# Elasticity of Demand

## Elasticity of Demand

Elasticity of Demand (draft)
Definition

A measure/ coefficient that show the responsiveness of quantity demanded in response to a change in market condition (price of the good, prices of related goods, income).

Price elasticity of demand (PED) Ed = %∆Qd/ %∆P.

Own-price elasticity of demand for normal goods is a negative value (quantity demanded responds negatively/inversely to price changes), but we usually talk about its absolute values.
Calculation

* Point method: Ed= %∆Qd/ %∆P = ∆Qd/ Q∆P/ P = ∆Qd∆P x pQ
* Qd= a+bP: Ed = dQddP x pQ = bpa+bp
Ed=-1 <=> - bp= a+bP <=> P= -a/2b, Qd= a/2
* When we know 2 prices P1, P2 (P1<P2) & coresponding Q1, Q2:
* Ed(P1)=
* Ed(P2)=
Ed(P2) & Ed(P1) are estimates of elasticity at P1 and P2, Ed (P1) tends to overestimate elasticity at P1(lower price), Ed (P2) tends to underestimate elasticity at P2 (higher price). The more P1 differ from P2, the less accurate the estimates are. Exception: in case of linear demand function, Ed computed from point method equal its point elasticity of demand computed by derivation.

If we have value P3>P2 (and Q3), we can estimate elasticity at P2 when price rises from P2 to P3 Ed(P2->P3) = > Ed(P2->P1) (calculated above). Thus, Ed using point methods can be confusing and not reliable when price range is big.

* Mid point (arc) elasticity (when we know 2 prices & Qd): Ed=. Mid-point formula is an estimate of average Ed in a price range. It is close to Ed in the middle of the range. The less curvature the D curve is, the more reliable the estimate is. Advantage of this method is that we do not have to concern about which price should be used as base value in calculating the % change.

Interpretation

Value | Descriptive Terms |
Ed =0 | Perfectly inelastic demand |
0<Ed <1 | Inelastic or relatively inelastic demand |
Ed=1 | Unit elastic, unit elasticity, unitary...