Question

Q1: The Wise Economists, a top rock band, have just finishedrecording their latest music CD. Their record company’s marketing department determines that the demand for theCD is as follows

Price (€) Number of CDs

24 10000
22 20000
20 30000
18 40000
16 50000
14 60000



The company can produce the CD with no fixed cost and aVariable cost of €5 per CD:


a) Find total revenue for quantity equal to 10 000, 20 000 andso on. What is the marginal revenue for each 10000increase in the quantity sold?

b) What quantity of CDs would maximize profit? Whatwould the price be?

Answer 1

a) Total revenue: $TR=P\times Q$

TR1=240,000.

TR2=440,000.

TR3=600,000.

TR4=720,000.

TR5=800,000.

TR6=840,000.

Marginal revenue: TR2-TR1, and so on.

MR1=0.

MR2=200,000.

MR3=140,000.

MR4=120,000.

MR5=80,000.

MR6=40,000.

b)To maximize profit we need MR=MC.

From the information provided we can find demand curve equation:

$P=26-0.0002\times Q.$

$TP=TR-TC=Q\times P - 5Q = 26Q-0.0002Q-5Q=21Q-0.0002Q^2.$

Tomaximaze profit we need to find the derevative of this equation and solve it to 0:

$TP'=21-0.0004Q=0.$

$Q=52,500.$

With that quantity the price will be:

$P=26-0.0002\times 52,500 = 10.5.$