Question

Q. The example uses the following data for 2007 :

P_G = wholesale price of natural gas ($ per 1000 cubic feet)

P_O = 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 + 0.72P_G + 0.05P_O

Demand for Natural Gas (trillion of cubic feet) QD = 0.02 – 1.8 P_G + 0.69P_O

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.

Answer 1

(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.