Elasticity Suppose that a particular variable (B) depends on another variable (A) B = f(A…) We define the elasticity of B with respect to A as The elasticity shows how B responds (ceteris paribus) to a 1 percent change in A

Price Elasticity of Demand The most important elasticity is the price elasticity of demand measures the change in quantity demanded caused by a change in the price of the good E P will generally be negative except in cases of Giffen’s paradox

Distinguishing Values of E P Value of E P at a Point Classification of Elasticity at This Point E P < -1Elastic E P = -1Unit Elastic E P > -1Inelastic

Price Elasticity and Total Expenditure Total expenditure on any good is equal to Total Expenditure = PQ Using elasticity, we can determine how total expenditure changes when the price of a good changes

Price Elasticity and Total Expenditure Responses of PQ Demand Price Increase Price Decrease ElasticFallsRises Unit Elastic No Change InelasticRisesFalls

Income Elasticity of Demand The income elasticity of demand (E I ) measures the relationship between income changes and quantity changes Normal goods  E I > 0 Luxury goods  E I > 1 Inferior goods  E I < 0

Cross-Price Elasticity of Demand The cross-price elasticity of demand (E Q,P’ ) measures the relationship between changes in the price of one good and and quantity changes in another Gross substitutes  E Q,P’ > 0 Gross complements  E Q,P’ < 0

Linear Demand Q = a + bP + cI + dP’ where: Q = quantity demanded P = price of the good I = income P’ = price of other goods a, b, c, d = various demand parameters

Linear Demand Q = a + bP + cI + dP’ Assume that:  Q/  P = b  0 (no Giffen’s paradox)  Q/ I = c  0 (the good is a normal good)  Q/  P’ = d ⋛ 0 (depending on whether the other good is a gross substitute or gross complement)

Linear Demand If I and P’ are held constant at I * and P’*, the demand function can be written Q = a’ + bP where a’ = a + c I * + dP’* Note that this implies a linear demand curve Changes in I or P’ will alter a’ and shift the demand curve

Linear Demand Along a linear demand curve, the slope (  Q/  P) is constant the price elasticity of demand will not be constant along the demand curve As price rises and quantity falls, the elasticity will become a larger negative number (b < 0)

Linear Demand Q P -a’/b a’ E P < -1 E P = -1 E P > -1 Demand becomes more elastic at higher prices