Suppose the demand and supply equations of crude oil are given as follows:

 

The Case:

Pakistan is producing a very limited percentage of oil to meet the overall demand of the country. Indigenous oil production is constrained by technological, technical, and financial constraints. This necessitates the import of crude oil and other oil products in large quantities to meet a significant share of the total demand. Statistics identified that the import bill of oil grew by 95.9 percent to US$17.03 billion during July-April FY2022 as compared to US$8.69 billion during the corresponding period last year.

Suppose the demand and supply equations of crude oil are given as follows:

Qs = 250 + 0.30P

Qd =340 - 0.10P 

Requirement:

a) Find the equilibrium price and quantity of crude oil.

b)Find out the price elasticity of demand for crude oil at the equilibrium price and quantity.

c) If the government imposes a tax of Rs. 25/liter and the price becomes Rs. 250 per liter then calculate the quantity demanded and quantity supplied at the new price.

       

Solution

a) Find the equilibrium price and quantity of crude oil.

Solution:

Crude oil demand = Crude oil supply   

Qd=Qs

340 -0.10P = 250 + 0.30P

340- 250 = 0.3OP + 0.1OP

90 = 0.40P

90/0.40 = 0.40P/0.40

225=P

P=225

 

Crude oil demand = Qd = 340-0.10P

= 340 – 0.10(225)

=340 – 22.5

Qd=317.5

Crude oil Supply = Qs = 250 + 0.30P

= 250 + 0.30(225)

= 250 + 67.5

Qs =317.5

b) Find out the price elasticity of demand for crude oil at the equilibrium price and quantity.

Solution:

    Formula for Point Elasticity = E = (∆Q/ ∆P) * (P / Q)

=-0.10 *0.70

= -0.070

=-0.070 in elastic

= 340 – 0.10P

=-0.10

= (P/ Q)

=225/317.5

= .70 

c) If the government imposes a tax of Rs. 25/liter and the price becomes Rs. 250 per liter then calculate the quantity demanded and quantity supplied at the new price.

Crude oil demand = Qd= 340 -0.10P

   = 340 – 0.10(250)

   = 340 – 25

   =315

    So, the demand for crude oil decreases.

Crude oil supply =Qs = 250+0.3OP

                                     =250 +0.30(250)

                                     = 250 + 75

                                     =325

    So, the Supply of crude oil Increases.