Lecture 7. Market Demand.ppt

1、Lecture Seven,Market Demand & Elasticity,Intermediate Microeconomics,Think of an economy containing n consumers, denoted by i = 1, ,n. Consumer is ordinary demand function for commodity j is When all consumers are price-takers, the market demand function for commodity j is,From Individual to Market

2、Demand Functions,From Individual to Market Demand Functions,p1,p1,20,15,35,p1,p1”,p1,p1”,p1,p1”,Market demand curve is the “horizontal sum”of the demand curvesof individuals A and B.,Suppose there are two consumers,Representative Consumer,The aggregate demand depends on prices and the distribution o

3、f incomes. Representative consumer is a imaginary people who has an income that is just the sum of all individual incomes has a demand same with the aggregate demand. The representative consumer assumption means the aggregate demand function has the form,The Inverse Demand Function,Inverse demand fu

4、nction is the inverse of the demand function, Pj(X). This function measures what the market price for good j would have to be for X units of it to be demanded. If all consumers face the same prices, the inverse demand function measures the marginal willingness to pay of every consumer who is purchas

5、ing the good.,Discrete Goods,p1,p1,1,1,35,p1,p1”,p1,p1”,p1,p1”,A decrease in the price increase the number of consumers.,Suppose the good is available only in units of zero or one,Extensive and Intensive Margin,Intensive margin: When price changes, each consumer decides to consume more or less of so

6、me goods. Extensive margin: When price changes, the consumers decides whether or not to enter the market for some goods (reservation-price model). The slope of the aggregate demand curve will be affected by both sorts of decisions.,The slope of a demand function could be a measure of how responsive

7、the demand is to the change in price. The problems of this measure is that the slope depends on the units to measure price and quantity. Elasticity could be another measure, and it is unit-free.,Price Elasticity of Demand,Price Elasticity of Demand,5,50,10,10,Slope = - 2,Slope = - 0.2,p,p,10-packs,S

8、ingle Units,q,q,In which case is the quantity demanded q more sensitive to changes in p1?,It is the same in both cases.,The elasticity of variable X with respect to variable Y is The price elasticity of demand is dened to be the rate of change in quantity divided by the rate of change in price.,Pric

9、e Elasticity of Demand,The sign of the elasticity of demand is generally negative. Verbal treatments tend to drop the minus sign, while the signs is often kept in writing. When compare magnitudes, absolute value of elasticity is used, as bigger absolute value means “more elastic”.,Some Notes,Conside

10、r the linear demand curve:q = abp. The slope of the curve is a constant, b. The elasticity is When p = 0, the elasticity of demand is zero. When q = 0, the elasticity is (negative) innity. When p = a/2b, the elasticity is 1.,Example with Linear Demand,12,Example with Linear Demand,13,p,q,a,q = a bp,

11、a/b,a/2,a/2b,elastic,inelastic,unit elastic,The elasticity will depends upon where the price and quantity lie on the demand curve, which will cause trouble. Point elasticity measures elasticity at a point on the demand curve. If the change in price is quite small, point elasticity will work well.,Po

12、int and Arc Elasticity,If the change is not that so, there will be problems using point elasticity. Arc elasticity calculates elasticity over a range of prices,Point and Arc Elasticity,Consider the linear demand curve, q = kpa. The slope of the curve is The point elasticity is That is, the point ela

13、sticity everywhere along the demand curve is constant.,Point Elasticity of Demand,EXAMPLES,Demand Curve with Power Function,16,Point Elasticity of Demand,17,EXAMPLES,Demand Curve with Power Function,p,q,If raising a commoditys price causes little decrease in quantity demanded, then sellers revenues

14、rise. Hence own-price inelastic demand causes sellers revenues to rise as price rises. If raising a commoditys price causes a large decrease in quantity demanded, then sellers revenues fall. Hence own-price elastic demand causes sellers revenues to fall as price rises.,Revenue and Elasticity,Sellers

15、 revenue is So,Revenue and Elasticity,As So, if , then a change to price does not alter sellers revenue If , then a price increase raises sellers revenue. If , then a price increase reduces sellers revenue.,Revenue and Elasticity,A sellers marginal revenue is the rate at which revenue changes with t

16、he number of units sold by the seller. Use p(q) to denote the sellers inverse demand function, then And,Marginal Revenue and Elasticity,As We have That is, the rate at which a sellers revenue changes with the number of units it sells depends upon the price elasticity of demand.,Marginal Revenue and

17、Elasticity,As So, if , then a increase on output does not alter sellers revenue If , then a output increase reduces sellers revenue. If , then a output increase raises sellers revenue.,Marginal Revenue and Elasticity,Consider the linear inverse demand:P(q) = abq Revenue is The slope of the curve is

18、And marginal revenue is,Example with Linear Demand,Example with Linear Demand,a,a/b,p,q,a/2b,Marginal Revenue for A Constant Elasticity Demand,a,p,q,Other Elasticities in Economics,Cross-price elasticity of demand demand for commodity i with respect to the price of commodity j（需求交叉价格弹性） Income elasticity of demand demand for commodity i with respect to