The XYZ Corporation provides accounting services to a wide variety of customers.
ID: 1202076 • 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:
A) 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?
B) Calculate the consumer surplus and producer surplus if XYZ charges a uniform price for its services.
C) 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?
D) Calculate the consumer surplus and producer surplus if XYZ can perfectly price discriminate.
Explanation / Answer
Equilibrium, MR = MC
10,000 – 20Q = 5Q. => Q = 10,000 / 25
Q = 400
A) P = 10,000 – 10Q
Plugging Q = 400, P = 6000
b)HIghest Willingness to pay of consumer at Q = 0 is 10.000
Consumer Surplus is area of triangle whosse base = Q and Length = Difference in WTP and Price which is 10000-6000 = 4000
CS = 1/2 x 4000 x 400 =) 800000
Producer Surplus is area of rectangle plus area of traingle
Rectangle = Lx B where L = difference in Price and MR and B = Q
MR at 400 = 10,000 – 20Q => 2000
L = 6000 - 2000 = 4000
Area of Rectangle = 4000 x 400 =1600,000
Area of triangle = 1/2 x MR x Q => 1/2 x 2000x400 => 400,000
Producer Surplus = 1600,000 + 400,000 => 2,000,000
c) Lowest price charged will be equal to MR as in case of perfect competition = 2000 and Q will remain same as 600
d) Consumer Surplus = Area of triangle whose base = Q and Length = WTP - MR (10,000 - 2000= 8000)
CS = 1/2 x 600 x 8000 = 2,400,000
Producer Surplus = Area of triangle whose base = Q and Length = MR
PS = 1/2 x 600 x 2000 = 600,000
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