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Chapter 9: Q10. (page 364)

In Example 9.1 (page 332), we calculated the gains and losses from price controls on natural gas and found that there was a deadweight loss of \(5.68 billion. This calculation was based on a price of oil of \)50 per barrel.

a. If the price of oil were \(60 per barrel, what would be the free-market price of gas? How large a deadweight loss would result if the maximum allowable price of natural gas were \)3.00 per thousand cubic feet?

b. What price of oil would yield a free-market price of natural gas of $3?

Short Answer

Expert verified

  1. The free-market price of gas would be $8.94. The deadweight loss will be $63.45.

  2. The price of natural gas would be $3 at a price of oil =$19.75

Step by step solution

01

Step 1. Determining the free-market price of gas and deadweight loss

The supply and demand equations for natural gas are:

The supply equation of gas (QS) is: QS = 15.90 + 0.72PG+ 0.05PO

The demand equation of gas, (QD) is: QS = 0.02 - 1.8PG+ 0.69PO

(PG is the price of natural gas in dollars per thousand cubic feet, and PO is the price of oil in dollars per barrel.)

The free-market price of the gas will be calculated by equating the supply equation (QS) of gas with the demand equation of gas (QD). The price of oil (PO) is $60 per barrel. The free-market price of the gas is calculated below:

Qs=QD15.90+0.72PG++0.0560=0.02-1.8PG+0.696041.4-15.90-3+0.02=1.8P-0.72PP=8.94

The price of natural gas is $8.94 per thousand cubic feet.

Deadweight loss:Deadweight loss is the loss to society because of restrictive policies of the government. It is calculated by multiplying the difference between the prices (P2- P1) and quantities (Q1– Q2) of the free-market situation and after the price ceiling.

The quantity demanded by the society during the free market situation is:

Q1=0.02-1.88.94+0.6960=0.02-16.092+41.4=25.33

The quantity demanded by the society after the maximum allowable price policy:

Q2=0.02-1.83+0.6960=0.02-5.4+41.4=36.02

The value of the deadweight loss is calculated by putting the values of P1 (Free market equilibrium price), P2 (maximum allowable price policy price), Q1 (free-market quantity), and Q2 (quantity after maximum allowable price policy).

DWL=P2-P1Q1-Q2=8.94-336.02-25.33=5.94×10.69=63.45

The deadweight loss to society because of the government’s maximum allowable price policy is $63.45 billion.

02

Step 2. Determining the price of oil when the natural gas is $3

The price of oil can be calculated by putting the price of natural gas (PG = $3) in the free market demand-supply equations. It is calculated below:

15.90+0.723+0.05PO=0.02-1.83+0.69PO12.64=0.69P-0.05PP=12.640.64=19.75

The price of oil would be $19.75 per barrel.

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