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 short run equilibrium quantity is 23.84 billion barrels per year. derive the linear demand and supply equations.

The linear demand equation is; Qd=25.65 - 0.0604P

The linear supply equation is; Qs = 0.07P + 21.73

Step-by-step explanation

The short run world demand elasticity for crude oil which is -0.076 is given by the formula;

The short run world demand elasticity for crude oil = (dQd/dP)*P/Q, where P=$30 and Q=23.84 billion.

(dQd/dP)*30/23.84 = -0.076

(dQd/dP) = -0.076*23.84/30

(dQ/dP) = -0.0604.

The slope of the linear demand equation is given by dP/dQ;

but dQ/dP =  -0.0604.

dP/dQ = 1/ -0.0604 = -16.56

Slope = (P-30)/(Q-23.84)

-16.56 = (P-30)/(Q-23.84)

-16.56*(Q-23.84) = P-30

Q-23.84 = 1.8116-0.0604P

Q=25.65 - 0.0604P, this is the  linear demand equation.

The short run world supply elasticity for crude oil = (dQs/dP)*P/Q, where P=$30 and Q=23.84 billion.

(dQs/dP)*30/23.84 = 0.088

(dQs/dP) = 0.088*23.84/30

(dQs/dP) = 0.07

The supply curve slope = dP/dQs = 1/0.07 = 14.29

(30-P)/(23.84-Qs )= 14.29

30-P = 340.57 - 14.29Qs

0.07Qs=P+340.57-30

14.29Qs = P + 310.57

Qs = 0.07P + 21.73 , this is the linear supply equation.