Question

Example 2.9 (page 76) analyzes the world oil market. Using the data given in that example:

a. Show that the short-run demand and competitive supply curves are indeed given by

D = 36.75 - 0.035P

SC= 21.85 + 0.023P

b. Show that the long-run demand and competitive supply curves are indeed given by

D = 45.5 - 0.210P

SC= 16.1 + 0.138P

c. In Example 2.9 we examined the impact on price of a disruption of oil from Saudi Arabia. Suppose that instead of a decline in supply, OPEC production increases by 2 billion barrels per year (bb/yr) because the Saudis open large new oil fields. Calculate the effect of this increase in production on the price of oil in both the short run and the long run.

Short answer

1. Yes, the short-run demand curve is D = 36.75 – 0.035P, and the supply curve is S = 21.85 + 0.023P.

2. Yes, the long-run demand curve is D = 45.5 – 0.210P, and the supply curve is S = 16.1 + 0.138P.

3. The price fall in the short run will be by $34.48, and in the long run, by $40.23.

Step-by-step solution

Explanation for part (a)

Let the demand curve be Q = a + bP, where b is the slope of the demand curve; a is the intercept of the curve. The price is $50, the quantity demand is 35 bb/yr, and the elasticity of demand is -0.05. The elasticity of demand will be:

$$\begin{gathered} E_D=\frac{△Q}{△P}\times \frac{P}{Q} \\ -0.05=\frac{△Q}{△P}\times \frac{50}{35} \\ \frac{△Q}{△P}=\frac{-0.05\times 35}{50} \\ b=-0.035 \end{gathered}$$

The value of a is calculated below:

35 = a -0.035(50)

a = 35 + 1.75

= 36.75

The demand curve will be Q = 36.75 – 0.035P.

Let the supply curve be Q = c + dP, where d is the slope of the supply curve, and c is the intercept of the curve. The price is $50, the quantity supply (non-OPEC) is 23 bb/yr, and the elasticity of demand is 0.05. The elasticity of supply will be:

role="math" localid="1643369777829" $$\begin{gathered} E_s=\frac{△Q}{△P}\times \frac{P}{Q} \\ 0.05=\frac{△Q}{△P}\times \frac{50}{23} \\ \frac{△Q}{△P}=\frac{0.05\times 23}{50} \\ b=0.023 \end{gathered}$$

The value of c is calculated below:

23 = c + 0.023(50)

c = 23 - 1.15

= 21.85

The supply curve will be Q = 21.85 – 0.023P.

Thus, the short-run demand and competitive supply curves are indeed given by D = 36.75 - 0.035P, and SC = 21.85 + 0.023P respectively.

Explanation for part (b)

Let the demand curve be Q = a + bP, where b is the slope of the demand curve, and a is the intercept of the curve. The price is $50, the quantity demand is 35 bb/yr, and the elasticity of demand is -0.30. The elasticity of demand will be:

$$\begin{gathered} E_D=\frac{△Q}{△P}\times \frac{P}{Q} \\ -0.30=\frac{△Q}{△P}\times \frac{50}{35} \\ \frac{△Q}{△P}=\frac{-0.30\times 35}{50} \\ b=-0.21 \end{gathered}$$

The value of a is calculated below:

35 = a -0.21(50)

a = 35 + 10.5

= 45.5

The demand curve will be Q = 45.5 – 0.210P.

Let the supply curve be Q = c + dP, where d is the slope of supply cure, i.e., rate of change in quantity by the change in price; c is the intercept of the curve. The price is $50, the quantity supply (non-OPEC) is 23 bb/yr, and the elasticity of demand is 0.30. The elasticity of supply will be:

$$\begin{gathered} E_s=\frac{△Q}{△P}\times \frac{P}{Q} \\ 0.30=\frac{△Q}{△P}\times \frac{50}{23} \\ \frac{△Q}{△P}=\frac{0.30\times 23}{50} \\ b=0.138 \end{gathered}$$

The value of c is calculated below:

23 = c + 0.138(50)

c = 23 - 6.9

= 16.1

The supply curve will be Q = 21.85 – 0.023P.

Thus, the long-run demand and competitive supply curves are indeed given by D = 45.5 - 0.210P, and SC = 16.1 + 0.138P respectively.

Explanation for part (c)

The OPEC’s supply increase by 2 bb/yr, i.e., the new OPEC’s supply will be 14 bb/yr (=12 + 2). The new short and long-run supply will be:

The short-run price and quantity are calculated below:

The price will be $15.52, and the quantity will be 36.21 bb/yr.

The long-run price and quantity are calculated below:

The price will be $9.77, and the quantity will be 43.45 bb/yr.

The price fall in the short run will be by $34.48 (=50 – 15.52), and in the long run, by $40.23 (=50 – 9.77).