Question

If P=24-Q what price maximizes total revenue? (Can you solve using the point elasticity formula?)

Enter as a value.

Answer 1

Answer

Demand is given by :

P = 24 - Q.=> Q = 24 - P => dQ/dP = -1

Total Revenue maximizes when Point elasticity of demand = -1 (i.e. demand is unitary elastic)

Point elasticity of demand = = (dQ/dP)(P/Q) ans want Point elasticity of demand = -1

=> (dQ/dP)(P/Q) = -1 => -1*(P/Q) = -1 => P = Q

=> P = 24 - P => 2P = 24 => P = 12.

Hence Price that maximizes Total revenue is P = 12.

Note ;

Total Revenue(TR) = PQ = (24 - Q)*Q

First order condition :

d(TR)/dQ = 0 => 24 - 2Q = 0 => Q = 12

Hence P = 24 - Q = 24 - 12 = 24.

Hence P = 12 will maximize the revenue (same as above)