Question

1. Market demand for laptop computers is y = 500 - p. But the computers are developed by a hardware firm with a cost function c(y) = 100, & the operating system is developed by a software firm with a cost function of c(y) = 150. a. Calculate the optimal prices for the hardware & software firm to charge, & the total market quantity. (4 points) b. Calculate the optimal price & quantity if it were to behave like a merged firm

Answer 1

a.

Market Demand: y = 500 - p

p = 500 - y

Total Revenue TR = P * y = (500 - y) * y

TR = 500y - y²

MR = d(TR) / dy

MR = 500 - 2y

For Hardware firm:

at equilibrium, MR = MC

500 - 2y = 100

y = 200

p = 500 - 200 = 300

For Software firm:

at equilibrium, MR = MC

500 - 2y = 150

y = 175

p = 500 - 175 = 325

b. When both firms merge, then consider lower MC = 100

So, MR = MC

500 - 2y = 100

y = 200

p = 500 - 200 = 300