1 Market Demand Molly W. Dahl Georgetown University Econ 101 – Spring 2009

2 From Individual to Market Demand Functions Consumer i’s demand for commodity j Market demand for commodity j

3 From Individual to Market Demand Functions The market demand curve is the “horizontal sum” of the individual consumers’ demand curves. Suppose there are only two consumers, i = A,B.

4 From Individual to Market Demand Functions p1p1 p1p p1’p1’ p1”p1” p1’p1’ p1”p1”

5 From Individual to Market Demand Functions p1p1 p1p1 p1p p1’p1’ p1”p1” p1’p1’ p1”p1” p1’p1’

6 From Individual to Market Demand Functions p1p1 p1p1 p1p p1’p1’ p1”p1” p1’p1’ p1”p1” p1’p1’ p1”p1”

7 From Individual to Market Demand Functions p1p1 p1p1 p1p p1’p1’ p1”p1” p1’p1’ p1”p1” p1’p1’ p1”p1” The “horizontal sum” of the demand curves of individuals A and B.

8 Elasticities Elasticity measures the “sensitivity” of one variable with respect to another. The elasticity of variable X with respect to variable Y is

9 Own-Price Elasticity pipi Xi*Xi* pi’pi’ What is the own-price elasticity of demand in a very small interval of prices centered on p i ’? is the elasticity at the point

10 Own-Price Elasticity Consider a linear demand curve. If p i = a – bX i then X i = (a-p i )/b and Therefore,

11 Own-Price Elasticity pipi Xi*Xi* p i = a - bX i * a a/b

12 Own-Price Elasticity pipi Xi*Xi* p i = a - bX i * a a/b

13 Own-Price Elasticity pipi Xi*Xi* a p i = a - bX i * a/b a/2 a/2b

14 Own-Price Elasticity pipi Xi*Xi* a p i = a - bX i * a/b a/2 a/2b

15 Own-Price Elasticity pipi Xi*Xi* a p i = a - bX i * a/b a/2 a/2b own-price elastic own-price inelastic own-price unit elastic

16 Revenue, Price Changes, and Own-Price Elasticity of Demand Inelastic Demand:  Raising a commodity’s price causes a small decrease in quantity demanded Sellers’ revenues rise as price rises. Elastic Demand:  Raising a commodity’s price causes a large decrease in quantity demanded Seller’s revenues fall as price rises.

17 Revenue, Price Changes, and Own-Price Elasticity of Demand Sellers’ revenue is

18 Revenue, Price Changes, and Own-Price Elasticity of Demand Sellers’ revenue is So

19 Revenue, Price Changes, and Own-Price Elasticity of Demand Sellers’ revenue is So

20 Revenue, Price Changes, and Own-Price Elasticity of Demand Sellers’ revenue is So

21 Revenue, Price Changes, and Own-Price Elasticity of Demand so ifthen and a change to price does not alter sellers’ revenue.

22 Revenue, Price Changes, and Own-Price Elasticity of Demand but ifthen and a price increase raises sellers’ revenue.

23 Revenue, Price Changes, and Own-Price Elasticity of Demand And ifthen and a price increase reduces sellers’ revenue.

24 Revenue, Price Changes, and Own-Price Elasticity of Demand In summary: Own-price inelastic demand: price rise causes rise in sellers’ revenue. Own-price unit elastic demand: price rise causes no change in sellers’ revenue. Own-price elastic demand: price rise causes fall in sellers’ revenue.

25 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand A seller’s marginal revenue is the rate at which revenue changes with the number of units sold by the seller.

26 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand p(q) denotes the seller’s inverse demand function (i.e., the price at which the seller can sell q units). Then so

27 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand and so

28 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand says that the rate at which a seller’s revenue changes with the number of units it sells depends on the sensitivity of quantity demanded to price; i.e., upon the of the own-price elasticity of demand.

29 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand Ifthen Ifthen Ifthen

30 Selling one more unit raises the seller’s revenue. Selling one more unit reduces the seller’s revenue. Selling one more unit does not change the seller’s revenue. Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand Ifthen Ifthen Ifthen

31 Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand An example with linear inverse demand. Then and

32 Marginal Revenue and Own-Price Elasticity of Demand a a/b p qa/2b