Question

Suppose that the short-run world demand and supply elasticities for crude oil are -0.076 and 0.088, respectively. The current price per barrel is $30 and the short-run equilibrium quantity is 23.84 billion barrels per year. Derive the linear demand and supply equations. Also verify your answers.

Answer 1

Demand elasticity Ed = -0.076

Supply elasticity Es = 0.088

Equilibrium price P = 30

Equilibrium quantity Q = 23.84 billion barrels per year

Finding the demand equation:

$E_d = \frac{dQ}{dP} \times \frac{P}{Q} \\ \frac{dP}{dQ} = \frac{1}{E_d} \times \frac{P}{Q} \\ = \frac{1}{-0.076} \times \frac{30}{23.84} = -16.558$

Slope of demand = -16.558

The demand equation:

P = a + bQ

a = intercept

b = slope

b = -16.558

P = 30

Q = 23.84

$30 = a + (-16.558) \times 23.84 \\ a = 424.743$

The demand equation:

P = 424.743 - 16.558Q

Finding supply equation:

$E_s = \frac{dQ}{dP} \times \frac{P}{Q} \\ \frac{dP}{dQ} = \frac{1}{E_s} \times \frac{P}{Q} \\ = \frac{1}{0.088} \times \frac{30}{23.84} \\ = 14.3$

The supply equation:

P = c + dQ

c = intercept

d = slope

d = 14.3

$30 = c + 14.3 \times 23.84 \\ 30 = c + 340.192 \\ c = -310.192$

The supply equation:

P = -310.192 + 14.3Q