资源描述
Click to edit Master title style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,*,*,*,Chapter Fifteen,Market Demand,From Individual to Market Demand Functions,Think of an economy containing n consumers,denoted by i=1,n.,Consumer is ordinary demand function for commodity j is,From Individual to Market Demand Functions,When all consumers are price-takers,the market demand function for commodity j is,From Individual to Market Demand Functions,p,1,p,1,p,1,20,15,35,p,1,p,1,”,p,1,p,1,”,p,1,p,1,”,The“horizontal sum”of the demand curvesof individuals A and B.,Elasticities,Elasticity measures the“sensitivity”of one variable with respect to another.,The elasticity of variable X with respect to variable Y is,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 commoditys 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,i,is a,point elasticity,.,Arc Own-Price Elasticity,p,i,X,i,*,p,i,p,i,+h,p,i,-h,What is the“average”own-priceelasticity of demand for pricesin an interval centered on p,i,?,Arc Own-Price Elasticity,p,i,X,i,*,p,i,p,i,+h,p,i,-h,What is the“average”own-priceelasticity of demand for pricesin an interval centered on p,i,?,Point Own-Price Elasticity,p,i,X,i,*,p,i,p,i,+h,p,i,-h,What is the own-price elasticityof demand in a,very small interval,of prices centered on p,i,?,As h,0,Point Own-Price Elasticity,p,i,X,i,*,p,i,What is the own-price elasticityof demand in a,very small interval,of prices centered on p,i,?,is the elasticity,at the point,Point Own-Price Elasticity,E.g.Suppose p,i,=a-bX,i,.Then X,i,=(a-p,i,)/b and,Therefore,Point Own-Price Elasticity,p,i,X,i,*,a,p,i,=a-bX,i,*,a/b,a/2,a/2b,Point Own-Price Elasticity,p,i,X,i,*,a,p,i,=a-bX,i,*,a/b,a/2,a/2b,own-price elastic,own-price inelastic,(own-price unit elastic),Point Own-Price Elasticity,E.g.,Then,so,Point Own-Price Elasticity,p,i,X,i,*,everywhere alongthe demand curve.,Revenue and Own-Price Elasticity of Demand,If raising a commoditys price causes little(a lot of)decrease in quantity demanded,then sellers revenues rise.,Hence own-price,inelastic,(elastic)demand causes sellers revenues to rise(drop)as price rises.,Revenue and Own-Price Elasticity of Demand,Sellers revenue is,So,Revenue and Own-Price Elasticity of Demand,so if,then,and a change to price does not altersellers revenue.,Revenue and Own-Price Elasticity of Demand,but if,then,and a price increase raises sellersrevenue.,Revenue and Own-Price Elasticity of Demand,And if,then,and a price increase reduces sellersrevenue.,Marginal Revenue and Own-Price Elasticity of Demand,A sellers,marginal revenue,is the rate at which revenue changes with the number of units sold by the seller.,Marginal Revenue and Own-Price Elasticity of Demand,p(q)denotes the sellers inverse demand function;i.e.the price at which the seller can sell q units.Then,so,Marginal Revenue and Own-Price Elasticity of Demand,and,so,Marginal Revenue and Own-Price Elasticity of Demand,If,then,If,then,If,then,Marginal Revenue and Own-Price Elasticity of Demand,An example with linear inverse demand.,Then,and,Marginal Revenue and Own-Price Elasticity of Demand,a,a/b,p,q,a/2b,Marginal Revenue and Own-Price Elasticity of Demand,a,a/b,p,q,a/2b,q,$,a/b,a/2b,R(q),
展开阅读全文