The demand by senior citizens for showings at a local movie theater has a constant price elasticity equal to -4

In this case, we have the unusual situation where both marginal cost (MC) and the price elasticity of demand (for all three categories of users) are constant. For a constant elasticity demand curve, it can be shown that the following is true:

MR = P(1-1/E).

Since the profit maximizing condition is

MC = MR. we can write

MC = P(1-1/E).

Solving for P gives the following pricing equation for this situation

P = MC(E/(E-1)).

The theater should therefore charge the following prices.

Seniors: P = MC(E/(E-1)) = $2(4/(4-1)) = $2.67.

Students: P = MC(E/(E-1)) = $2(3/(3-1)) = $3.00.

All others: P= MC(E/(E-1)) = $2(2/(2-1)) = $4.00.