Answer to Question #236653 in Microeconomics for Sherry

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 answer

Answer 1

Linear demand equation is: $Q = a - bP$

Elasticity of demand $= \frac{dQ}{dP} \times \frac{P}{Q} = -b \times \frac{P}{Q}$

When

$P = 30 \\ Q = 23.84 -0.076 = -b \times \frac{30}{23.84} \\ b = 0.06$

From demand function,

$23.84 = a - (0.06 \times 30) \\ 23.84 = a - 1.8 \\ a = 25.64$

Linear demand equation: $Q = 25.64 - 0.06P$

Linear supply equation: $Q = c + dP$

Elasticity of supply $= \frac{dQ}{dP} \times \frac{P}{Q} = d \times \frac{P}{Q}$

When

$P = 30 \\ Q = 23.84 \\ 0.088 = d \times \frac{30}{23.84} \\ b = 0.07$

From supply function,

$23.84 = c + (0.07 \times 30) \\ 23.84 = c + 2.1 \\ c = 21.74$

Linear demand equation: $Q = 21.74 + 0.07P$