Chapter Fifteen Market demand
Chapter Fifteen Market Demand
From Individual to market demand Functions o Think of an economy containing n consumers, denoted by i= 1 Consumer is ordinary demand function for commodity j is 了(P1p2,m)
From Individual to Market Demand Functions ◆Think of an economy containing n consumers, denoted by i = 1, … ,n. ◆Consumer i’s ordinary demand function for commodity j is xj p p m *i i ( , , ) 1 2
From Individual to market demand Functions When all consumers are price-takers, the market demand function for commodity j is j(P1,P2,m,…,m)=∑(P1,P2,m)
From Individual to Market Demand Functions ◆When all consumers are price-takers, the market demand function for commodity j is Xj p p m m n xj i p p m i i n ( , , , , ) ( , , ). * 1 2 1 1 2 1 = =
From Individual to market demand Functions p1 p vddd 20 5 p1 The horizontal sum p of the demand curves of individuals a and B 35 A x1+x1
From Individual to Market Demand Functions p1 p1 x A 1 * x B 1 * x x A B 1 1 * + p1 20 15 35 p1 ’ p1 ” p1 ’ p1 ” p1 ’ p1 ” The “horizontal sum” of the demand curves of individuals A and B
Elasticities ◆ Elasticity measures the“ sensitivity of one variable with respect to another o The elasticity of variable x with respect to variable y is 0△X ex,y o△y
Elasticities ◆Elasticity measures the “sensitivity” of one variable with respect to another. ◆The elasticity of variable X with respect to variable Y is x y x y , % % = .
Own-Price Elasticity of Demand .Q: Why not just use the slope of a demand curve to measure the sensitivity of quantity demanded to a change in a commodity's own price? P A: Because the value of sensitivity then depends upon the(arbitrary) units of measurement used for quantity demanded
Own-Price Elasticity of Demand ◆Q: Why not just use the slope of a demand curve to measure the sensitivity of quantity demanded to a change in a commodity’s own price? ◆A: Because the value of sensitivity then depends upon the (arbitrary) units of measurement used for quantity demanded
Arc and point elasticities ◆An“ average”own- price elasticity of demand for commodity i over an interval of values for p i is an arc elasticity, usually computed by a mid-point formula. Elasticity computed for a single value of p, is a point elasticity
Arc and Point Elasticities ◆An “average” own-price elasticity of demand for commodity i over an interval of values for pi is an arcelasticity, usually computed by a mid-point formula. ◆Elasticity computed for a single value of pi is a point elasticity
Arc Own-Price Elasticity What is the“ average”oWn- price elasticity of demand for prices in an interval centered on p;? p, th 0△X p1 X,P%△ X," Xi X*
Arc Own-Price Elasticity pi Xi * pi ’ pi ’+h pi ’-h What is the “average” own-price elasticity of demand for prices in an interval centered on pi ’? Xi X '" i " X p i i i i X p * , % * % =
Arc Own-Price Elasticity What is the“ average”oWn- price elasticity of demand for prices in an interval centered on p;? p1+ 6△X p1 X,P%△ X," Xi X* 2h 0△pi=100×,%AX1=100× X1"-X) Pi (X1"+X")/2
Arc Own-Price Elasticity pi Xi * pi ’ pi ’+h pi ’-h What is the “average” own-price elasticity of demand for prices in an interval centered on pi ’? X p i i i i X p * , % * % = % ' p h p i i = 100 2 % ( " '") ( " '") / * X X X X X i i i i i = − + 100 2 Xi X '" i
Point own-Price elasticity What is the own-price elasticity of demand in a very small interval of prices centered on pi? p, th Ash→0, p1 X," Xi X*
Point Own-Price Elasticity pi Xi * pi ’ pi ’+h pi ’-h What is the own-price elasticity of demand in a very small interval of prices centered on pi ’? Xi X '" i " As h → 0