Market Demand

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 p1 p1 p1’ p1’ p1” p1” 20 15

5. From Individual to Market Demand Functions p1 p1 p1’ p1’ p1” p1” 20 15 p1 p1’

6. From Individual to Market Demand Functions p1 p1 p1’ p1’ p1” p1” 20 15 p1 p1’ p1”

7. From Individual to Market Demand Functions p1 p1 p1’ p1’ p1” p1” 20 15 p1 The “horizontal sum”of the demand curvesof individuals A and B. p1’ p1” 35

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 What is the own-price elasticityof demand in a very small intervalof prices centered on pi’? pi pi’ is the elasticity at the point Xi*

10. Own-Price Elasticity Consider a linear demand curve. If pi = a – bXi then Xi = (a-pi)/b and Therefore,

11. Own-Price Elasticity pi = a - bXi* pi a a/b Xi*

12. Own-Price Elasticity pi = a - bXi* pi a a/b Xi*

13. Own-Price Elasticity pi = a - bXi* pi a a/2 a/2b a/b Xi*

14. Own-Price Elasticity pi = a - bXi* pi a a/2 a/2b a/b Xi*

15. Own-Price Elasticity pi = a - bXi* pi a own-price elastic own-price unit elastic a/2 own-price inelastic a/2b a/b Xi*

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 if then and a change to price does not altersellers’ revenue.

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

23. Revenue, Price Changes, and Own-Price Elasticity of Demand And if then 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 changeswith the number of units it sellsdepends on the sensitivity of quantitydemanded to price; i.e., upon theof the own-price elasticity of demand.

29. Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand If then If then If then

30. Marginal Revenue, Quantity Changes, and Own-Price Elasticity of Demand Selling onemore unit does not change the seller’srevenue. If then Selling onemore unit reduces the seller’s revenue. If then If then Selling onemore unit raises the seller’s revenue.

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 p a a/2b a/b q