Question

The current world production of oil is 350 million barrels per day and the current world price of oil is N$850 per barrel. The price elasticity of demand (ε) is -0.3 and the elasticity of supply (η) is 0.1. Shiwa Investment is planning to enter the world oil market with a daily production of 13 million barrels of oil per day. For simplicity, assume that the supply and demand curves are linear

Answer 1

the question: Calculate market price and total supply of oil after Shiwa investment has enter the world oil market and explain why the total supply of oil increases with less than 13 million.

solution

We need to derive the demand and supply functions first, then show the effects of an increase in supply when the new seller enters the market.

(i) Linear demand function: $Q = a - bP$

When $P = 850, Q = 350$

$350 = a - 850b..........(1)$

Also,

Elasticity of demand$= \frac{dQ}{dP} \times \frac{P}{Q} = - 0.3$

$- b \times \frac{850} { 350} = - 0.3$

$b x 2.43 = 0.3$

$b = 0.12$

$a = 350 + 850b \space [from (1)]\space = 350 + 850 \times 0.12$

$= 350 + 102 = 452$

So,

Demand function: $Q = 452 - 0.12P$

(ii) Linear supply function: $Q = c + dP$

When$P = 850, Q = 350$

$350 = c + 850d..........(2)$

Also,

Elasticity of supply $= \frac{dQ}{dP} \times \frac{P}{Q} = 0.1$

$d \times\frac{P}{Q} = 0.1$

$d \times \frac{850}{ 350} = 0.1$

$d = 0.04$

$c = 350 - 850d\space [from (2)]\space = 350 - (850 \times 0.04)$

$350 - 34 = 316$

So,

Supply function: $Q = 316 + 0.04P$

(iii) In initial equilibrium, Demand = Supply

$452 - 0.12P = 316 + 0.04P$

$0.16P = 136$

$P = \$850$

$Q = 452 - (0.12 \times 850) = 452 - 102 = 350$

After Shiwa enters market, the market supply increases by 13 million. New supply function is

$Q = (316 + 0.04P) + 13 = 329 + 0.04P$

Equating Demand and New supply,

$452 - 0.12P = 329 + 0.04P$

$0.16P = 123$

$P = \$768.75$

$Q = 452 - (0.12 x 768.75) = 452 - 92.25 = 359.75$

Increase in quantity $= 359.75 - 350 = 9.75$

So, increase in equilibrium quantity is lower than 13 million. The reason is that demand is not perfectly elastic. With an upward rising demand curve, the increase in equilibrium quantity is less than the increase in output produced by the additional seller.