Question

5. Microsoft Corporation decides how many packets of the new operating system (Windows Vista) it is going to sell on the market. The research (fixed) costs associated with the development of the new system amounts to F = $1000. The variable costs of the packet is negligible C(y) = 0. Microsoft’s inverse demand for the new operating system is given by P (y) = 100 − y. • Assume that Microsoft cannot discriminate among its customers. Find geometrically and analytically the level of sales that maximizes profit, the market price, and the maximal profit.

• Find the deadweight loss (DWL) geometrically and analytically.

• Find the elasticity of the demand at the optimal level of production. Is the monopolistic firm operating on elastic or inelastic part of the demand?

Answer 1

ans a)

maximum profit is achieved where

MR=MC

TR= P(y)*y= (100-y)y = 100y-y2

MR= dTR/dy =100- 2y

TC= TFC+TVC =1000+0=1000

MC= dTC/dy =0

MR=MC

100- 2y =0

y= 50 is profit maximising output

P(y) =100-y= 100- 50 = 50 is profit maximising price

profit= TR- TC =100y-y2 - 1000 = 100(50)- (50)2 -1000 =1500 is maximum profit

graphically

y	MC	MR	P
0	0	100	100
10	0	80	90
20	0	60	80
30	0	40	70
40	0	20	60
50	0	0	50
60	0	-20	40
70	0	-40	30
80	0	-60	20
90	0	-80	10
100	0	-100	0
110	0	-120	-10

ans b) for Perfect competitive market equilibrium, P= MC but for monopoly equilibrium condition is MR= MC, deadweight loss arises because of this difference.

in above example if perfect competition operates than 100 units must have been produced whereas in monopoly only 50 units is being produced

deadweight loss is the area between this units 50 to 100 , above MC and below price line

this traingular area will have base and height =50 each

n area = (1/2)*base* height = (1/2)*50*50 =1250

so deadweight loss of 1250

ans c) elasticity of demand at optimal point= (dy/dP)*( P/y)

P = 100 − y

dP/dy = -1

elasticity of demand = (dy/dP)*( P/y) = (1/-1)* (50/50)= -1

so monopoly is opearting where elasticity is unity