The BCY Corporation provides accounting services to a wide variety of customers,
ID: 1120362 • Letter: T
Question
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. 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. 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. 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?
Please show ALL work for part c) I have asked this question 3 times and every expert has given me a different answer for part c) please let me know if you are 100% sure your answer to part c) is correct. Thank you very much!
Explanation / Answer
a) MR = 10000 - 20Q and MC = 5Q
10000 - 20Q =5Q
Q = 400
and P = 10000 - 10 *400 = 10000 - 4000 = $6000
COnsumer surplus = 1/2 * (10000 - 6000) * 400
CS = $800000
b) the first degree price discrimination would set the output where p is equal to MC
so ,
10000 - 10Q = 5Q
Q = 666
P = 10000 - 10*666 = $3340
C ) Total profit is out total revenue - TC
profit = (3340*666 ) - ( 5*666)
profit = 2224440 - 3330 = $2221110
CS from perfect price = 1/2 * (10000 - 3340) * 666
CS = $2217780
CS captured = ( 2217780 -800000)
CS = $1417780
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