Problem 18.1 - Elasticity of demand KEY
Problem:
Suppose a firm sells 20,000 units when the price is $16,
but sells 30,000 units when the price falls to $14.
a.
b.
c.
d.
Calculate the percentage change in the quantity
sold over this price range using the midpoint
formula.
Calculate the percentage change in the price
using the midpoint formula.
Find the price elasticity of demand over this
range of prices. State whether demand is elastic
or inelastic over this range.
Suppose the firm's elasticity of demand is
constant over a large range of prices, equal to
the value found in part c. If the price were to
fall another 4%, what should the firm predict
will happen to its quantity sold?
Answer:
a.
b.
c.
d.
The midpoint formula uses the average of the
two quantities as the reference point for
computing the percentage change. In this
example, the percentage change is (30,000 –
20,000)/25,000 = 0.40, or 40%.
The percentage change is (16 – 14)/15 =
0.133, or 13.3%.
The price elasticity of demand is the ratio of the
percentage change in quantity to the
percentage change in price. In this example, Ed
= 40/13.3 = 3. Since Ed is bigger than one,
demand is elastic.
The elasticity of demand equals the percentage
change in quantity divided by the percentage
change in price. Rearranging this relationship,
the percentage change in quantity is equal to
the elasticity of demand times the percentage
change in price. In this example, Ed = 3 and the
price change is 4%, so quantity sold will
increase by 12%. 12% = 3 x 4%.
Problem 18.2 - Total-revenue test KEY
Problem:
Suppose a firm sells 70 units when the price is $6, but
sells 80 units when the price falls to $4.
a.
b.
c.
Calculate the firm's revenue at each of the
prices.
Use the total-revenue test to determine whether
demand is elastic or inelastic over this range.
Verify your previous answer by calculating the
elasticity of demand using the midpoint formula.
Answer:
a.
b.
c.
Revenue equals price times quantity sold. At P
= $6, revenue equals $420. $420 = $6 x 70. At
P = $4, revenue = $4 x 80 = $320.
Revenue falls when the price falls, suggesting
demand is inelastic over this range.
Ed = [(80 – 70)/75] / [(6 – 4)/5] = .133/.40 =
.33, or 1/3. This is less than one, verifying that
demand is inelastic.
Problem 18.3 - Consumer and producer surplus
Problem:
Suppose the market for watermelons can be described
by the graph below.
Answer:
a.
b.
c.
d.
e.
a.
b.
c.
d.
e.
If Jon is willing to pay as much as $8 for a
watermelon, how much surplus would he receive
if he pays the market price for a watermelon?
Suppose Figgy Farms requires at least $5 per
watermelon to be willing to sell in this market.
What is Figgy's producer surplus for one
watermelon in this market?
How much total consumer surplus is received in
this market?
How much total producer surplus is received in
this market?
What is the total surplus (combined consumer
and producer surplus) in the market?
Consumer surplus is the difference between the
maximum Jon is willing to pay and the price he
actually pays. The equilibrium price in this
market is $6, so his consumer surplus is $2. $2
= $8 – $6.
Producer surplus is the difference between the
market price and the minimum a seller requires
to offer the product for sale. In this case,
Figgy's producer surplus is $6 – $5 = $1.
Total consumer surplus is the area below the
demand curve but above the market price. The
area of this triangle on the graph is ½ x ($11 –
$6) x 200 = $500.
Total producer surplus is the area above the
supply curve but below the market price. The
area of this triangle on the graph is ½ x ($6 –
$4) x 200 = $200.
The total surplus is the sum of consumer and
producer surplus, or $500 + $200 = $700.