Question

2.(10) Suppose that you have a choice between monopoly outcomes

and competitive outcomes. Demand is D=160‐4P, and supply/mc=20.

a. What is the equilibrium (price and quantity) under both situations?

Competition:

Monopoly :

b.

(4) What is the welfare under both situations? Use the standard monopoly model and

measures of welfare.

Competition :

Monopoly :

Answer 1

2. Q = 160 - 4P
So, 4P = 160 - Q
So, P = (160/4) - (Q/4)
So, P = 40 - 0.25Q

a. Under competition, output is determined where P = MC.
So, 40 - 0.25Q = 20
So, 0.25Q = 40 - 20 = 20
So, Q = 20/0.25 = 80
So, Qc = 80 and Pc = 20

Under monopoly, output is determined where MR = MC.
Total Revenue, TR= P*Q = (40 - 0.25Q)*Q = 40Q - 0.25Q²
So, Marginal Revenue, MR = d(TR)/dQ = 40 - 2(0.25Q) = 40 - 0.5Q
So, MR = MC gives,
40 - 0.5Q = 20
So, 0.5Q = 40 - 20 = 20
So, Q = 20/0.5 = 40
So, Qm = 40 and P = 40 - 0.25Q = 40 - 0.25(40) = 40 - 10 = 30
So, Pm = 30

b. Maximum value of P (when Q = 0), Pmax = 40 - 0.25Q = 40
Competition:
Total welfare = Area below demand curve and above MC curve = area of triangle = (1/2)*base*height
= (1/2)*(Qc)*(Pmax - MC) = (1/2)*(80)*(40 - 20) = 40*20 = 800

Monopoly:
Under monopoly, there is a deadweight loss (DWL) as Pm > Pc and Qm < Qc.
DWL = area of triangle = (1/2)*(Qc - Qm)*(Pm - Pc) = (1/2)*(80 - 40)*(30 - 20) = (1/2)*40*10 = 200
So, Total welfare = Total welfare under competition - DWL = 800 - 200 = 600