4 Natural Monopoly and Regulation (10 points) A monopolist faces a market (inver
ID: 1147624 • Letter: 4
Question
4 Natural Monopoly and Regulation (10 points) A monopolist faces a market (inverse) demand curve P-50-Q. Its total cost is C = 100-10Q+ a. (1 point) What is the competitive equilibrium benchmark in this market? What profit does the firm earn if it produces at this point? b. (2 points) What is the monopoly equilibrium price and quantity? What profit does the firm earn if it produces at this point? c. (2 points) What is the deadweight loss at the monopoly outcome? d. (2 points) If we implement some form of regulation here (don't worry about different forms of pricing and rate structure yet, just stick with the basic model), what would the welfare- maximizing regulated price and quantity be? What is deadweight loss at that point? e. (1 point) Why is there still deadweight loss at the regulated outcome? f. (2 points) Draw a graph illustrating your answers (hint: feel free to freehand-draw the AC curve, don't spend too much effort calculating it)Explanation / Answer
a )
Competitive Equilibrium P =MC
P = 50 –Q
TC = 100+10Q +Q^2
On differentiating TC.
MC = 10+2Q
P = MC
50 –Q = 10+2Q
40 = 3Q
Q = 40/3
=13.3
P = 50 – 13.3
= 36.7
Profit = TR –TC
=13.3*36.7 – 100 – 10(13.3) – (13.3)^2
=488.11 -100 -133-176.89
=$78.22
b)
Monopolist Equilibrium MR =MC
P = 50 –Q
TR = 50Q – Q^2
MR = 50 – 2Q
TC = 100+10Q +Q^2
On differentiating TC.
MC = 10+2Q
MR = MC
50 –2Q = 10+2Q
40 = 4Q
Q = 40/4
=10
P = 50 – 10
= 40
Profit = TR –TC
=10*40 – 100 – 10(10) – (10)^2
=400 -100 -100 -100
=$100
c)
Dead Weight Loss = 0.5 (13.3 -10)(100 -78.22)
= 0.5* 3.3* 21.78
=35.88
d)
Government can regulate Price by setting it equal to AC.
P = AC
It will reduce the price level but still not equal to competitive market.
Hence, Still dead weight loss persists here.
Deadweight loss gets reduced only still there.
e)
Output does not increase sufficiently, hence DWL persists even here also.
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