3. Example 2.10 on pages 59 and 60 of the textbook 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
where Q = quantity, PG = price of natural gas, and PO = price of oil. Also, determine the free-market price of natural gas when the price of oil is $50.
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 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?