Consumption- Dead and supply Elasticities · The slope of the demand curve is△ easure of the responsiveness of demand to prices. However, it depends upon the units demand and price are measured in The price elasticity of demand does not. It is written n and given br emanded dP % Change in price This is negative, so absolute values are often taken. If the result is 1. there is unit elasticity. If it is less than 1 inelastic. otherwise it is elastic. Consider the linear demand curve P= 1-X. Elasticity is given by n=-P/(1-P). This is not constant along the curve- it ranges from -oo at the vertical axis, through -l at P= 0.5 to O at the X axis. m-m Ar s dr- change in quantity demanded dn If Tn >0 the good is normal, if not it is inferior. If nm >I the good is a luxury Denand and Supply Revenue Revenue is the quantity of the good sold times its price: R=PX R'=(X+△X)(P+△P. Multiplying this out gives:F"=Px+P△X+X△P+△P△X. Subtracting one from the other gives△R=R-R=P△X+X△P+△P△x. The last term is tiny.So Marginal revenue the additional revenue from a small increase in quantity is: For the linear case then MR=P(l-(1-P)/P)=P-(1-P)=2P-1=1-2x.Consumption — Demand and Supply 5 Elasticities • The slope of the demand curve is ∆X/∆P. This is a measure of the responsiveness of demand to prices. However, it depends upon the units demand and price are measured in. • The price elasticity of demand does not. It is written η and given by: η = P X ∆X ∆P ≈ P X dX dP = %Change in quantity demanded %Change in price • This is negative, so absolute values are often taken. If the result is 1, there is unit elasticity. If it is less than 1 demand is inelastic, otherwise it is elastic. • Consider the linear demand curve P = 1 − X. Elasticity is given by η = −P/(1 − P). This is not constant along the curve — it ranges from −∞ at the vertical axis, through −1 at P = 0.5 to 0 at the X axis. • Elasticities can be found for other variables, for example the income elasticity of demand is: ηm = m x ∆x ∆m ≈ m x dx dm = %Change in quantity demanded %Change in income • If ηm ≥ 0 the good is normal, if not it is inferior. If ηm > 1 the good is a luxury. Consumption — Demand and Supply 6 Revenue • Revenue is the quantity of the good sold times its price: R = P X. • If a small amount more, X + ∆X, is sold at a slightly different price P + ∆P, the new revenue becomes R0 = (X + ∆X)(P + ∆P). Multiplying this out gives: R0 = P X + P ∆X + X∆P + ∆P ∆X. • Subtracting one from the other gives ∆R = R0 − R = P ∆X + X∆P + ∆P ∆X. The last term is tiny. So: • Marginal revenue — the additional revenue from a small increase in quantity is: MR = ∆R ∆X = P + X ∆P ∆X ≈ P + X dP dX = P µ 1 − 1 |η| ¶ • For the linear case then MR = P(1 − (1 − P)/P) = P − (1 − P) = 2P − 1 = 1 − 2X