21 votes
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How does one derive the elasticity of substitution?

How to derive elasticity of substitution The first step is to recall the definition of a differential. If you have a function $f: \Bbb R^n \to \Bbb R$, say, $f(x_1,\cdots,x_n)$, then: $${\rm d}f = \...
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13 votes

Intuition - Why does elasticity vary along a curve?

Think of it this way. A yacht costs $\$0.01$. How much do you demand? Then double the price. Now how many would you demand? Then consider something closer to a market price. Something in 6 or 7 ...
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  • 2,167
12 votes
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Econometrics: Is elasticity meaningful in my, or any, regression?

The answer to the question is yes, it is indeed meaningful (at least mathematically speaking). If you estimate the linear equation $$ W = \beta_0 + \beta_1 PTR, $$ then $\beta_1=\frac{\partial W }{\...
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11 votes
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How is price elasticity determined in practice?

In many practical instances, price elasticity of demand (PED) is calculated in a back of the envelope fashion, just as taught in the textbooks! Firms can adjust their price by some small amount and ...
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11 votes
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Why are elasticities defined as logarithmic derivatives?

If I understand your question, first the elasticity haven't units. The problem with $\partial Y/\partial X$ is that if you change the measure units the result is different. Is less problematic to ...
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10 votes

What are Giffen Goods?

Consider the Slutsky equation, $$ \frac{\partial x}{\partial p} = \frac{\partial x^c}{\partial p} - \frac{\partial x}{\partial I} x. $$ A giffen good is the case where the income effect $\frac{\...
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  • 9,107
10 votes

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

Because $\Bbb E[\varepsilon \mid x]= 0$ is one of the key assumptions for the estimation.
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  • 1,262
9 votes

What are Giffen Goods?

There is rather low probability for demand of a good to exhibit the Giffen property at market level, where averaging over heterogeneous preferences, different income levels and consequent ...
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9 votes
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Elasticity of demand equals -1 but income decreases!

We discourage numeric questions as they are unlikely to be useful for future visitors but this is a very good example of why using non-marginal quantities can be misleading. The exact definition of ...
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  • 26.1k
8 votes

Econometrics: Is elasticity meaningful in my, or any, regression?

Like people have said in the comments, log-log is commonly used. It amounts to estimating a constant elasticity model $Y = \alpha X^\beta$, which is a commonly used functional form within economics. ...
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  • 9,107
8 votes

How is price elasticity determined in practice?

The truth is that it's unclear if firms use the concept at all. Alan Blinder wrote this wonderful little book called "Asking about prices". A survey of firms asking them how they set prices. And it's ...
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8 votes
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Elasticity and logarithms

Because $a$ is a parameter, and so $$ \eta = \frac{ d \log y}{d \log x} = \frac{ d \log a + d \ b \log x}{d \log x} = 0 + b. $$
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7 votes

Econometrics: Is elasticity meaningful in my, or any, regression?

Alright, the other respondents have covered the logic behind a log-log regression pretty well, so I'm just going to add some practical tips. If you want to check whether your specification is ...
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  • 1,996
7 votes
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Why absolute value in elasticities and marginal rate of substitution?

I think there are pedagogical advantages to discussing both the raw numbers and the absolute values and I think the benefits of both explain why they both show up (sometimes in the same text, even). ...
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  • 1,040
7 votes

Is elasticity purely an aggregate concept or can it be individualized

In theory, the elasticity quantifies in proportional terms the "reaction" of the dependent variable to a change of the independent variable, where the two are related through a functional relationship....
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7 votes
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What determines the outcome of a price war, and why isn't that outcome reached instantaneously?

Answer to question If we take your assumptions literally, Jim will decide not to enter the widget business. For suppose he did incur the cost of entry and that Mary is selling at price $p_m$. Jim can ...
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7 votes

How exactly does elasticity relate to slope?

The two demand functions $D_1(p),D_2(p)$ cross at the point $(Q,p)$. Their respective elasticities at price $p$ are \begin{align*} \epsilon_1(p) & = \frac{\text{d}D_1(p)}{\text{d}p}\frac{p}{D_1(p)}...
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7 votes

Elasticity and logarithms

Differentiating both sides of the equation with respect to $x$, using the chain rule for the left hand side and noting that, since $a$ is a parameter, $da/dx=0$: $$\frac{1}{y}\frac{dy}{dx}=b\frac{1}{x}...
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  • 6,718
7 votes

Does Modern Monetary Theory (MMT) provide a useful insight into how to manage the economy?

Does Modern Monetary Theory (MMT) provide a useful insight into how to manage the economy? That depends on your definition of MMT, because it is not generally agreed on what it even is. You will find ...
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  • 41.6k
6 votes

Intuition - Why does elasticity vary along a curve?

Say elasticity (of demand) gives the percentage change in quantity demanded in response to a one percent change in price. Since the change is porcentual, if you are in a point of the demand where ...
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  • 840
6 votes

What are Giffen Goods?

The usual textbook example of a Giffen good (i.e. a good whose demand curve slopes upwards) is the Irish potato famine. The idea is that as potatoes (a staple food) became more expensive, people could ...
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  • 16.6k
6 votes
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Calibration of utility function parameters controlling labor disutility

$\alpha$ handles the conversion between the units in which labor is measured and the the units in which consumption is measured. Consider the leisure part of the utility function: $$ - \alpha \frac{...
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6 votes
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Constant Elasticity of Substitution: Special Cases

We know that if $u$ represents $\succeq$ on $X$, then for any strictly increasing function $f: \mathbb{R} \rightarrow \mathbb{R}$, then $v(x) = f(u(x))$ represents $\succeq$ on $X$ ($X$ in this case ...
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  • 6,409
6 votes
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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?

Recall the following equivalent definitions for luxury goods and necessities: A good $x$ is considered a necessity if $e_{(x,I)}<1$. A good $x$ is considered a luxury good if $e_{(x,I)}>1$. As ...
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  • 231
6 votes
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Intuition for the CES consumption index in New-Keynesian DSGE models

Heuristically, you can think of the integral as just a sum: $$ \bar{C} = \left( \sum_{i=1}^n C_i^{1-\frac{1}{\epsilon}} \right)^{\frac{\epsilon}{\epsilon - 1}} $$ where $\bar{C}$ is an index of ...
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6 votes
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First order condition of log functions in general and interpretation

It just comes from the derivative of profit function. I assume that $a_i$ is the choice variable here so the derivative of $\pi$ wrt $a_i$ is (step by step): $$\frac{\partial \pi}{ \partial a_i} = \...
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6 votes

First order condition of log functions in general and interpretation

The $\gamma$ on the RHS comes from applying chain rule when differentiating the second term with respect to $a_i$. Regarding elasticity, note that with a differentiable function $f$, the ratio $f'(x)/...
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  • 14.3k
6 votes

Microeconomics question on elasticity

The answer by Herr K is correct so far as it goes and is probably what your teacher is looking for, but it's worth adding the following. Walt and Jessie place their orders before looking at the price. ...
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  • 6,718
5 votes

Why absolute value in elasticities and marginal rate of substitution?

Related to the MRS, this is a more general problem regarding negative slopes. I confess to continuously being confused for many-many years on the matter (and having to pose and think), until I ...
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5 votes

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

These papers look relevant, to one degree or the other: Karlan, D., & Zinman, J. (2009). Observing unobservables: Identifying information asymmetries with a consumer credit field experiment. ...
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