Consider a monopoly producing a good with the following inverse demand curve: P
ID: 1248732 • Letter: C
Question
Consider a monopoly producing a good with the following inverse demand curve:P (q) = 20 - 2q
Assume that marginal cost is
MC = 4 + 4q
(i) What is the optimal quantity for the monopolist? What is the corre-
sponding price?
(ii) What is the socially optimal quantity?
(iii) Assume now that Congress is debating regulating this monopolistic industry so as to get rid of the monopoly distortions. Some economists object that setting-up a regulatory agency whose operation is costly. Let F denote this cost. What is the maximal value of F beyond which it makes no sense to set up the regulatory agency?
Explanation / Answer
For a monopoly profit is maximised when MR= MC.
Price = 20-2q
When multiplying both sides with q we get
Pq= 20q - 2q^2
TR= 20q - 2q^2
differentiating TR we get MR.
dTR/dQ= MR = (1 x 1x 20q^1-1) - (2x2 xq^2-1)
MR= 20 - 4q
MC= 4+ 4q
MR=Mc is the profit maximizing condition
20- 4q= 4+4q
8q= 16
q= 16/8= 2 uits.
Monopoly price= 20- 2q
= 20 - 2(2)
= $16
b)
Social optimu quantity is produced when monopoly charges price equal to MC
P= MC
20-2q= 4+ 4q
6q= 16
q= 16/6= 2.6 units.
Price= 20- 2(2.6)
= 20 - 5.2
Socially efficent price =$14.8
c) Government will set socially efficent price as slab.
this is equal to $14.8.
The cost should not be more than the dead weitht loss due to monopoly price:
Dead weight loss= 1/2 x differnce in output x P-MC
= 0.5 x 0.6 x (16 -12)
= 0.5 x 0.6 x 4
= $1.2
F should not be more than $1.2
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