Background
Arc elasticity is an important concept in economics used to measure responsiveness. Specifically, it provides a way to analyze how one economic variable (such as quantity demanded) changes in response to a change in another variable (such as price), over a finite range. This concept is particularly useful when studying supply and demand curves, where factors change over specific intervals rather than infinitely small points.
Historical Context
The concept of elasticity, including arc elasticity, emerged as economists sought to understand and quantify how sensitive quantities like demand and supply are to changes in prices and other factors. While the general idea of elasticity has roots going back to Alfred Marshall’s work in the late 19th century, arc elasticity has been developed to handle cases where changes are not marginal but occur over discrete intervals.
Definitions and Concepts
Arc elasticity measures the average elasticity between two points on a curve. It is contrasted with point elasticity, which measures elasticity at an infinitesimal point.
Mathematically, arc elasticity (E) between two points (Q1, P1) and (Q2, P2) can be represented as:
\[ E = \frac{\Delta Q / [(Q1 + Q2) / 2]}{\Delta P / [(P1 + P2) / 2]} \]
Where:
- \( \Delta Q \) is the change in quantity
- \( \Delta P \) is the change in price
- \( (Q1 + Q2) / 2 \) is the average of the two quantities
- \( (P1 + P2) / 2 \) is the average of the two prices
Major Analytical Frameworks
Classical Economics
In classical economics, the concept of elasticity predates the formal notion of arc elasticity. Classical economists typically dealt with broad changes over distinct intervals which are inherently arc-elastic considerations.
Neoclassical Economics
Neoclassical economists advanced the idea of elasticity to include more precise and mathematical characterizations of demand and supply, yielding additional precision with concepts like point elasticity versus arc elasticity.
Keynesian Economics
Keynesians would use arc elasticity to explain shifts in aggregate demand and supply levels, particularly during different phases of the economic cycle, where adjustments are over shorter, distinct intervals.
Marxian Economics
Elasticity measures like arc elasticity are less frequently focused on in Marxian economics, which often involves broader social and historical analyses. However, it can be applied in discussions of market power and responses within aggregate sectors.
Institutional Economics
Institutional economists might refer to arc elasticity when looking at changes in quantity and price within institutional contexts such as labor markets, employment unions, and regulatory impacts.
Behavioral Economics
Behavioral economics could use arc elasticity to understand how consumers’ non-rational decisions span considerable intervals and how behavioral changes influence economic variables over these ranges.
Post-Keynesian Economics
Post-Keynesian theories would apply arc elasticity when analyzing non-linearities and wider ranges in economic behaviors, incorporating expectations and “real-world” data anomalies.
Austrian Economics
Austrian economists, focusing on individual action and market process over time, would interpret arc elasticity as indicative of how individuals adjust to changes over discrete periods.
Development Economics
Development economics often employs arc elasticity when analyzing changes in considerable sectors — such as agricultural products responding to price changes due to policy.
Monetarism
Arc elasticity could be useful in monetarist discussions when examining the responses of money supply and price level over specific periods.
Comparative Analysis
Arc elasticity provides a more generalized measure over specific intervals compared to point elasticity, offering an average responsiveness. It is crucial in policy-making, planning, and various applied economic contexts where changes happen over periods that are never infinitesimal.
Case Studies
- Price Sensitivity in the Tech Market: Analysis of how price reductions over finite intervals affect demand for new smartphones.
- Agricultural Product Response to Subsidies: Study of quantity produced in response to subsidy changes over a planting season.
Suggested Books for Further Studies
- Elasticity: Theory, Applications, and Measurements by Ronald E. Miller
- Price Theory and Applications by Steven E. Landsburg
- Principles of Microeconomics by N. Gregory Mankiw
Related Terms with Definitions
- Point Elasticity: Elasticity measured at a single point on a demand curve.
- Price Elasticity of Demand: Degree to which the quantity demanded of a good responds to a change in price.
- Cross-Price Elasticity: Measurement of the change in demand for one good in response to a price change of another good.
- Income Elasticity: Sensitivity of
