Exercise Set 10
ELASTICITY

I. Objectives

• To compute price elasticity of demand
• To determine the elastic, inelastic and unit-elastic regions on a linear demand curve
• To understand why an increase in price might actually decrease total revenue
• To understand the link between elasticity and total revenue

II. Data

• Consider the demand curve P = 40 - 2Q.
• Suppose the firm is currently charging a price P₁. Let Q₁ denote the corresponding sales (from the demand curve).
• If the firm changes its price, what will happen to its sales (quantity) and total revenue (TR)?
• What is the price elasticity of demand (e)? Use the midpoint formula to compute e.
• Using the calculator below:
  1. Select values for the prices.
  2. Click on Gimme Elasticity or gimme death! to confirm your computations.

III. Questions

1. Sketch the given demand curve. The horizontal intercept is ______, the vertical intercept is ________ and the slope is _______.
2. Select a value for P₁, and compute the corresponding quantity demanded.
   P₁ = _________, Q₁ = _________.
3. Indicate the point (Q₁,P₁) on the graph. This combination of price and quantity yields the firm a revenue of $ ______.
4. Choose a different price: P₂ = _______.
   The corresponding quantity demanded is _____, and the firm's total revenue is $ _______.
5. Consider a change in price from P₁ to P₂.
   1. In this region the elasticity of demand is _______. Show calculations.
   2. The price change has caused the firm's revenue to [ increase | decrease | remain unchanged ].
6. On the graph, indicate the regions where: (a) e > 1, (b) e < 1, and (c) e = 1. In which of these regions will an increase in price lead to higher total revenue? Explain.
7. If the current price is below the midpoint of the demand curve, and the firm wishes to increase total revenue, it should [ increase | reduce ] its price. Explain.
8. If an increase in price leads to less total revenue, we may conclude that demand is [ elastic | inelastic | unit-elastic ]. Explain.
9. If the firm wishes to maximize total revenue, it should charge a price of $ _____. Explain.

IV. Additional questions

1. The government imposes an excise tax of $2 on cigarettes.
   1. Is the demand for cigarettes in the short run likely to be highly elastic, or highly inelastic? Why?
   2. Will the price of cigarettes increase by $2? Why? Provide a graph.
   3. Will the consumer, or the producer, bear the greater amount of the tax burden? Why? Use the graph in (b).
2. Consider the demand for gasoline in the short run. As the price of gasoline rises from $1/gallon to $3/gallon, the quantity demanded of gasoline falls from 220 gallons to 180 gallons.
   1. Compute the elasticity of demand for gasoline.
   2. What is likely to happen to the elasticity of demand for gasoline in the long run? Provide sound reasons.
3. Consider two points on the market demand curve for Coke. At point M, the price is $1.50/gallon and the quantity demanded is 45 gallons. At point N, the price is $2.50/gallon and the corresponding quantity demanded is 35 gallons.
   1. Sketch the demand curve. Indicate the points M and N on the graph.
   2. Compute the price elasticity of demand between the two points.
   3. Assume that Coke is currently charging a price of $2.50 per gallon. Will their total revenue increase if they lower their price? Explain, using the notion of elasticity.
4. If the price of a good falls and total expenditure on the good also falls, we can conclude that
   1. Demand is unit-elastic
   2. Demand is elastic
   3. Elasticity of demand is less than one
   4. Elasticity of demand is greater than one
   5. Both (a) and (c)
5. The demand curve for salt is more inelastic than the supply curve. Assuming, however, that demand is not perfectly inelastic, an excise tax of $1.00 on salt is likely to lead to
   1. An increase of more than $1 in the price of salt
   2. An increase of less than $1 in the price of salt
   3. An increase of $1 in the price of salt
   4. A greater tax burden on the producer
   5. Both (b) and (d)
6. If the demand curve for Lexus cars is highly elastic, a sales tax of $1000 on a Lexus is likely to lead to
   1. An increase of more than $1000 in the price of a Lexus
   2. An increase of less than $1000 in the price of a Lexus
   3. An increase of $1000 in the price of a Lexus
   4. A greater tax burden on the producer than on the consumer
   5. Both (b) and (d)
7. A demand curve is perfectly inelastic if
   1. The elasticity of demand is unity
   2. The elasticity of demand is zero
   3. A change in the price of the good has no effect on the quantity demanded
   4. Both (a) and (c)
   5. Both (b) and (c)
8. In the elastic region of the demand curve, if the price of the good rises by 10%,
   1. Quantity demanded will fall by less than 10%
   2. Quantity demanded will fall by more than 10%
   3. Quantity demanded will fall by exactly 10%
   4. There is no change in the quantity demanded
9. Bugle Boy raises the price of its jeans only to see its total revenue fall. From this we may infer that, in the relevant region of the demand curve for Bugle Boy jeans,
   1. Demand is unit-elastic
   2. Demand is elastic
   3. The elasticity of demand is less than one
   4. The elasticity of demand is greater than one
   5. Both (b) and (d) are correct
10. If two goods are complements, their cross elasticity of demand will be
    1. Zero
    2. A negative number
    3. A positive number
    4. Infinity
11. IBM raises the price of its personal computers by 12%. All else remaining the same, IBM's total revenue will also rise if
    1. The price elasticity of demand for IBM's personal computers is 0.8.
    2. The price elasticity of demand for IBM's personal computers is 1.5.
    3. Demand for IBM's personal computers is highly elastic.
    4. The demand curve for IBM's personal computers is perfectly flat (horizontal) .
    5. Both (b) and (c) are true.
12. The current price of Colgate toothpaste lies in the inelastic region of the demand curve for the toothpaste. If Colgate raises it price by 5%, we may infer that, ceteris paribus,
    1. Quantity demanded will fall by less than 5%.
    2. Quantity demanded will fall by more than 5%.
    3. Quantity demanded will fall by exactly 5%.
    4. Colgate's total revenue will fall.
    5. Both (a) and (d) are true.
13. The demand curve for a good is more elastic than the supply curve. If an excise tax of $2.00 is imposed on the good, it is likely that
    1. The demand curve will shift to the right.
    2. The price paid by the consumer will increase by $2.00.
    3. The greater part of the tax burden will be borne by the consumer.
    4. Both (b) and (c) will occur.
    5. None of the above will occur.
14. If consumers regard Nike shoes and Reebok shoes as substitutes, we may infer that
    1. Their cross elasticity of demand will be positive.
    2. Their cross elasticity of demand will be negative.
    3. An increase in the price of Nike shoes will cause consumers to buy fewer Reebok shoes.
    4. Both (a) and (c) are true.
    5. Both (b) and (c) are true.
15. The elasticity of demand for diamond rings is 0.4. If the price of a diamond ring falls by 10%, the quantity demanded of diamond rings will rise by
    1. 0.04%
    2. 0.4%
    3. 4%
    4. 40%
16. The demand curve for a good is perfectly elastic. We conclude that
    1. The demand curve is horizontal.
    2. The demand curve is vertical.
    3. A change in the price of the good has no effect on the quantity demanded.
    4. The elasticity of demand is 1.
    5. Both (b) and (c) are true.

	4c	5b	6e	7e	8b
	9e	10b	11a	12a	13e
	14a	15c	16a