Pricing the iPod
iPod Demand Curve Econ 1 Fall, 2007
$700
$600
$500
Price
$400
$300
$200
$100
$0
0
10
20
30
40
50
Quantity Sold
60
70
80
90
100
iPod Demand and Revenue Table
Quantity Price
6
10
12
17
26
46
58
74
90
100
Revenue
$700
$500
$450
$400
$350
$300
$250
$200
$150
$50
$4,200
$5,000
$5,400
$6,800
$9,100
$13,800
$14,500
$14,800
$13,500
$5,000
iPod Demand and Marginal
Revenue curves
$800
$600
$400
$200
$0
0
-$200
-$400
-$600
-$800
-$1,000
10
20
30
40
50
60
70
80
90
100
iPod Demand and Marginal
Revenue curves
$800
$600
$400
$200
$0
0
-$200
-$400
-$600
-$800
-$1,000
10
20
30
40
50
60
70
80
90
100
iPod Price and Profits with
Marginal Cost of $100
Quantity
Price
Revenue
6
$700
10
12
17
26
46
58
74
90
100
$500
$450
$400
$350
$300
$250
$200
$150
$50
$4,200
Total Cost Profit
$600
$3,600
$5,000 $1,000
$5,400 $1,200
$6,800 $1,700
$9,100 $2,600
$13,800 $4,600
$14,500 $5,800
$14,800 $7,400
$13,500 $9,000
$5,000 $10,000
$4,000
$4,200
$5,100
$6,500
$9,200
$8,700
$7,400
$4,500
-$5,000
Marginal cost of $100
$800
$600
$400
$200
$0
0
-$200
-$400
-$600
-$800
-$1,000
20
40
60
80
100
iPod Price and Profits with
Marginal Cost of $50
Quantity
Price
Revenue
Total Cost Profit
6
$700
$4,200
$300
$3,900
10
12
17
26
46
58
74
90
100
$500
$450
$400
$350
$300
$250
$200
$150
$50
$5,000
$5,400
$6,800
$9,100
$13,800
$14,500
$14,800
$13,500
$5,000
$500
$600
$850
$1,300
$2,300
$2,900
$3,700
$4,500
$5,000
$4,500
$4,800
$5,950
$7,800
$11,500
$11,600
$11,100
$9,000
$0
iPod Price and Profits with
Marginal Cost of $25
Quantity
Price
Revenue
Total Cost Profit
6
$700
$4,200
$150
$4,050
10
12
17
26
46
58
74
90
100
$500
$450
$400
$350
$300
$250
$200
$150
$50
$5,000
$5,400
$6,800
$9,100
$13,800
$14,500
$14,800
$13,500
$5,000
$250
$300
$425
$650
$1,150
$1,450
$1,850
$2,250
$2,500
$4,750
$5,100
$6,375
$8,450
$12,650
$13,050
$12,950
$11,250
$2,500
What do they really cost?
• 4 GB Nano is $149
• 8 GB Nano is $199
Why doesn’t Apple charge more?
• Our class estimates suggest that with MC of
$25-$50, Apple would maximize profits by
charging $250.
• Is there a reason for Apple to want bigger
volume of iPod sales?
• Hint: What about selling music downloads?
If demand for a monopolist’s product is
inelastic at the current price, he could
increase his profits by reducing output,
even if his marginal cost is very small.
1. True
2. False
Why is that?
• If demand is inelastic, then a small price
increase and the resulting quantity decrease
must increase revenue.
So by cutting back quantity he increases
revenue. Reducing quantity certainly won’t
increase his costs, so his profit must
increase.
A monopolist faces a demand curve with
equation P=100-Q. What is the
equation for its marginal revenue?
A)
B)
C)
D)
E)
MR=200-Q
MR=100-Q
MR=100-2Q
MR=200-2Q
MR=100-Q2
With linear demand, MR is a straight
line with same intercept, twice as steep
as demand. If demand equation is
P=100-Q, Marginal revenue is
MR=100-2q
100
Green Line Demand Curve
100-Q
Pink Line MR curve,
100-2Q
50
100
A monopolist faces a demand
curve with equation P=100-Q. Its
total costs are $10Q. What are its
marginal costs?
A)
B)
C)
D)
E)
$10 for all quantities
$10+Q
$(100/Q)-1
$100-2Q
$100-Q
Marginal cost is the extra cost of
producing one more unit if output
is Q. Therefore marginal cost is
$10(Q+1)-$10Q=$10.
Calculus answer:
Marginal cost is derivative of
$10Q with respect to Q, which
is $10.
A monopolist faces a demand
curve with equation P=100-Q. Its
total costs are $10Q. How much
should it produce to maximize its
profits?
A)
B)
C)
D)
E)
Q=100
Q=50
Q=45
Q=30
Q=25
How do we find that?
To maximize profits, the
monopolist sets marginal revenue
equal to marginal cost. The
equation is 100-2Q=10. The
solution is Q=45.
A monopolist faces a demand
curve with equation P=100-Q. Its
total costs are $10Q. What price
should it charge to maximize
profits?
A)
B)
C)
D)
E)
P=60
P=55
P=50
P=45
P=40
How do we find that?
We found that the profit
maximizing quantity is Q=45.
Since the demand curve is
P=100-Q, it must be that the price
is 100-45=55 when profits are
maximized.
Diagram for profit maximizing
monopoly
100
Green Demand Curve
100-Q
55
Blue Marginal Cost Curve
50
45
100
Pink MR curve,
100-2Q
A monopolist faces a demand
curve with equation P=100-Q. Its
total costs are $10Q. How much
profits can it make?
A)
B)
C)
D)
E)
$ 2025
$200
$1800
$600
$950
Diagram for profit maximizing
monopoly
Maximum profit is $45x45=$2025.
100
Green Demand Curve
100-Q
55
Profit
10
Blue Marginal Cost Curve
45
100
Pink MR curve,
100-2Q
And On to our Lecture