清华大学中级微观经济学讲义清华李稻葵(1)ppt课件

1、/Chapter FifteenMarket DemandWhat Is the Purpose of This Chapter?uWe aggregate individual demand and form a market demand function.uWe study a property of the market demand functionFrom Individual to Market Demand FunctionsuThink of an economy containing n consumers, denoted by i = 1

2、, ,n.uConsumer is ordinary demand function for commodity j isxp pmjii*(,)12From Individual to Market Demand FunctionsuWhen all consumers are price-takers, the market demand function for commodity j isX p pmmxp pmjnjiiin(,)(,).*121121 From Individual to Market Demand Functionsp1p1xA1*xB1*xxAB11* p120

3、1535p1p1p1p1p1p1The “horizontal sumof the demand curvesof individuals A and B.An Important Concept: ElasticityuElasticity measures the “sensitivity of one variable with respect to another.uThe elasticity of variable X with respect to variable Y is x yxy,%. Slope Vs. ElasticityuQ: Why not just use th

4、e slope of a demand curve to measure the sensitivity of quantity demanded to a change in a commoditys own price?uA: Because the value of sensitivity then depends upon the (arbitrary) units of measurement used for quantity demanded. Arc and Point ElasticitiesuAn “average own-price elasticity of deman

5、d for commodity i over an interval of values for pi is an arc-elasticity, usually computed by a mid-point formula.uElasticity computed for a single value of pi is a point elasticity. Point Own-Price ElasticitypiXi*piWhat is the own-price elasticityof demand in a very small intervalof prices centered

6、 on pi?Xi XpiiiiiipXdXdp*,* is the elasticity at the point (,).XpiiPoint Own-Price ElasticityE.g. Suppose pi = a - bXi. Then Xi = (a-pi)/b and XpiiiiiipXdXdp*,* .b1dpdXi*i Therefore, Xpiiiiiipapbbpap*,() /. 1Point Own-Price ElasticitypiXi*api = a - bXi*a/b Xpiiiipap*, 1 0a/2a/2b own-price elasticown

7、-price inelastic(own-price unit elastic)Point Own-Price Elasticity XpiiiiiipXdXdp*,* dXdpapiiia* 1 Xpiiaiaiaiaiipkpkapappa*,. 1Xkpiia*. E.g. ThensoPoint Own-Price ElasticitypiXi*Xkpkpkpiiaii* 22 2everywhere alongthe demand curve.Revenue and Own-Price Elasticity of DemandR ppXp( )( ).* Sellers revenu

8、e isSo Xp*( ).1 dpdX)p(Xp1)p(X*dRdpXppdXdp *( )Revenue and Own-Price Elasticity of Demand dRdpXp *( ) 1 so if 1thendRdp 0and a change to price does not altersellers revenue.Revenue and Own-Price Elasticity of Demand dRdpXp *( ) 1 but if 10 thendRdp 0and a price increase raises sellersrevenue.Revenue

9、 and Own-Price Elasticity of Demand dRdpXp *( ) 1 And if 1thendRdp 0and a price increase reduces sellersrevenue.Marginal Revenue and Own-Price Elasticity of DemanduA sellers marginal revenue is the rate at which revenue changes with the number of units sold by the seller.MR qdR qdq( )( ). Marginal R

10、evenue and Own-Price Elasticity of Demandp(q) denotes the sellers inverse demand function; i.e. the price at which the seller can sell q units. ThenMR qdR qdqdp qdqqp q( )( )( )( ) R qp qq( )( ) so p qqp qdp qdq( )( )( ).1Marginal Revenue and Own-Price Elasticity of DemandMR qp qqp qdp qdq( )( )( )(

11、 ). 1 dqdppqandsoMR qp q( )( ). 11 Marginal Revenue and Own-Price Elasticity of Demand 11)q(p)q(MRIf 1thenMR q( ). 0If 10 thenMR q( ). 0If 1thenMR q( ). 0Marginal Revenue and Own-Price Elasticity of DemandAn example with linear inverse demand.p qabq( ). ThenR qp q qabq q( )( )() andMR qabq(). 2Marginal Revenue and Own-Price Elasticity of Demandp qabq( ) MR qabq() 2aa/bpqa/2bMarginal Revenue and Own-Price Elasticity of Demandp qabq( ) MR qabq() 2aa/bpqa/2bq$a/ba/2bR(q)Summary: The Key C