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 output firms operate under the assumption that the rival will hold constant. The inverse market demand for computes 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 fond a process that allows it to manufacture each computer at a marginal cost of $500. How will this technological advance impact your production and pricing plans? How will it impact Blackspot’s bottom line? Comment

Explanation / Answer

P=5900 - Q But Q=QBS + QCC

P=5900- (QBS + QCC )

Marginal cost=800

Profit for BlackSpot Computer= (P-C) QBS

Profit BS= (5900-(QBS+ QCC) -800) QBS

QBS Profit BS= (5900- QBS-QCC-800) QBS

QBS Differentiate the function with respect to QBS

5900-QBS-QCC-800=0

QBS= 5100-QCC

Profit CC = (5900-(QBS+QCC)-800) QCC

Profit CC =5900QCC-QBSQCC+QCC^2 -800QCC

Differentiate the function with respect to QCC

5900-QBS+2QCC-800=0

5100-QBS+2QCC =0

QCC= -2550+0.5*QBS

Solve the two equations simultaneously

QBS=5100-(-2550+0.5*QBS)

QBS = 5100+2550 -0.5QBS

QBS=7650-0.5QBS

QBS = 15300

QCC= -2550+0.5QBS

QCC= -2550+7650

QCC=5100

P=5900- (QBS + QCC )

P=5900-(15300+5100)

P= -14500

Profit BS = 234090000

Profit CC = 78030000

Now after innovation marginal cost will be 500

So putting 500

5400QBS-QCC.QBS-QBS^2

Differentiating wrt QBS

5400-QCC-2QBS

QBS = 2700-0.5QCC

Profit for CC

(5900 – (QBS+QCC)-500)*QCC

5100QCC – QCC^2 – (QBS*QCC)

5100QCC –QCC^2 – (2700QCC-0.5QCC^2)

5100QCC-0.5QCC^2-2700QCC

2400QCC-0.5QCC^2

Differentiating wrt QCC

2400-QCC

QCC = 2400

QBS = 2700 –(0.5*2400)

QBS = 1500

Profit BS = (5900-QBS-QCC-500) 1500

= 1800000

Profit CC = (5900 – 2700-1500-500)*2700

= 3240000

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