We calculated the gains and losses from price controls on natural gas and found

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 $___ per thousand cubic foot. (Round response to two decimal places).

Explanation / Answer

QS = 15.90 + 0.72PG + 0.05PO

When PO = 50,

QS = 15.90 + 0.72PG + 0.05 x 50 = 15.90 + 0.72PG + 2.5

QS = 18.4 + 0.72PG

QD = 0.02 – 1.8PG + 0.69PO

When PO = 50,

QD = 0.02 – 1.8PG + 0.69 x 50 = 0.02 - 1.8PG + 34.5

QD = 34.52 - 1.8PG

Equating QD with QS,

34.52 - 1.8PG = 18.4 + 0.72PG

2.52PG = 16.12

PG = 6.40

Q = 34.52 - (1.8 x 6.40) = 23

If PO = 70, then

QS = 15.90 + 0.72PG + (0.05 x 70) = 15.90 + 0.72PG +3.5

QS = 19.4 + 0.72PG

QD = 0.02 - 1.8PG + (0.69 x 70) = 0.22 - 1.8PG + 48.3

QD = 48.32 - 1.8PG

Equating QD & QS:

48.32 - 1.8PG = 19.4 + 0.72PG

28.92 = 2.52PG

PG = 11.48 [Free market price of gas]

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