Question

The Economist sells yearly subscription. There are three types of consumers. Type A only reads the magazine online. Type B only reads the paper copy. Type C reads both. A’s willingness to pay is 100 dollars for online, 0 for paper copy. B’s willingness to pay is 250 dollars for paper, 0 for online. C’s willingness to pay is 75 dollars for paper, 75 for online. Assume there are twice as many A types as B and C types. Which strategy maximizes revenue?

(a) Sell one subscription that includes both the paper copy and online access at 100 dollars.

(b) Sell one subscription that gives only online access at 100 dollars and another one that includes both online access and paper copy at 150 dollars.

(c) Sell one subscription gives only online access at 100 dollars and another one that includes only the paper copy at 250 dollars.

(d) Sell one subscription that includes both the paper copy and gives online access at 150 dollars.

Answer 1

Ans ) Suppose A= $100U¹

B= $250U²

C= $75U¹+ $75U²

U¹= willingness to pay for online magazine

U²= willingness to pay for paper copy

And according to question the total no of consumer is:

2A= B+C( twice of A as many type of B&C)

Then :

2($100)= $250U²+ 75U¹+75U²

200U¹-75U¹= 250U²+75U²

125U¹= 325U²

U¹/U²= 325/125

U¹/U²= 13/5................(1)

a) U¹+ U²= 13+5 ( from 1)

And in question it is given $100 spent ;

Then 100/13+100/5= 20+7.7

= 27.7

The consumer will spent on both the online and paper copy = 27.7 as we have calculated their willingness to pay. Similarly we will see by which the seller will get revenue i.e by selling maximum copy

b) 100/13(for online)

150/18( for both online & paper copy ). On adding this we get

100/13+150/18= 7.7+8.3

16

c) 100/13( for online)

250/5( paper copy only )

Total seller will get form this subscription is:

100/13+250/5= 7.7+ 50

= 57.7

d) 150/13( for online)

150/5( for paper copy )

Total:

11.5+ 30 = 41.5

As we can from above that different strategies will pay different amount of revenue. From all of the above option C will give maximum amount of revenue to the seller i .e 57.7~ $58.