Question

There are two types of consumers of Sony PlayStation video game consoles. The first type of consumer is highly eager to purchase the newest game consoles (early adopters). Their inverse demand is:

P = 600 - 0.01Q_E

After the first quarter the new PlayStations are on the market, early adopter demand goes to zero at any price. The second type of consumer is more sensitive to price and will be the same one quarter after the consoles are on the market (late adopters). Their inverse demand is:

P = 300 - 0.01QL
The marginal cost to the manufacturer is constant at $100.

a) If Sony initially sets the system price at $400, calculate their producer surplus.  (Round to the nearest whole number, do not use commas or dollar signs)

b) Do any second type customers purchase the new PlayStations at the initial release?  (yes or no)

c) Sometime after the initial release, the manufacturer lowers the price to $200. If only late adopters purchase the console at this later date, calculate producer surplus from these sales.  (same rounding rules)

(Think about why Sony has an incentive to charge a high relative price at initial release and then lower the price considerably sometime later.)

Answer 1

Solution :-

(a) :-

The first type of consumer's (late adopters) their inverse demand is:

P = 600 - 0.01QE

The marginal cost to the manufacturer is constant at = $100.

If Sony initially sets the system price at P= $400,

Then,

P = 600 - 0.01QE

400 = 600 - 0.01QE

0.01QE = 600 - 400

0.01QE = 200

QE = 200/0.01

[ QE = 20000 ]

So,

Producer surplus = Profit =( P - MC) x QE

= ( 400 - 100) x 20000

= 300 x 20000

Producer surplus = 6000000.

(b) :-

No, second type ccustomers do not purchase the new PlayStations at the initial release.

Book price is $400 and maximum willingness to pay for second type is $300, so they will not buy it.

(c) :

The second type of consumer's (late adopters). Their inverse demand is:

P = 300 - 0.01QL

Now, the manufacturer lowers the price to=$200.

If only late adopters purchase the console at this later date.

So, from Demand curve :-

P = 300 - 0.01QL

200 = 300 - 0.01QL

0.01QL = 300 - 200

0.01QL = 100

QL = 100/0.01

[ QL = 10000 ]

So,

Producer surplus = (P - MC) x QL

= ( 200 - 100) x 10000

= 100 x 10000

Producer surplus = 1000000.

​​​​​