A television station is considering the sale of promotional DVDs. It can have th

Question

A television station is considering the sale of promotional DVDs. It can have the DVDs produced by one of two suppliers. Supplier A will charge the station a set-up fee of $1,200 plus $2 for each DVDs; supplier B has the no set-up fee and will charge $4 per DVD. The station estimates its demand for the DVDs to be given by Q = 1,600 – 200P, where P is the price in dollars and Q is the number of DVDs. (The price equation is P = 8 – Q / 200).

1. Suppose the station plans to give away the videos. How many DVDs should it order? From which supplier?

2. Suppose instead that the stations seek to maximize its profits from sales of the DVDs. What price should it charge? How many DVDs should it order from which supplier?

Explanation / Answer

PART-A)

Q = 1600 -200(0) = 1600

The number of DVD that should be ordered can be determined by the demand curve. Since the DVDs are being given away at no cost, the number of DVDs that should be ordered would be 1600.

?

Supplier A: Cost = 1200 + 2(1600) = $4400

Supplier B: Cost = 4(1600) = $6400

Therefore, the station should order from supplier A because it would be cheaper for the station.

?

PART-B)

We are given Q = 1600 – 200P

P = 8 - Q/200 (or 8 - 0.005Q )

R = P * Q = (8 - 0.005Q) (Q) = 8Q-.005Q2

MR = 8 - .01Q

Cost to Supplier A = 1200 + 2Q

Marginal cost Supplier A = 2

Cost to Supplier B = 4Q

Marginal cost Supplier B = 4

?

Supplier A:

MR = MC

8-.01Q = 2

The quantity of DVDs the station should order equals: Q = 600

Price they should charge for each DVD equals $5 [= 8- (.005 * 600)]

PIE = R – C

R = PQ

The company’s profit will be $600 [5(600) – 1200 + 2(600) = $600] if they got the DVDs from supplier A.

?

?

Supplier B:

MR = MC

8-.01Q = 4

?

The quantity of DVDs the station should order: Q = 400

The price they should charge equals $6 (=P = 8-.005(400) = $6) for each DVD.

?

PIE= R – C

R = PQ

The company’s profit equals $800 [=6(400) – 4(400) = $800] if they got the DVDs from supplier B.

?

Thus if the company wants to maximize profits they would choose supplier B.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.