EC6150 PROBLEMS 1
EC6150 Managerial Economics: LP5 Chapter Problems
Jina Bouknight-King
National American University – Online
EC6150 PROBLEMS 2
Chapter 10: problems 3, 8,12 (pg. 429-430)
Q = 25 – 0.05P TC = 700 + 200Q
a. What will be the price and quantity if Bramwell wants to;
1. maximize profits?
Q = 25 – 0.05P P = (25−𝑄)
0.05 P = 500 – 20Q
Calculate total revenue by multiplying the price and quantity and calculate marginal
revenue as follows:
TR = P x Q TR = (500 – 22Q) Q TR = 500Q – 20𝑄2 TR = 500 – 40Q
Calculate marginal cost as follows:
TC = 700 + 200Q MC = 200
Using the profit maximizing condition calculate Q as follows:
MR = MC
500 – 40Q = 200
40Q = 200-500
Q = 7.5
Substitute the values of Q in the given demand function and solve for P as follows:
Q = 25 – 0.05P
7.5 = 25 – 0.05P
0.05P = 25 – 7.5
P = 350
So if the Bramwell company wants to maximize profits, then the price would be P =
350, and the quantity would also be Q = 7.5.
2. Maximize revenue?
First, find the average revenue by dividing the by Q as follows:
TR = 500Q – 20𝑄2 AR = 500 – 20Q
Calculate average cost by dividing TC by Q as follows:
TR = 700 + 200Q
AC = 700
𝑄 + 200
EC6150 PROBLEMS 3
Using the revenue maximizing condition, the price and quantity are then calculated as follows:
AR = AC
500 – 20Q = 700
𝑄 + 200
500Q -20𝑄2 = 700 + 200Q
20𝑄2 – 300Q + 700 = 0
Q = 12.105
Substitute the value of Q in the demand function and solve for P as follow:
P = 500 – 20Q
= 500 – 20 (12.5)
= 500 – 250
= 250
Therefore, the revenue maximizing price is P=250 and the quantity is Q =12.105
3. maximize revenue but require the profit to be a minimum of $300? P=350 and Q = 7.5
