322 PART • Producers, Consumers, and Competitive Markets EX A M P L E PRICE CONTROLS AND NATURAL GAS SHORTAGES In Example 2.10 (page 59), we discussed the price controls that were imposed on natural gas markets during the 1970s, and we analyzed what would happen if the government were once again to regulate the wholesale price of natural gas Specifically, we saw that, in 2007, the free-market wholesale price of natural gas was about $6.40 per thousand cubic feet (mcf), and we calculated the quantities that would be supplied and demanded if the price were regulated to be no higher than $3.00 per mcf Now, equipped with the concepts of consumer surplus, producer surplus, and deadweight loss, we can calculate the welfare impact of this ceiling price Recall from Example 2.10 that we found that the supply and demand curves for natural gas could be approximated as follows: Supply: QS = 15.90 + 0.72PG + 0.05PO Demand: QD = 0.02 - 1.8PG + 0.69PO where QS and QD are the quantities supplied and demanded, each measured in trillion cubic feet (Tcf), PG is the price of natural gas in dollars per thousand cubic feet ($/mcf), and PO is the price of oil in dollars per barrel ($/b) As you can verify by setting QS equal to QD and using a price of oil of $50 per barrel, the equilibrium free market price and quantity are $6.40 per mcf and 23 Tcf, respectively Under the hypothetical regulations, however, the maximum allowable price was $3.00 per mcf, which implies a supply of 20.6 Tcf and a demand of 29.1 Tcf Figure 9.4 shows these supply and demand curves and compares the free market and regulated prices Rectangle A and triangles B and C measure the changes in consumer and producer surplus resulting from price controls By calculating the areas of the rectangle and triangles, we can determine the gains and losses from controls To the calculations, first note that Tcf is equal to billion mcf (We must put the quantities and prices in common units.) Also, by substituting the quantity 20.6 Tcf into the equation for the demand curve, we can determine that the vertical line at 20.6 Tcf intersects the demand curve at a price of $7.73 per mcf Then we can calculate the areas as follows: A = (20.6 billion mcf ) * ($3.40/mcf) = $70.04 billion B = (1/2) * (2.4 billion mcf) * ($1.33/mcf ) = $1.60 billion C = (1/2) * (2.4 billion mcf ) * ($3.40/mcf ) = $4.08 billion (The area of a triangle is one-half the product of its altitude and its base.) The annual change in consumer surplus that would result from these hypothetical price controls would therefore be A - B = 70.04 - 1.60 = $68.44 billion The change in producer surplus would be -A - C = -70.04 - 4.08 = -$74.12 billion And finally, the annual deadweight loss