TaxAct has developed a iew tax preparation program It incurr

TaxAct has developed a iew tax preparation program. It incurred a substantial cost to develop the program Question 19 Not yet answered Points out of 1.00 P Flag question but that cost is sunk now. The only cost TaxAct will incur going forward is a cost of $40 per customer for copying and shipping the program. The demand for the new program is Q 50-0.25P, where Q is the number of copies of the program demanded and P is the price for the program. TaxAct is planning to sell its program for $120. Suppose instead it decided to set a price that would maximize the sum of its profits and the profits to its customers. How much would total ppofits (TaxAct plus its customers) increase if it charged this price instead of $120? of Select one: a. Zero b. $200 C. $400 d. $600 e. $800

Solution

Option (e).

When P = $120, Q = 50 - (0.25 x 120) = 50 - 30 = 20

From demand function, when Q = 0, P = 50 / 0.25 = $200 (Reservation price)

Customer profit = Area between demand curve and price = (1/2) x $(200 - 120) x 20 = 10 x $80 = $800

TaxAct profit = Area between supply curve (Marginal cost) and price = $(200 - 40) x 20 = 10 x $160 = $1,600

Total profit = $(800 + 1,600) = $2,400

The price that maximizes total profits is obtained by setting it equal to Marginal cost.

Q = 50 - 0.25P

0.25P = 50 - Q

P = 200 - 4Q

Equating P and MC,

200 - 4Q = 40

4Q = 160

Q = 40

P = MC = $40

Customer profit = (1/2) x $(200 - 40) x 40 = 20 x $160 = $3,200

TaxAct profit = $(40 - 40) x 40 = 0 [Since Price = MC, (P - MC) = 0]

Increase in profit = $3,200 - $2,400 = $800