Could anyone help me with this question Thx Microsoft used t

_{Could anyone help me with this question? Thx}

Microsoft used to be a de-facto monopoly in the operating systems\' market in the | 1990s. Assume that inverse market demand for Windows registered is given by P(Q) = 100 - 2Q, and Microsoft\'s marginal cost of producing Windows registered is MC(Q) = 20. What will be Microsoft\'s profit maximizing output quantity and price? How large is the deadweight loss from Microsoft\'s monopoly position?

Solution

a. P = 100 - 2Q

   TR = P*Q = 100Q - 2Q²

   MR = 100 - 4Q

   MC = 20

Profot will be maximized at MR = MC

=> 100 - 4Q = 20

=> 4Q = 80

=> Q = 80/4 = 20

And, P = 100 - 2(20) = $60

TR = $60 * 20 = $1200

b. The competitive equilibrium is at P = MC

=> 100 - 2Q = 20

=> 2Q = 80

=> Q = 80/2 = 40

And, P = 100 - 2(40) = $20

TR = $20 * 40 = $800

DWL = [($60 - $20) * ( 40 - 20)] / 2 = $400