The XYZ Corporation provides accounting services to a wide variety of customers.
ID: 1203953 • Letter: T
Question
The XYZ Corporation provides accounting services to a wide variety of customers. XYZ's demand and marginal revenue functions are P = 10,000 - 10Q and MR = 10,000 - 20Q. XYZ's marginal cost of providing its services is MC = 5Q. Answer the following questions: If XYZ charges a uniform price for its services, what price will it charge per unit of service and how many units of services will it produce to maximize profit? Calculate the consumer surplus and producer surplus if XYZ charges a uniform price for its services. If XYZ could perfectly price discriminate, what is the lowest price it would charge for its service and how many units of services would it produce to maximize profit? Calculate the consumer surplus and producer surplus if XYZ can perfectly price discriminate.Explanation / Answer
(a) Profit is maximized by equating MR with MC:
10,000 - 20Q = 5Q
25Q = 10,000
Q = 400
P = 10,000 - (10 x 400) = 10,000 - 4,000 = 6,000
(b) Consumer surplus (CS) is area between demand curve & price.
From demand curve, when Q = 0, P = 10,000
CS = (1/2) x (10,000 - 4,000) x 400 = (1/2) x 6,000 x 400 = 1,200,000
Producer surplus (PS) is area between supply curve & price.
From MC (Supply) function, when Q = 0, P = 0
PS = (1/2) x (4,000 - 0) x 400 = 800,000
(c) With perfect price discrimination, the lowest price the firm could charge is ts MC. When P = MC,
10,000 - 10Q = 5Q
15Q = 10,000
Q = 666.7
P = 10,000 - (10 x 666.7) = 10,000 - 6,667 = 3,333
(d)
CS = (1/2) x (10,000 - 3,333) x 666.7 = (1/2) x 6,667 x 666.7 = 4,444,889
PS = (1/2) x (3,333 - 0) x 666.7 = 2,222,111
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