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

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.

Answer 1

we derive demand and supply function then show the effects of increase in supply as shown in the following steps:

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

When $P = 850, Q = 350$

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

Also,

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

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

$b \times2.43 = 0.3$

$b = 0.12$

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

$= 350 + 102 = 452$

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.