Question

1.

ou are the manager of a local sporting goods store and recently purchased a shipment of 60 sets of skis and ski bindings at a total cost of $25,000 (your wholesale supplier would not let you purchase the skis and bindings separately, nor would it let you purchase fewer than 60 sets). The community in which your store is located consists of many different types of skiers, ranging from advanced to beginners. From experience, you know that different skiers value skis and bindings differently. However, you cannot profitably price discriminate because you cannot prevent resale.

There are about 20 advanced skiers who value skis at $400 and ski bindings at $275; 20 intermediate skiers who value skis at $300 and ski bindings at $400; and 20 beginning skiers who value skis at $200 and ski bindings at $350.

What is your maximum revenue if you charge a separate price for skis and bindings?


What is your maximum revenue if you sell skis and bindings as a bundle?

2. A monopoly is considering selling several units of a homogeneous product as a single package. A typical consumer’s demand for the product is Q^d = 110 - 0.25P, and the marginal cost of production is $160.

a. Determine the optimal number of units to put in a package.

b. How much should the firm charge for this package?

Answer 1

Answer 1)

What is your maximum revenue if you charge separate price for skis and bindings?

Answer :

Here there are three classes from which we can charge different prices as below.

20 advance skiers (skis at $400 and ski bindings at $275)

20 intermediate skiers(skis at $300 and ski bindings at $400)

20 beginner skiers (skis at $200 and ski bindings at $350)

Now total revenue from all of the above classes as below

TOTAL REVENUE = PRICE ×QUANTITY

Advanced =(400+275)×20

=13500$

Intermediate =(300+400)×20

=14000$

Beginner =(200+350)×20

=11000$

Total revenue from all the classes is:

=$13500+$14000+$11000

=$38500

What is your maximum revenue if you sell skis and bindings as a bundle?

Answer :

If we want to sell in bundle price then we have to keep that price which all class can be affordable then and only we can sell all the quantity of ski and ski bindings. So the price of skis and ski bindings can be as below:

Ski at $200

Ski bindings at 275$

Total revenue= price × quantity

=(200$+275$)×60

=28500$.

2)

Answer :

First, set the demand function in the form of inverse demand function to later generate MR=MC. Here MR = MC is the profit maximization point. Where we can produce our maximum output and charge price at that point.

Qd= 110 - 0.25p

0.25p = 110-Q

P=(110-Q)/0.25

P= 440-4Q .................. 1.

Now we will find marginal revenue by deriving total revenue in respect to Q.

TR= P × Q

TR= (440 - 4Q) × Q (PUT equation....1 at the place of P)

TR=440Q - 4Q^2

MR = 440- 8Q ...................... 2

Now MR=MC

440-8Q =160

8Q=440-160

Q=280/8

Q=35

Now put Q=35 in demand function so we can find P.

Q=110-0.25P

35=110-0.25p

0.25p=110-35

P=75/0.25

P=300

A. Determine the optimal number of units to put in a package.

Q= 35

b. How much should the firm charge for this package.

P=300