You are the manager of BlackSpot Computers, which competes directly with Condens

Question

You are the manager of BlackSpot Computers, which competes directly with Condensed Computers to sell high-powered computers to businesses. From the two businesses’ perspectives, the two products are indistinguishable. The large investment required to build production facilities prohibits other firms from entering this market, and existing firms operate under the assumption that the rival will hold output constant. The inverse market demand for computers is P = 5,900 – Q and both firms produce at a marginal cost of $800 per computer. Currently, BlackSpot earns revenues of $4.25 million and profits (net of investment, R&D, and other fixed costs) of $890,000. The engineering department at BlackSpot has been steadily working on developing an assembly method that would dramatically reduce the marginal cost of producing these high-powered computers and has found a process that allows it to manufacture each computer at a marginal cost of $500. How much will this process improve BlackSpot's profits?

(Hint: Consider solving for the duopoly outcome before and after the change in BlackSpot's marginal costs.)

Explanation / Answer

Answer:

Given that information is:

The inverse market demand for computers is P = 5,900 – Q

The two firms marginal cost is: $800 per computer

Currently, Black Spot earns revenues of $4.25 million and profits of $890,000

The marginal cost of firm2 reaction function is:

                P = 5,900 - Q

                = 5,900 – (q1 + q2)

                = 5,900 - q2 - q1

MR for firm 1: MR1 = 5,900 – q2 – q1

The decision rule for firm1:

                MR1 = MC1

MR1 = 5,900 – q2 – q1   and        MC1 = 800

Therefore, 5,900 – q2 – q1 = 800

                q1 + q2 = 5,100

Thus      Q = 5,100

Now the marginal cost of $500 for high-powered computers. So the marginal cost for firm2 has not changed, thus the reaction function of firm2 should remain the same:

                  q2 = 5,100 - q1

Firm 1’s reaction function changes now because of the change of its marginal cost:

                MR1 = 5,900 – q1 – q2    and        MC1 = 500

                q1 = 5,900 – q2 – 500

                q1 = 5,400 - q2

Solving the two equations together:

                q1 = 5,400 - q2

                q2 = 5,100 – q1

We can substitute q2 into q1 then, we get

                q1 = 5,400 – (5,100 – q1)

                q1= 300 – q1

                q1 = 150

Now q2 = 4,950

Therefore, P = 5,900 – (q1 + q2)

Q = 5,100

P = 5,900 – 5100 = 300

Profit for firm2: TR – TC

                = Pq2 – TC

                = 300*4950 – 300*500 – 1,000,000

                = 1,485,000 – 150,000 - 1,000,000

                = 335,000

      Therefore, this technological advance will increase firm 1’s market share and production, lowers market price and firm 1’s profit increases over $335,000.

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