Questions tagged [elasticity]

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

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Can an inferior good be necessary?

Usually the definition of necessary goods is the income elasticity between 0 and 1. But can a good with -0.5 income elasticity be considered necessary? There is this link that says that all the ...
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Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic?

As we know that $Q*P=const.$ for Cobb-Douglas preferences, we can thus conclude that $\frac{dQ/Q}{dP/P}$ is always $-1$: $$ QP=const. \implies 0=d(PQ)=Q\ dP+P\ dQ \implies \frac{dQ}{Q}=-\frac{dP}{P} $$...
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How do I determine PED from price consumption curve with slope of zero?

Given a budget for two goods $x_1$ and $x_2$, a fixed price for good 2 and three prices for good 1 with the corresponding optimal amount of good 1 ($x_1$), I like to calculate the PED for good 1. By ...
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Without knowing the Slutsky equation and income/substitution effect, how can I show a certain good is inferior or Giffen?

Say I've got a function $x_1(p_1,p_2,m)$ where $p_1, p_2$ are the prices for good 1, good 2 respectively and m is the income. Now, I haven't heard of the Slutsky equation yet nor the income/...
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Elasticity Cobb-Douglas production function

I am given the production function $y=x_1^\alpha x_2^{1-\alpha}$, where $0< \alpha <1$ I found the demand functions for minimum production cost to be $ x_1^{*}(w_1,w_2,y)=\left ( \frac{w_2}{w_1}\...
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Relation of Engel-curve to income elasticity of demand; is the slope of the Engel-curve equal to the elasticity of income?

I learnt that $\frac{\Delta x}{\Delta m} \gt 0$ for normal goods, $\frac{\Delta x}{\Delta m} \lt 0$ for inferior goods, $\frac{\Delta x}{\Delta m} \gt 1$ for luxury goods and $0 \lt \frac{\Delta x}{\...
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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, ...
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Why are constant price elasticities reported?

Price elasticity of demand $\mathrm{e_{D,P} = \dfrac{dD}{dP}. \dfrac{P}{Q^*}}$ clearly depends on the levels of price and quantity. Then why is everywhere (research papers, textbooks etc.) a constant ...
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Calculating elasticity for $y^2e^{x+\frac{1}{y}}=3$

I want to calculate elasticity of y with respect to x for $$y^2e^{x+\frac{1}{y}}=3$$ My attempt: I calculate $y'$ using: $$y'= -\frac{f_1'(x,y)}{f_2'(x,y)} = - \frac{y}{2-y}$$ I calculated this using ...
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Pricing optimisation when elasticities are positives? [duplicate]

I’m performing some exercises in order to get the optimal price of some product such a potato chips, biscuits, drinks, etc. (I’m taking price per unit and sales in units) But I’ve found that some of ...
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Optimal price when elasticity of demand is positive? [closed]

I’m performing some exercises in order to get the optimal price of some product such a potato chips, biscuits, drinks, etc. But I’ve found that some of them have positive elasticities. This can makes ...
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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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107 views

Find Price Elasticity of Demand for p = 0

Given a linear demand curve $q(p) = a - bp$, how would one find the price elasticity of demand at $p = 0$? The quantity that would be demanded is given: $Q_0 = a$ The formula for the price elasticity ...
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Why do vacationers spend more on food and essentials than the locals?

I cannot think of an answer to this question from the chapter on elasticity in Tyler Cowen and Alex Tabarrok's Modern Principles of Economics, Second Edition: How might elasticities explain why ...
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Intuition behind Engel Aggregation and Cournot Aggregation

Could anyone provide a possibly intuitive and friendly explanation to the Engel Aggregation $(\sum s_i \eta_i = 1)$ and Cournot Aggregation$(\sum s_i \epsilon_{ij} = -s_j)$? Here, $s_i = \frac{p_i,x_i}...
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Relation between marginal cost and output elasticities

Does anyone know of any results that show the link between marginal cost and the output elasticities analytically? I am looking at production and cost theory books but can't find any results that ...
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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 ...
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Question about using elasticities to compare difference rates but with different normalization

Lets say I am estimating a regression of a death rate per 100k people on an economic shock, so: $y = \beta_o + \beta_1 * X+ error$ where the dependent variable is the death rate, and x is the measure ...
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When do workers versus capital owners share of income increase?

The share of total income obtained by workers rather than capital owners is for obvious reasons of interest. Assuming that the economy can be desribed by an aggregate production function $$Y = F(K,L)$$...
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Why wouldn't other firms follow suit if an individual firm decides to cut its price?

Why doesn't the demand curve an individual firm faces in a perfectly competitive market have the same elasticity as it does in a oligopolistic market? Under perfect competition, if a firm increases ...
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238 views

Monthly price elasticity and possibility of using daily values

I am calculating the price elasticity as a starting point to find a theoretical optimal price that would maximize our revenue. I am looking at 2 years data and to use the price elasticity formula, I ...
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What's the minimum number of datapoints in order to run a diff-in-diff?

I was thinking about running a diff-in-diff with fixed effect in order to deal with a panel data experiment. The problem is that I don't know how many datapoints I need in order to the experiment be ...
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Price optimization with demand forecast

I have one year sales data of a retail company and lets say I am forecasting the next month sales for the product. I have got the sales using time series in R. Now I want to forecast the price as well....
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Does Modern Monetary Theory (MMT) provide a useful insight into how to manage the economy?

According to advocates of MMT, the primary risk once the economy reaches full employment is inflation, which can be addressed by gathering taxes to reduce the spending capacity of the private sector. ...
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Does elasticity make sense for different levels of prices? If not, how can we fix that?

Let's say we know that our customers can't make sense of a raise in 5% of the price. It's too little for them to notice. However, an increase above 10% is easily noticed. If this is true, different ...
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Does it make sense to calculate price elasticity in respect to some percentage?

I was trying to calculate how much the price of a product impacts some company I'm analysing. At college, we learn that the price elasticity of demand is the percentage change in demand divided by the ...
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Finding data on (estimated) trade cost elasticities of imports

I'm an undergrad student of economics, and I need to find estimates of the trade cost elasticity of the UK's imports for some homework. My instructors pointed me to the World Bank's databases, ...
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Elasticity of real marginal costs with respect to production

How does one get the formula for the Elasticity of real marginal costs with respect to production ($\omega$)? Woodford(2003) at page 152 says "$\omega$ represents the elasticity of s (real ...
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Homework Question - Price Floor / Elasticity of Demand

I'm currently taking undergrad microeconomics and came across the following question: The current price floor in the agricultural lettuce market makes it such that price of lettuce is 25% higher than ...
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First order condition of log functions in general and interpretation

In the following, a first order condition for a log function is calculated. I know how the left part was calculated, however, I am a little bit confused where the gamma on the right site comes from ...
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107 views

Long-term equilibrium price inelastic?

I have doubts about some economic interpretation: Why is the long-term equilibrium price inelastic? But in the short run, the equilibrium price is not necessarily inelastic. What is the economic ...
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71 views

Production function and elasticity

Let $y=x_1^\alpha x_2^\beta$ where $\beta=1-\alpha$ be a Cobb-Douglas production function. Find the elasticity of the optimal demand functions (for minimizing production cost) for both goods wrt. $w_2/...
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176 views

Elasticity of demand

I'm reading a paper from Pindyck (1988) where $$P_t=X_t-\gamma Q_t.$$ $P_t$ is the price, $X_t$ is the demand state variable, $Q_t$ production and $\gamma\geq0$ is apparently the ''(constant) demand ...
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Mathematical framework for modelling the relationship between price and sales of a product

In my job as a data scientist, I am required to model the relationship between the price of a product and the sales or number of unit sold. I am trying to build a simplistic model, the assumptions of ...
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Are economic profits above normal for many firms in a perfectly-competitive increasing-cost industry?

In a perfectly-competitive constant-cost industry, all firms will have normal profits in the long run. This fact is very clear to me as the long run supply curve is perfectly elastic and hence each ...
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32 views

Profit-maximization for a monopoly

Between two countries, Richland and Poorland, with a strict ban on cross-border sales agreed with the Poorlandian government. The respective demand functions for both countries are: $Q_{poor} = 10 - ...
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What does the following mean: "supply has positive elasticity”?

What confuses me in particular is that I always thought of the concept of ‘elasticity’ with respect to something. That is, supply of x can be elastic with respect to y. Am I missing something?
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Why does short run market supply become more elastic with more firms

I have heard a justification along the lines of this: The supply curve becomes flatter (more elastic) with more firms in the market, because a given increase in price calls forth more production when ...
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Explanation of differential equation for Price Elasticity of Demand

I understand that Price Elasticity of Demand (PED) measures the percentage change in quantity demanded of a good with respect to a percentage change in its price. However, I don't quite understand ...
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Solving problem for optimal price (maximize profit) *attempt inside*

Let a demandfunction be defined as $D(p)=B-bp$, where $b,B>0$. A firm has some production cost, $c$, and can set the price $p$ under the constrain given by the Demand. What is the optimal price? ...
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Do barriers to entry increase the (collective) market power of incumbent suppliers?

For example in the case of the labour market lower immigration means that low-skilled labour can ask higher wages or better conditions (other things equal). Low skilled labour may have even put the ...
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How can I formulate price elasticity of demand equation when I want to add cross price elasticity?

I am trying to calculate the price elasticity of demand for a product where I used the equation log(volume) = elasticity * log(price) + seasonality dummies + trend index + CPI Here CPI is the consumer ...
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Examples of bounded, positive, inverse demand curves

The three most common examples of demand curves I am aware of are \begin{align} Q&= b - aP,\\ Q&= bP^a,\\ Q&= b e^{-aP}\\ \end{align} The first being our classic linear demand curve, the ...
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Elasticity of intertemporal sustitution with composite CRRA function

In the usual CRRA $\frac{c^{1-\sigma}-1}{1-\sigma}$ function we have that the intertemporal elasticity of sustitution $\partial\frac{c_{t+1}}{{c_{t}}{\partial r}}$ is $\frac{1}{\sigma}$. But how can ...
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Price elasticity of demand of CES

Anyone would like to help me show the following ( or a book/paper reference would be a great help) " The price elasticity of demand is equal to $\sigma$ for the demand function of CES preference,...
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Is saying that the demand is elastic or inelastic too oversimplified?

As we know that elasticity varies from infinity to zero as we move along a linear demand curve, then is it correct to label any demand curve elastic or inelastic as a whole?
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Estimating $dL/dw$ with direct dependencies using total differential

I have $U(C,L) = U(C) - v(L)$ where $C$ is consumption and $L$ is labor supply. From my first order conditions, $C$ is a function of $w$, wage, and $L$. $L$ is a function of $w$ and $C$. Leisure is $N ...
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why does income of executives level out in the long term after tax increases?

Marginal Revolution University has the following question in its Elasticity unit: In 1993, then President Clinton passed a law raising income taxes. This tax hike was fully expected: He campaigned on ...
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Calculating price elasticity by asking a “this” or “that” question

Let's say 2 goods exist: A for 10 and B for 20 (B is more premium in this example) If I decrease the price of both goods by 10% and ask: "Do you prefer A for 9 or B for 18 " What sort of insights (...
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133 views

confusion regarding elasticity of a demand curve

The following question is on a quiz at Marginal Revolution University: https://mru.org/practice-questions/calculating-elasticity-demand-practice-questions The elasticity of demand is 2.0. Is the ...

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