7) [15pt] The BCY Corporation provides accounting services to a wide variety of

Question

7) [15pt] The BCY Corporation provides accounting services to a wide variety of customers, most of whom have had a business association with BCY for more than five years. BCY's demand and marginal revenue curves are:

P = 10,000 - 10Q

MR = 10,000 - 20Q.

BCY's marginal cost of service is:

MC = 5Q.

a. [5pt] If BCY charges a uniform price for a unit of accounting service, Q, what price must it charge per unit, and how many units must it produce per time period in order to maximize profit? Calculate the consumer surplus.

b. [4pt] If BCY could enforce first-degree price discrimination, what would be the lowest price that it would charge and how many units would it produce per time period?

c. [6pt] With perfect price discrimination and ignoring any fixed cost, what is total profit? How much additional consumer surplus is captured by switching from a uniform price to first-degree price discrimination?

Explanation / Answer

a). Solution :- The firm will maximize profits where marginal revenue (MR) equals to the marginal cost (MC).

Equating MC and MR in the given question,

5Q = 10000 - 20Q

5Q + 20Q = 10000

25Q = 10000

Q = 10000 / 25

Q = 400 units.

P = 10000 - 10 * 400 (Put the value of Q = 400 in the demand curve equation).

P = 10000 - 4000

P = $ 6000.

Consumer surplus = 0.50 * 400 * (10000 - 6000)

= 0.50 * 400 * 4000

= $ 800000.

Conclusion :-

b). Solution :- For the calculation of lowest price in the given question, Equate price (P) and marginal cost (MC).

10000 - 10Q = 5Q

10000 = 10Q + 5Q

10000 = 15Q

  Q = 10000 / 15

Q = 666.67

P = 10000 - 10 * 666.67 (Put the value of Q = 666.67 in the demand curve equation)

P = 10000 - 6666.70

P = $ 3333.33 (approx)

Conclusion :-

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