Pricing the iPod

iPod Demand and Revenue Table

Quantity Price Revenue6 $700 $4,200

10 $500 $5,00012 $450 $5,40017 $400 $6,80026 $350 $9,10046 $300 $13,80058 $250 $14,50074 $200 $14,80090 $150 $13,500

100 $50 $5,000

iPod Demand and Marginal Revenue curves

iPod Demand and Marginal Revenue curves

iPod Price and Profits with Marginal Cost of $100

Quantity Price Revenue Total Cost Profit6 $700 $4,200 $600 $3,600

10 $500 $5,000 $1,000 $4,00012 $450 $5,400 $1,200 $4,20017 $400 $6,800 $1,700 $5,10026 $350 $9,100 $2,600 $6,50046 $300 $13,800 $4,600 $9,20058 $250 $14,500 $5,800 $8,70074 $200 $14,800 $7,400 $7,40090 $150 $13,500 $9,000 $4,500

100 $50 $5,000 $10,000 -$5,000

Marginal cost of $100

iPod Price and Profits with Marginal Cost of $50

Quantity Price Revenue Total Cost Profit6 $700 $4,200 $300 $3,900

10 $500 $5,000 $500 $4,50012 $450 $5,400 $600 $4,80017 $400 $6,800 $850 $5,95026 $350 $9,100 $1,300 $7,80046 $300 $13,800 $2,300 $11,50058 $250 $14,500 $2,900 $11,60074 $200 $14,800 $3,700 $11,10090 $150 $13,500 $4,500 $9,000

100 $50 $5,000 $5,000 $0

iPod Price and Profits with Marginal Cost of $25

Quantity Price Revenue Total Cost Profit6 $700 $4,200 $150 $4,050

10 $500 $5,000 $250 $4,75012 $450 $5,400 $300 $5,10017 $400 $6,800 $425 $6,37526 $350 $9,100 $650 $8,45046 $300 $13,800 $1,150 $12,65058 $250 $14,500 $1,450 $13,05074 $200 $14,800 $1,850 $12,95090 $150 $13,500 $2,250 $11,250

100 $50 $5,000 $2,500 $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) MR=200-Q

B) MR=100-Q

C) MR=100-2Q

D) MR=200-2Q

E) 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

10050

Green Line Demand Curve 100-Q

Pink Line MR curve,100-2Q

A monopolist faces a demand curve with equation P=100-Q. Its total costs are $10Q. What are its

marginal costs?

A) $10 for all quantities

B) $10+Q

C) $(100/Q)-1

D) $100-2Q

E) $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) Q=100

B) Q=50

C) Q=45

D) Q=30

E) 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) P=60

B) P=55

C) P=50

D) P=45

E) 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

100

50

Green Demand Curve 100-Q

Pink MR curve,100-2Q

55

Blue Marginal Cost Curve

45

A monopolist faces a demand curve with equation P=100-Q. Its total costs are $10Q. How much

profits can it make?

A) $ 2025

B) $200

C) $1800

D) $600

E) $950

Diagram for profit maximizing monopoly

Maximum profit is $45x45=$2025.

100

100

Green Demand Curve 100-Q

Pink MR curve,100-2Q

55

Blue Marginal Cost Curve

Profit

45

10

And On to our Lecture