Q. The example uses the following data for 2007 : P G = wholesale price of natur
ID: 1146042 • Letter: Q
Question
Q. The example uses the following data for 2007 :
PG = wholesale price of natural gas ($ per 1000 cubic feet)
PO = average price of a barrel of crude oil = $50,
Production and consumption of natural gas were 23 trillion cubic feet,
Supply of Natural Gas (trillion of cubic feet): QS = 15.90 + 0.72PG + 0.05PO
Demand for Natural Gas (trillion of cubic feet) QD = 0.02 – 1.8 PG + 0.69PO
a. Find the equilibrium price for natural gas
b. Suppose the regulated price of gas were $7.00 per thousand cubic feet instead of $3.00. How much excess demand or supply would there have been?
b. Suppose the market for natural gas remained unregulated. If the price of oil increased from $50 to $100, calculate the cross- price elasticity of natural gas with respect to crude oil.
Explanation / Answer
(a)
PO = $50
QS = 15.90 + 0.72PG + 0.05PO
QS = 15.90 + 0.72PG + (0.05 * 50) = 15.90 + 0.72PG + 2.5 = 18.4 + 0.72PG
QD = 0.02 - 1.8PG + 0.69PO =
QD = 0.02 - 1.8PG + (0.69*50) = 0.02 - 1.8PG + 34.5 = 34.52 - 1.8PG
At equilibrium,
QD = QS
34.52 - 1.8PG = 18.4 + 0.72PG
0.72PG + 1.8PG = 34.52 - 18.4
2.52PG = 16.12
PG = 6.396 or 6.4
PG = 6.4
The equilibrium price for natural gas is $6.4 per 1,000 cubic feet.
(b)
Regulated price = $7 per 1,000 cubic feet
Quantity supplied at regulated price -
QS = 18.4 + 0.72PG = 18.4 + (0.72 * 7) = 23.44
Quantity demanded at regulated price -
QD = 34.52 - 1.8PG = 34.52 - (1.8 * 7) = 21.92
At regulated price, quantity supplied is greater than the quantity demanded
So, there is excess supply.
Excess supply = QS - QD = 23.44 - 21.92 = 1.52
Thus, there have been excess supply of 1.52 trillion of cubic feet at the regulated price.
(c)
Price of oil has increased from $50 to $100
New PO = $100
QS = 15.90 + 0.72PG + 0.05PO
QS = 15.90 + 0.72PG + (0.05 * 100) = 15.90 + 0.72PG + 5 = 20.9 + 0.72PG
QD = 0.02 - 1.8PG + 0.69PO
QD = 0.02 - 1.8PG + (0.69*100) = 0.02 - 1.8PG + 69 = 69.02 - 1.8PG
At equilibrium,
QD = QS
69.02 - 1.8PG = 20.9 + 0.72PG
0.72PG + 1.8PG = 69.02 - 20.9
2.52PG = 48.12
PG = 19.1
The new equilibrium price for natural gas is $19.1 per 1,000 cubic feet.
New equilibrium quantity = 20.9 + 0.72PG = 20.9 + (0.72 * 19.1) = 20.9 + 13.75 = 34.65
Increase in quantity demanded of natural gas = New equilibrium quantity - old equilibrium quantity
Increase in quantity demanded of natural gas = 34.65 - 23 = 11.65
Percentage increase in quantity demanded of natural gas = (Increase in quantity demanded of natural gas/old equilibrium quantity) * 100
Percentage increase in quantity demanded of natural gas = (11.65/23) * 100 = 50.65%
Increase in price of oil = $100 - $50 = 50
Percentage increase in price of oil = (Increase in price of oil/Old price) * 100 = (50/50) * 100 = 100%
Calculate the cross- price elasticity of natural gas with respect to crude oil -
Cross-price elasticity = % change in quantity demanded of natural gas/% change in price of oil
Cross-price elasticity = 50.65/100 = 0.5065 or 0.51
The cross-price elasticity of natural gas with respect to crude oil is 0.51.
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