Refer to Example 2.10, which analyzes the effects of price controls on natural gas.
a. Using the data in the example, show that the following supply and demand curves describe the market for natural gas in 2005–2007:
Supply: Q  15.90  0.72PG  0.05PO
Demand: Q  0.02  1.8PG  0.69PO
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?