Answer to Question #189850 in Microeconomics for Sheyan patel

Question

Suppose the (inverse) daily demand for oil is given by P= 130 - Q , where Q denotes millions of barrels of oil and P is the price per barrel of oil.

The marginal private cost of extracting oil is given by MPC= 10 + Q. Oil extraction gives rise to environmental pollution, such that the marginal social cost of extracting oil is given by MSC= 10+2Q

 

(a) Find the daily production and price of oil if the market for oil extraction is perfectly competitive.

(b) Find the socially optimal production and price of oil and explain why it differs from the market outcome in (a).

 

(c) Find the daily production and price of oil if there is a monopoly oil company and comment on your answer. [6 marks]

 

(d) Illustrate your answers to (a), (b) and (c) in one diagram with Q on the horizontal axis and P on the vertical axis.

 

(e) Does the monopoly oil company generate a deadweight loss? Is monopoly justified in this market?

Answer 1

a)

$P=MPC$ in a perfectly competitive market.

$130-Q=10+2Q$

$3Q=120$

$Q=40$

$P=130-40$

$P=90$

b)

$P=MPC+MSC$ (in socially optimal income)

$130-Q=10+2Q+10+3Q$

$120=6Q$

$Q=20$

$P=130-20$

$P=110$

c)

$MR=PMC$ in a monopoly market.

Total revenue$=P\times Q$

$(130-Q)Q=130Q-Q^2$

$MR=\frac{dTR}{dQ}=130-2Q$

so $130-2Q=10+2Q$

$4Q=120$

$Q=30$

$P=130-30=100$

$P=100$

d)

e)

The deadweight loss under monopoly is measured by the area BCEF.

In this market, monopoly is acceptable since it is closer to social equilibrium than perfect competition.