Elasticity

1. Elasticity Elasticity:Responsiveness to changes.How much do you stretch?

2. The x elasticity of y measures the responsiveness of y to changes in x.

3. The x elasticity of y measures the responsiveness of y to changes in x.

4. The x elasticity of y measures the responsiveness of y to changes in x.

5. The x elasticity of y measures the responsiveness of y to changes in x. • The price elasticity of demand measures the responsiveness of demand to changes in price. • The price elasticity of supply measures the responsiveness of supply to changes in price. • Formally, we ask about the percentage change in demand/supply resulting from a 1% increase in price (relative to some baseline). • It’s clear from this that demand elasticities are negative and supply elasticities are positive.

6. What is the price elasticity of demand at point A? • By what percent does demand change if we start at point A and then increase price by 1%? • We have to specify point A because otherwise this question doesn’t usually make sense. (In almost all cases, elasticity will change at different points along a demand curve.) • Because we’re using linear demand curves, we can follow the spirit rather than the letter of the 1% definition. Let’s see how…

7. What is the price elasticity of demand at point A? • Pick any other point B on the demand curve. (In keeping with the spirit of the 1% definition, point B should be near point A, but on a linear demand curve any other point will work.) • Write down pA, qA, pB, qB. Then calculate:

8. What is the price elasticity of supply at point A? • Same formula, just make sure point B is on the supply curve. • (Obviously, point A has to be on the supply curve too.) • These formulas will be on the exam cheat sheet; you just have to apply them. • Also on the cheat sheet will be the definitions of elastic and inelastic...

9. Elastic/inelastic/etc. D • Perfectly inelastic demand/supply: Not at all responsive. A 1% increase in price produces a 0% change in demand/supply. • Short-run demand for electricity is close to perfectly inelastic, as is short-run supply of apartments in Seattle. • What do these curves look like? • Vertical: All prices lead to the same quantity.

10. Elastic/inelastic/etc. D • Inelastic demand/supply: A 1% increase in price produces a change in demand/supply of, e.g., -½ for demand, +½ for supply. • Unit elastic demand (-1) or supply (+1) • Elastic demand/supply: A 1% increase in price produces a change in demand/supply of, e.g., -2 for demand, +2 for supply.

11. Elastic/inelastic/etc. D • Perfectly elastic demand/supply: Infinitely responsive. A 1% increase in price produces an infinite change in demand/supply. • What do these curves look like? • Horizontal: Increase or decrease the price by a little bit and demand/supply jumps. • Think of this as the extreme case as demand/supply gets more and more flat.

12. Perfect elasticity in the long-run • Hard to think of a good example of perfectly elastic demand, but there are lots of examples of perfectly elastic supply, especially in the long run. • As always, you can think of these either as market supply curves or as market marginal cost curves.

13. Perfect elasticity in the long-run (marginal cost perspective)

14. Perfect elasticity in the long-run (marginal cost perspective)

15. Perfect elasticity in the long-run (supply curve perspective)

16. Perfect elasticity in the long-run (supply curve perspective) • At any price below $10 per unit, sellers want to sell 0 units. • At any price above $10 per unit, sellers want to sell infinitely many units. • At a price exactly equal to $10 per unit, sellers are indifferent about how much to sell: they’d sell 0 units or 10 units or 1 million units, etc.

17. Perfect elasticity in the long-run (supply curve perspective) • At $10 per unit, sellers are making the market rate of return. That’s why they’re indifferent! • At prices below $10, sellers are making below the market rate of return. In the long run… • …they’ll all get out of the business. • At prices above $10, sellers are making above the market rate of return. In the long run… • …they’ll all pile into the business.

18. Application #1: Monopoly pricing • Claim: A profit-maximizing monopolist will never pick a price that corresponds to a point on the inelastic portion of the demand curve. • If it did, it could raise its price by 1% and increase profits (revenue – costs): pq-C(q). • Raising the price by 1% increases p by 1% and decreases q by less than 1%. (Why?) • Raising the price by 1% decreases C(q). (Why?) • Revenue goes up, costs go down: more profit!

19. Application #2: Government pricing • Consider a proposal to raise bus fares. • If the current price is on the elastic portion of the demand curve, an increase in prices will reduce total revenue (pq). (Why?) • Similarly, a proposal to raise taxes will reduce tax revenue if you’re on the elastic portion of the labor supply curve. (Why?) • This is the Laffer curve idea! (But it’s a big if.)

20. Application #3: Tax burdens

21. Application #3: Tax burdens

22. Application #3: Tax burdens

23. At market equilibrium, elasticities of demand and supply are equal…

24. …so buyers and sellers will divide the economic burden equally.

25. At market equilibrium, supply is way more elastic than demand…

26. …so sellers will bear less of the tax burden and buyers will bear more.

27. In the extreme case of perfectly elastic long-run supply…

28. …buyers will bear the entire tax burden. Let’s see why:

29. Tax on buyers: Market price is still $10, so buyers bear whole burden.

30. Tax on sellers: Price rises to $14, so buyers bear whole tax burden.