1. Elasticity and Demand  Elasticity concept is very important to business decisions.  It measures the responsiveness of quantity demanded to changes in price  It is also important for public policy-makers when dealing with tax issues on commodities – if we increase cigarette taxes, what will happen to the consumption of cigarettes?

2. The Coefficient of Demand Elasticity  The coefficient of demand elasticity is defined as the ratio of the percentage change in quantity demanded to the percentage change in price.

3. Classifying Elasticity Numbers ElasticityResponsivenessCoefficient Value Elastic |%  Q| > |%  P| |E| > 1 Unitary Elastic |%  Q| = |%  P| |E| = 1 Inelastic |%  Q| < |%  P| |E| < 1

4. Using Elasticity Information Suppose we know that the price elasticity of demand for automobiles is –4.0 and manufactures plan on increasing auto prices by 10% this year. What doe we predict will happen to the number of automobiles that will be sold?

5. Answer: -4.0 = X/0.10 or X = (-4.0)0.10 or X = -0.40 Thus, we predict a 40 percent reduction in quantity demanded

6. Elasticity and Total Revenue  Total Revenue(TR) is merely the firms sales measured in dollar terms.  It can be obtained by taking the price(P) of a product times the number of units sold(Q).  TR = P x Q  Remember that demand curves are negatively sloped – so quantity demanded will decrease when price is increased and vice-versa.

7. Elasticity and Total Revenue TR = P x Q  For any price change, if quantity demanded remains constant, total revenue will move in the same direction. This is often referred to as the price effect on total revenue.  However, in most cases quantity demanded will not remain constant but will move in the opposite direction of price. This will be the quantity effect.

8. Elasticity and Total Revenue  To determine what happens to TR when price is changed requires looking at the relative sizes of the price and quantity effects – which is embodied in the elasticity coefficient.

9. Elasticity and Total Revenue  What happens to TR if price increases and demand is elastic? TR = P X Q

10. Elasticity and Total Revenue  What happens to TR if price increases and demand is inelastic? TR = P X Q

11. Elasticity and Total Revenue ElasticInelasticUnitary Q effect dominates P effect dominates No effect dominates Price risesTR fallsTR risesNo change in TR Price fallsTR risesTR fallsNo change in TR

12. Factors Affecting Demand Elasticity  Three Important Factors Related to Elasticity –Availability of substitutes – directly related to elasticity –Percentage of a consumer’s budget – directly related to elasticity –Time period of adjustment – directly related to elasticity

13. Calculating Demand Elasticity  Two basic “types” of elasticity that can be calculated. –Arc elasticity compute elasticity over an arc or interval on the demand curve very imprecise if interval is wide –Point elasticity compute elasticity at a point on the demand curve very precise

14. Computing Arc Elasticity

15. Calculating Point Elasticity Linear Demand: P=a+bQ

16. Calculating Point Elasticity An Application Suppose the demand for a good is P=1000- 20Q, calculate the point price elasticity of demand at a price of $800.

17. Elasticity Along a Demand Curve  If a demand curve is negatively sloped and linear, –the elasticity will vary from point to point –elasticity will be higher the higher the price Reciprocal of slope

18. Other Elasticities  Elasticity is a concept from applied mathematics.  It can be applied to any functional relationship.  We develop two additional demand elasticities –Income –Cross price

19. Income Elasticity  Measures the responsiveness of quantity demanded to changes in income.

20. Income Elasticity If E M is positive we have a normal good. If E M is negative we have an inferior good.

21. Cross Price Elasticity  Measures the responsiveness of one good to a change in the price of another good.

22. Cross Price Elasticity If cross price elasticity is positive, goods X and Y are substitutes. If cross price elasticity is positive, goods X and Y are complements. If cross price elasticity is zero, goods X and Y are independent.

23. Demand, Marginal Revenue, and Elasticity  Marginal Revenue (MR) is the change in Total Revenue(TR) in response to increasing output (Q) by a single unit.  MR is the slope of the total revenue curve.  MR is also the derivative of the total revenue function. Note corrections from originals.

24. Relationships  If Demand: P=100-2Q (note linear)  TR = PQ = (100-2Q)Q = 100Q-2Q 2  MR = TR`= 100-4Q –MR is also linear –MR has same intercept as demand –MR decreases at twice the rate of demand –MR will always be less than price for all units sold but the first

25. Relationship between MR, P & E What if E = -0.5? Note inelastic. What if E=-4.0? Note elastic. See Figure 3.7.