1. Chapter 15 MARKET DEMAND

2. 15.1 From Individual to Market Demand Consumer i’s demand for good 1: x i 1 (p 1,p 2,m i ) Consumer i’s demand for good 2: x i 2 (p 1,p 2,m i ) n consumers in the economy: i=1, …,n Market demand for good 1: the sum of these individual demands over all consumers.

3. 15.1 From Individual to Market Demand If we fix all the monetary incomes and the price of good 2, we can illustrate the relation between the aggregate demand for good 1 and its price.

4. 15.1 From Individual to Market Demand Substitutes: increasing the price of good 2 will tend to shift the aggregate demand curve for good 1 outward. Complements: increasing the price of good 2 will shift the aggregate demand curve for good 1 inward. Normal good: increasing monetary income, holding everything else fixed, will shift the aggregate demand curve outward.

5. 15.2 The Inverse Demand Function Inverse demand function, P(X)  It measures what the market price for good 1 would have to be for X units of it to be demanded.

6. EXAMPLE: Adding Up “Linear” Demand Curves Since the demand curves are only linear for positive quantities, there will be a kink in the market demand curve.

7. 15.3 Discrete Goods

8. 15.4 The Extensive and the Intensive Margin Adjustment on the intensive margin: when the price changes, the consumer changes the quantities demanded, but still ends up consuming both goods. Adjustment on the extensive margin: when the price changes, the consumers enter or exit the market for one of the goods.

9. 15.5 Elasticity Elasticity: a measure of responsiveness. Price elasticity of demand: the percent change in quantity divided by the percent change in price.

10. EXAMPLE: The Elasticity of a Linear Demand Curve Linear demand curve: q=a-bp. Elasticity:  =-bp/q=-bp/(a-bp)  p=0:  =0;  p=a/b :  =-  ;  p=a/2b:  =-1;  p>a/2b:  <-1;  p -1;

11. EXAMPLE: The Elasticity of a Linear Demand Curve

12. 15.6 Elasticity and Demand Elastic Demand: elasticity of demand is greater than 1 in absolute value. Inelastic Demand: elasticity of demand is less than 1 in absolute value. Unit Elastic Demand: elasticity of demand is exactly -1.

13. 15.7 Elasticity and Revenue Revenue: R=pq Price change: p+ △ p Quantity change: q+ △ q New revenue: R=(p+ △ p)(q+ △ q)=pq+q △ p+p △ q+ △ p △ q Change in revenue: △ R= q △ p+p △ q+ △ p △ q

14. 15.7 Elasticity and Revenue

15. Small values of △ p and △ q: the last term can safely be neglected. △ R= q △ p+p △ q or △ R/ △ p=q+p △ q/ △ p △ R/ △ p>0: p △ q/q △ p>-1 or |  (p)|<1 Revenue increases when price increases if the elasticity of demand is less than 1 in absolute value. Revenue decreases when price increases if the elasticity of demand is greater than 1 in absolute value.

16. 15.7 Elasticity and Revenue Differential approach |  |>1: dR/dp<0; |  | 0.

17. 15.8 Constant Elasticity Demands A unit elastic demand curve has a constant elasticity of -1. For this demand curve, price times quantity is constant at every point.

18. 15.9 Elasticity and Marginal Revenue △ R= q △ p+p △ q Marginal revenue: MR= △ R/ △ q = p+ q △ p/ △ q MR = p(1+ q △ p/p △ q) =p(1+ 1/  (p)) =p(1-1/|  (p)|)

19. 15.9 Elasticity and Marginal Revenue  =-1: MR=0  Revenue doesn’t change when the firm increases output. |  |<1: MR<0  Revenue will decrease when the firm increases output. |  |>1: MR>0  Revenue will increase when the firm increases output.

20. 15.10 Marginal Revenue Curves Linear (inverse) demand curve: p(q)=a-bq Marginal revenue: MR= △ R/ △ q = p(q)+q △ p(q)/ △ q = p(q)-bq =a-bq-bq =a-2bq

21. 15.10 Marginal Revenue Curves The marginal revenue curve has the same vertical intercept as the demand curve, but has twice the slope.

22. 15.11 Income Elasticity Income elasticity of demand: it describes how the quantity demanded responds to a change in income.

23. 15.11 Income Elasticity Normal good: an increase in income leads to an increase in demand. Inferior good: an increase in income leads to a decrease in demand. Luxury good: a one percent increase in income leads to more than one percent increase in demand.

24. 15.11 Income Elasticity Two different levels of income: m and m 0 Budget constraints: p 1 x 1 +p 2 x 2 =m p 1 x 1 0 +p 2 x 2 0 =m 0 Substraction: p 1 △ x 1 + p 2 △ x 2 = △ m Further manipulation: (p 1 x 1 /m)( △ x 1 /x 1 )+ (p 2 x 2 /m)( △ x 2 /x 2 )= △ m/m

25. 15.11 Income Elasticity Finally: s 1 ( △ x 1 /x 1 )/( △ m/m)+ s 2 ( △ x 2 /x 2 )/( △ m/m)=1 Expenditure share of good i: s i = p i x i /m The weighted average of the income elasticity is unity.  The weights are the expenditure shares.