Answer to Question #236447 in Microeconomics for Ali Bilal

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

Linear demand function is given by  $Q_{d}$ = a – bP

In this case a is not given

P= 30

$Q_{d} ​$ =23.84

0.076 = b($\frac{30}{23.84}$ )

b= 0.06

23.84 = a - 0.06(30)

solving this we get a=25.64

Therefore Linear demand function $Q_{d} ​$ = 25.64 - 0.06p

Linear supply function is given by $Q_{s} ​$ = d + cP

$Q_{s}$ =23.84

0.088 = c( $\frac{30}{23.84}$ )

c=0.070

23.84 =d + 0.07(30)

solving this we get d=21.74

Therefore Linear supply function $Q_{s}$ = 21.74 +0.07p

Plugging in the values of price in each of the linear functions we get the same quantity demanded and supplied as 23.84.

Please note that equilibrium quantity in this case refers to the quantity supplied and quantity demanded