11. Refer to Example 2.10 (page 59), which analyzes the effects of price controls on natural gas. a. Using the data in the example, show that the fol- lowing supply and demand curves describe the market for natural gas in EGGS200?: Supply: Q = 15.90 + 03213,; + 0.05Pg Demand: Q = 0.02 1.813,; + 0.69130 Also, verify that if the price of oil is $50, these curves imply a free-market price of $6.40 for natural gas. b. Suppose the regulated price of gas were $4.50 per thousand cubic feet instead of $3.00. How much excess demand would there have been? c. Suppose that the market for natural gas remained unregulated. If the price of oil had increased from $50 to $100, what would have happened to the free- market price of natural gas? EXAMPLE 2. l 0 PRICE CONTROLS AND NATURAL GAS SHORTAGES In 1954, the federal government began regulat- ing the wellhead price of natural gas. Initially the controls were not binding; the ceiling prices were above those that cleared the market. But in about 1962, when these ceiling prices did become binding, excess demand for natural gas developed and slowly began to grow. In the 1970s, this excess demand, spurred by higher oil prices, became severe and led to wide- spread curtailments. Soon ceiling prices were far below prices that would have prevailed in a free market.22 Today, producers and industrial consumers of natural gas, oil, and other commodities are con- cerned that the government might respond, once again, with price controls if prices rise sharply. Let's calculate the likely impact of price controls on natu- ral gas, based on market conditions in 2007. Figure 2.25 shows the wholesale price of natural gas, in both nominal and real (2000 dollars) terms, from 1950 through 2007. The following numbers describe the U.S. market in 2007: o The (free-market) wholesale price of natural gas was $6.40 per mcf [thousand cubic feet); 0 Production and consumption of gas were 23 ch {trillion cubic feet); . The average price of crude oil (which affects the supply and demand for natural gas) was about $50 per barrel. A reasonable estimate for the price elastic- ity of supply is 0.2. Higher oil prices also lead to more natural gas production because oil and gas are often discovered and produced together; an estimate of the crossprice elasticity of supply is 0.1. As for demand, the price elasticity is about -0.5, and the cross-price elasticity with respect to oil price is about 1.5. You can verify that the fol lowing linear supply and demand curves fit these numbers: Supply: C1 = 15.90 + 0.72PG + 0.05P0 Demand: 0 = 0.02 1.8a,3 + 0.69P0