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). With a $70.00 price of oil per barrel, the free market price of gas would be $11.48 per thousand cubic foot. The deadweight loss would be $28.16 billion.

What price of oil would yield a free-market price of natural gas of $4.00? The free-market price of natural gas would be $4.00 if the price of oil were $___.

Explanation / Answer

QS = 15.90 + 0.72PG + 0.05PO

QD = 0.02 – 1.8PG + 0.69PO

Equating QS with QD:

15.90 + 0.72PG + 0.05PO = 0.02 – 1.8PG + 0.69PO

15.88 + 2.52PG = 0.64PO

If PG = 4.00:

15.88 + (2.52 x 4) = 0.64PO

Or, PO = 25.96 / 0.64 = $40.56

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