Question

The producer of a downloadable antivirus software program spends exactly ​$3,150,000 producing the first copy and incurring various costs required to make the software​ "user-friendly." The firm can produce and distribute additional copies at a​ per-unit cost of ​$2.00. If the company sold as many copies as consumers wished to purchase at a price of ​$2.00 per​ copy, it would sell 450,000 copies. If the company maximizes its economic profits in the​ short-run, it sells 250,000 copies at a price of ​$45. ​Finally, the company earns zero economic profits when it sells 300,000 copies.

What are the​ firm's economic profits​ (or losses) if it sells 450,000 copies of the antivirus software program at a ​$2.00 price per​ copy?

​What are the maximum economic profits that the firm can earn in the short​ run?

What is marginal revenue when the firm maximizes its​ short-run economic​ profits?

In the long​ run, after entry of competing​ firms, to the nearest​ dollar, and including the correct​ sign, what amount of economic profits will this firm​ earn?

​Please provide detailed step-by-step instructions on how you arrived at each answer, thank you.

Answer 1

Selling of 450,000 units:

EP = Total revenue (TR) – Total cost (TC)

TR = Units × Sale price

      = 450,000 × $2

      = $900,000

The cost of first unit is $3,150,000. Therefore, the additional units are (450,000 – 1 =) 449,999.

TC = Cost of first unit + Cost of additional units

      = 3,150,000 + (449,999 × 2)

      = 3,150,000 + 899,998

      = $4,049,998

Economic profit = TR – TC

                            = 900,000 – 4,049,998

                            = - $3,149,998

Since this is negative, it is actually a loss.

Answer: economic loss is $3,149,998.

Maximum profit:

TR = Units × Sale price

      = 250,000 × $45

      = $11,250,000

The cost of first unit is $3,150,000. Therefore, the additional units are (250,000 – 1 =) 249,999.

TC = Cost of first unit + Cost of additional units

      = 3,150,000 + (249,999 × 2)

      = 3,150,000 + 499,998

      = $3,649,998

Economic profit = TR – TC

                            = 11,250,000 – 3,649,998

                            = $7,600,002 (Answer)

Marginal revenue:

This is the difference in total revenue in two consecutive units.

Marginal revenue = TR of 250,000 units – TR of 249,999 units

                             = ($45 × 250,000) – ($2 × 249,999)

                             = 11,250,000 – 499,998

                             = $10,750,002 (Answer)

Long-run economic profit:

There would be no economic profit or loss in the long-run, since in the long-run all factors of production become variable and there will be no fixed cost. The firm can earn normal profit but zero economic profit. It happens if it sells 300,000 units.

Economic profit = TR – TC

                           = ($2 × 300,000) – ($2 × 300,000)

                           = $600,000 - $600,000

                           = 0

Note: The cost of first unit is $3,150,000. This is a fixed cost in the short-run and has no relevance in the long-run.