Question

the Edmond Theatre is contemplating charging a different price for a ticket to an afternoon show than for the same film that evening. In adopting a price strategy, the Edmond must consider that fixed costs are 20$ per week and variable costs are .50$ per customer.

Pa = 8.5 - 0.4 Qa

Pb = 4.5 - 0.2 Qb

Calculate the Edmond's prices, output and profit, with and without price discrimination.

Answer 1

Here, total cost = 20$ + 0.50$q

Then, MC=0.50

Now, P_A =8.5-0.4Q_A is the demand for afternoon show

Hence, MR=8.5-0.8Q_A

For equilibrium, MR=MC

or, 8.5-0.8Q_A = 0.50

or, 0.8Q_A = 8

or, Q_A = 10 and P_A = 8.5-0.4Q_A = 8.5-0.4*10 = $4.5

Similarly , P_B = 4.5 - 0.2Q_B is the demand for night show

Hence, MR = 4.5- 0.4Q_B

For equilibrium, MR=MC

or, 4.5-0.4Q_B = 0.50

or, 0.4Q_B = 4

or, Q_B = 10 and P_B = 4.5-0.2Q_B = 4.5-0.2*10 = $2.5

Hence, with price discrimination Edmond charges $4.5 for afternoon show at an output equal to 10 and $2.5 for evening show at an output equal to 10. Profit = 10*4.5+10*2.5 - 0.50*20 = $60

Without price discrimination , Edmond will charge same price for both shows.

Total demand Q_A+Q_B =20

or, (8.5-P)/0.4 + (4.5-P)/0.2 =20

or, 8.5-P+9-2P = 20*0.4

or, 3P = 17.5-8

or, P = 9.5/3 = 3.166

Here, profit = 3.166 *20 - 0.50*20 = $53.32