Question

For each of the following demand functions, assume that the price p must be greater than 0 and less than or equal to 100. For each demand function, determine all prices at which demand is elastic and all prices at which demand is inelastic. For each demand function, what price would you recommend the business use?

• q(p)=100−p

• q(p) = 216 + 100 p

Answer 1

WHAT PRICE SHOULD WE PREFER IS THAT PRICE WHICH maximizes PROFIT which is always greater than or equal to the price which maximizes revenue.

revenue= P*Q = 100P - P2

Ist order condition

d(PQ)/dP = 100 - 2P = 0

P = 50

second order condition (differntiation of Ist order condition )

= -2 (< 0 , so p= 50 maximize revenue ).

as in our demand curve clearly we can see from the above figure that elasticity is less than 1 ie inelastic for all prices.

WHAT PRICE SHOULD WE PREFER IS THAT PRICE WHICH maximizes PROFIT which is always greater than or equal to the price which maximizes revenue.

revenue= P*Q = 216P + 100P2

Ist order condition

d(PQ)/dP = 216 + 200P = 0

P = -216/200 = - 1.08

second order condition (differntiation of Ist order condition )

= 200 (> 0 , so p= -1.08 will not maximize revenue and it is not practically possible ).

so price = 0