Question

A firm that sells e-books - books in digital form downloadable from the Internet - sells all e-books relating to do-it-yourself topics (home plumbing, gardening, and so on) at the same price. At present, the company can earn a maximum annual profit of $30,000when it sells 10,000 copies within a year's time. The firm incurs a 50 -cent expense each time a consumer downloads a copy, but the company must spend $140,000 per year developing new editions of the e-books. The company has determined that it would earn zero economic profits if price were equal to average total cost, and in this case it could sell 30,000 copies. Under marginal cost pricing, it could sell 110,000 copies.In the short run, to the nearest cent, what is the profit-maximizing price of e-books relating to do-it-yourself topics?

$.

At the profit-maximizing quantity, to the nearest cent, what is the average total cost of producing e-books?

$ .

Answer 1

Here the cost of the company for downloading each copy is 50 cent and the cost of developing new edition is $140,000. So variable cost is 50 cent per copy and fixed cost is $140,000 per year. Now the cost equation we can write down as TC = TVC +TFC= v*Q + TFC , where v is per copy variable cost. If we do derivative this total cost against quantity we will get marginal cost. So MC = v , because first part will be v and second part is zero because fixed cost is fixed value.

Now we know that v= 50 cent and profit maximising condition is MR = MC. We have got the MC = 50 cent. Now we have to find out where MR = 50 cent.

At output level of 30000, TR= TC, So in 30000 output total revenue equal to 140000 + 30000*0.50 = 155,000 dollar. Now we need to find out change in revenue due to change in quantity is 0.50 dollar. Change in quantity will be double than change in revenue. We get this if the output increases from 30000 to 110000, then the revenue is 110000*0.50 + 140000 = 195,000 dollar, So change in revenue is 195000 - 155000 = 40000 and change in output is 110000 - 30000 = 80000, So marginal revenue is 40000/80000 = 0.50 dollar or 50 cent. So 110,000 is the profit maximising output.

Profit maximising output is 110000 and Average total cost at this level of output is 195000/110000 = 1.77