) states the following about price-elasticity of demand: Given two demand curves that go through a specific point on graphs with the same scale, ...
3
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2answers
1k views

Elasticity and logarithms

Let's consider a relationship between $ y $ and $ x $, $ y = a x^b $. Taking log on both sides, we have $$ \log y = \log a + b \log x $$ Now, my textbook, Nicholson and Snyder's Basic Principles and ...
3
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2answers
113 views

Terminology, is elasticity used as “mean elasticity”?

Given a demand $q$ and a price $p$ sutch that $q=q(p)$, the elasticity of demand is given by, $\epsilon = \frac{p}{q}\frac{dq}{dp}$ which depends on the price. But, when reading papers about ...
3
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2answers
51 views

elasticity from inverse demand

I was wondering of my thinking here was right: Given $$ e=\frac{dQ}{dp}*\frac{p}{Q}, $$ where $ e $ is elasticity, $ dQ/dp $ is first derivative of demand function, $p$ is price and $Q$ is quantity. ...
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2answers
88 views

Why is the Supply of Labour More Elastic in a Single Province/State then it is in the Country as a Whole?

Apparently, the federal government has a greater ability than provincial government to increase tax revenues by raising tax rates because the supply of labour is more elastic in a single province than ...
3
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2answers
4k views

What is the difference between constant elasticity of substitution and elasticity of substitution?

What is the difference between constant elasticity of substitution and elasticity of substitution? Are these formulas related? How are they different concepts? I just did a whole problem set involving ...
3
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1answer
87 views

Why is the graph of unitary elastic demand a hyperbola?

My teacher said that the graph of unitary elastic demand is a parabola: But i fail to understand how in a hyperbola the percentage change of price and quantity demanded remains same. Can someone ...
3
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1answer
424 views

Usefulness of the value for the slope of the demand curve

I see the elasticity value(s) of demand being used frequently to determine the relation between demand and variables such as price and income. I have however been unable to find any uses for the slope ...
3
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1answer
34 views

Does one include inflation when computing elasticity?

I am attempting to compute the price elasticity of a good with the help of a time series, and am unsure whether to correct the prices for inflation. Is there a standard argument for one or the other ...
3
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2answers
138 views

Elasticity when the demand function is given

Given the demand function, $ q = kp^{-\epsilon} $, how do I calculate the elasticity? As a result, I do know that the elasticity when the demand function is in this form is $ - \epsilon $. But I'd ...
3
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2answers
41 views

Is there any work on equality in a market versus friction?

This is a question about educational economics. There is a phenomenon when studying countries like the USA and Chile (that have implemented voucher systems) that reducing the friction in a "...
3
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2answers
428 views

Very elastic supply + very inelastic demand

Suppose we have a very elastic supply curve and a very inelastic demand curve. Further suppose there is a decrease in input prices which shifts the supply curve outward. By taking an extreme ...