ECO 284 - Microeconomics - Dr. D. Foster Elasticity Problems ECO 284 - Microeconomics - Dr. D. Foster

Elasticity Problems A. What do execs at Pepsi expect TR to do when they have a sale on their soft drink? Why? Expect revenues to rise!!! Demand is elastic . . . lots of substitutes. B. You manage a concert hall that seats 500. Consider the following demand information. What do you charge? A price of $15 will max. revenue. At a price of: Amount sold is: $10 500 $15 400 $20 200

Elasticity Problems εD = 10%/50% = .20 1. If the price of butter goes up 50% and the quantity demanded falls by 10%, what is the price elasticity of demand? Is this elastic or inelastic? Why? εD = 10%/50% = .20 This is inelastic (< 1.0) … It is likely to be a small portion of our budgets.

Elasticity Problems εD = 10%/[$2/$20] = 10%/10% = 1.0 2. If the price of the Rolling Stones’ CD, Semi-Serious, is reduced from $20 to $18, and the quantity demanded (say, on a per month basis) rises by 10%, what is the price elasticity of demand? Is this elastic or inelastic? Why? εD = 10%/[$2/$20] = 10%/10% = 1.0 This is “unit elastic” (= 1.0) … It doesn’t easily fit into any categories insofar as elastic vs. inelastic goes.

Elasticity Problems εD = [100,000/1,000,000]/30% = 10%/30% = .33 3. If the price of gas goes up by 30% and the quantity demanded falls from 1,000,000 gallons/day to 900,000 gallons/day, what is the price elasticity of demand? Is this elastic or inelastic? Why? εD = [100,000/1,000,000]/30% = 10%/30% = .33 This is inelastic (< 1.0) … It is likely to be considered a necessity.

Elasticity Problems 3. (con’t) If the price, then, falls back by 30%, would you predict the response by consumers will be elastic or inelastic? Why? It would still be inelastic… Consumers will buy more when the price falls. (that is just the law of demand at work) But, they will not buy a lot more.

Elasticity Problems εD = [10,000/10,000]/[$40/$80] = 100%/50% = 2.0 4. A popular pair of Nike shoes, the Paris Hilton Liteweights, is reduced in price from $80 to $40, while the quantity demanded rises from 10,000 pairs/week to 20,000 pairs/week. What is the price elasticity of demand? Is this elastic or inelastic? Why? εD = [10,000/10,000]/[$40/$80] = 100%/50% = 2.0 This is elastic (> 1.0) … It is likely that there are many substitutes available.

Elasticity Problems 5. DishTV has lowered its subscription TV prices by 10% and its subscription base rose by 15%. (a) What is the price elasticity of demand for DishTV? Is this elastic or inelastic? Why? εD = 15%/10% = 1.5 It is elastic – substitutes? (b) If DirecTV sees its subscription base fall by 8%, what is the cross price elasticity of demand for DirecTV? For DishTV? εXZ = -8%/+10% = -.8 It is a substitute & inelastic. Can’t tell! (c) If incomes rise by 3% and subscription base for DishTV rises by 9%, what is the income elasticity of demand for DishTV? εy = 9%/3% = 3.0 It is a normal good and income elastic.

Elasticity Problems 6. Consider the demand curve. As it is a straight line, there is an elastic portion, an inelastic portion and point of unitary elasticity. Identify where, along this demand, the total revenue would be maximized. [Total revenue equals price times quantity.] Q P Increase TR by P along elastic portion and P along inelastic portion.

Elasticity Tax Problem price DA DB quantity $1.40 $1.10 $1.00 $.90 $.60 100 80 50 7/8. For the accompanying graph, assume that equilibrium starts at point A. Consider the effects of a tax, which will decrease the supply, for two alternative demand curves, DA and DB. Yes, supply “decreases” and shifts up by $.50 (see q=80). a. A $.50 per unit tax is placed on this good – does S’ show the new supply curve?

Elasticity Tax Problem price DA DB quantity $1.40 $1.10 $1.00 $.90 $.60 100 80 50 For the accompanying graph, assume that equilibrium starts at point A. Consider the effects of a tax, which will decrease the supply, for two alternative demand curves, DA and DB. $112 $55 $100 b. What is the change in total revenue along DA and DB? DA - From $100 to $55; total revenue fell by $45. DB - From $100 to $112; total revenue rose by $12.

Elasticity Tax Problem price DA DB quantity $1.40 $1.10 $1.00 $.90 $.60 100 80 50 For the accompanying graph, assume that equilibrium starts at point A. Consider the effects of a tax, which will decrease the supply, for two alternative demand curves, DA and DB. c. What does this tell you about the price elasticity for each demand curve? DA is elastic (P - TR) while DB is inelastic (P - TR).

D for DA is (50/100)/(.1/1) = 50%/10% = 5.0 Elasticity Tax Problem S’ S A price DA DB quantity $1.40 $1.10 $1.00 $.90 $.60 100 80 50 For the accompanying graph, assume that equilibrium starts at point A. Consider the effects of a tax, which will decrease the supply, for two alternative demand curves, DA and DB. Calculate the price elasticity for each demand curve: D for DA is (50/100)/(.1/1) = 50%/10% = 5.0 D for DB is (20/100)/(.4/1) = 20%/40% = 0.5

Elasticity Tax Problem price DA DB quantity $1.40 $1.10 $1.00 $.90 $.60 100 80 50 For the accompanying graph, assume that equilibrium starts at point A. Consider the effects of a tax, which will decrease the supply, for two alternative demand curves, DA and DB. $40 $25 d. What will be the tax revenue collected in each case? DA - Tax revenue = ($.50)*50 units = $25. DB - Tax revenue = ($.50)*80 units = $40.

Elasticity Tax Problem price DA DB quantity $1.40 $1.10 $1.00 $.90 $.60 100 80 50 For the accompanying graph, assume that equilibrium starts at point A. Consider the effects of a tax, which will decrease the supply, for two alternative demand curves, DA and DB. e. Shade in the lost consumer & producer surplus.

ECO 284 - Microeconomics - Dr. D. Foster Elasticity Problems ECO 284 - Microeconomics - Dr. D. Foster