Demand Elasticity and Regression Coefficient Interpretations

All flashcards

Elasticity

The percentage change in a response variable divided by the percentage change in a related variable; this makes responsiveness comparable across units.

Price elasticity from a linear demand slope

At a point, price elasticity is $b(P/Q)$, where $b$ is the price coefficient.

Point-of-means elasticity

For a demand regression, calculate it as $b(\bar{P}/\bar{Q})$ using sample mean price and quantity.

Log-level model

In $\log(Y)=a+bX$, a one-unit increase in $X$ is associated approximately with a $100b\%$ change in $Y$.

Log-log model

In $\log(Y)=a+b\log(X)$, the coefficient $b$ is the elasticity of $Y$ with respect to $X$.

Quiz questions

1. In an OLS regression of quantity on price, what does the price coefficient represent?Answer: The estimated unit change in quantity for a one-unit increase in price.
2. Why can elasticity vary along a straight-line demand curve even though its slope is constant?Answer: The price-to-quantity ratio changes along the curve.
3. For a demand regression with price coefficient $b$, how is elasticity at the point of means calculated?Answer: $b(\bar{P}/\bar{Q})$
4. In the model $\log(Y)=a+b\log(X)$, how is the coefficient $b$ interpreted?Answer: As the percentage change in $Y$ associated with a one-percent increase in $X$.
5. A demand elasticity has an absolute value of exactly 1. How is demand classified?Answer: Unit elastic, because quantity changes proportionally with the related variable.