Question

1. The demand curve for petroleum product is downward sloping and linear in the form of P=a+bQ. In your opinion is b>0 or <0?. What in your opinion is the relationship between MR and Q? Can you show mathematically, the relationship between P,MC and Elasticity of Demand?

Answer 1

Demand curve is given by P=a+bQ, According to a law of demand as price increases , quantity demand decreases and as price decreases quantity demand increases. Hence there is inverse relationship between quantity demand and price. Hence this implies that in P=a+bQ, b must be negative.

MR = d(TR)/dQ and TR = Total revenue = PQ

=> MR = d(Q(a+bQ))/dQ = = a + 2bQ , where b is negative

MR = d(PQ)/dQ

=> MR = Q*dP/dQ + P

=> MR = P((Q/P)(dP/dQ) + 1)

=> MR = P(1 + 1/e)-----------------Relation between MR, P and elasticity of demand.

where e = elasticity of demand

Also According to profit maximizing condition a firm produces that quantity at which MR = MC

Hence We get MC = MR = P(1 + 1/e) => MC = P(1 + 1/e) -------------Relation between MC , P and elasticity of demand