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Suppose that JVC is trying to decide how to price a new stereo system composed of a receiver, CD player, and speakers. The company's economists have estimated that two different groups will purchase these products: students and club owners. The economists analysis suggests that the total market for its brand of stereos consists of 10,000 students and 50,000 club owners. In addition, it is estimated that the maximum amount each group will pay for each stereo component is as follows:
Group Receiver CD Player Speakers
Students $250 $150 $100
Club owners $200 $75 $250
Required:
a) Suppose that JVC markets the receiver, CD player, and speakers are sold separately and together. What prices should JVC charge to maximize revenues?

Respuesta :

The revenues table is:

[tex]\text{Receivers} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 200\\\\\text{CD player}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 75\\\\\text{Speaker} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 250\\\\\text{Combined ( bundling )} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 500[/tex]

Calculating the pricing JVC will charge in order to increase revenues:

Calculating the separate price for the receiver:

when

[tex]P = 250[/tex] only for the students to buy

[tex]\to TR = 250 \times 10,000 = 2,500,000[/tex]

[tex]P = 200[/tex], both types will buy

[tex]\to TR = 200 \times (60,000) = 12,000,000[/tex]

Therefore, the higher [tex]TR[/tex], with [tex]P = 200[/tex], and the charge [tex]P = 200[/tex], for Receiver:

Calculating the value of CD player:

[tex]If \ P = 150,\ \ TR = 150\times 10,000 = 1,500,000 \\\\If \ P = 75, \ \ TR = 75 \times (60,000) = 4,500,000[/tex]

Therefore, the higher [tex]TR[/tex], with [tex]P = 75[/tex],

Speakers,

if[tex]P = 100[/tex] , both types buy

[tex]\to TR = 100 \times (60,000) = 6,000,000[/tex]

If [tex]P = 250[/tex], only club owners buy

[tex]\to TR = 250 \times 50,000 = 12,500,000[/tex]

So higher [tex]TR[/tex] with [tex]P = 250[/tex]

Now combined Willingness to pay

For students, [tex]250+150+100 = 500[/tex]

For club owners, [tex]200+75+250 = 525[/tex]

So if [tex]P = 500[/tex], both types buy

[tex]\to TR = 500 \times 60,000 = 30,000,000[/tex]

if [tex]P = 525[/tex], only club owners buy, then

[tex]\to TR = 525 \times 50,000 = 26,250,000[/tex]

so higher [tex]TR[/tex] with [tex]P = 500[/tex]

Therefore, the calculated table values are:

[tex]\text{Receivers} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 200\\\\\text{CD player}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 75\\\\\text{Speaker} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 250\\\\\text{Combined ( bundling )} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 500[/tex]

Find out more information about the revenues here:

brainly.com/question/15602440

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