Question

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 and utilized the following equations:
Supply: QS = 15.90 + 0.72PG + 0.05PO

Demand: QD = 0.02 – 1.8PG + 0.69PO

Where QS and QD are the quantities supplied and demanded, each measured in trillion cubic feet (Tcf), PG is the price of natural gas in dollars per thousand cubic feet ($/mcf), and PO is the price of oil in dollars per barrel ($/b).

If the price of oil were $70.00 per barrel, what would be the free-market price of gas?

With a $70.00 price of oil per barrel, the free market price of gas would be $11.48 per thousand cubic foot.

What would be the deadweight loss if the price of natural gas were regulated to be $4.00? The deadweight loss would be $___ billion. (Round answer to two decimal places)

Answer 1

Answer:

Explanation:

1. If the price of oil were $70.00 per barrel, what would be the free-market price of gas?

The free-market price is defined by the equilibrium point: when the quantity demanded and the quantity supplied are equal.

QS = 15.90 + 0.72PG + 0.05PO

QD = 0.02 – 1.8PG + 0.69PO

15.90 + 0.72PG + 0.05(70.00) = 0.02 – 1.8PG + 0.69(70.00)

19.4 + 0.72 PG= 48.32-1.8PG

PG(0.72+1.8)=48.32-19.4

PG= 28.92/2.52

PG= $11.48

QS=QD= 15.90+0.72(11.48)+0.05(70.00)

QS=QD= 27.66

What would be the deadweight loss if the price of natural gas were regulated to be $4.00? The deadweight loss would be $___ billion. (Round answer to two decimal places)

If PG is $4.00

The quantity supplies will be less than the quantity demanded. The quantity supplied will be the quantity sold in the market.

QS=  15.90+0.72(4)+0.05(70.00)

QS= 22.28

To find the deadweight loss we must evaluate the quantity supplied in the demand curve:

22.28 = 0.02 – 1.8PG + 0.69(70.00)

1.8PG= 48.32-22.28

PG= 26.04/1.8

PG= 14.47

And now we calculate the area shown in the figure attached:

Base: 14.47-4= 10.47

Height: 27.66-22.28= 5.38

Deadweight loss: (10.47*5.38)/2

Deadweight loss: 28.1643

The deadweight loss would be $28.16 billion.