Managerial Economics, 7e (Keat)
(Online Only) Review of Mathematical Concepts Used in Managerial Economics
Analytical Questions
1) The demand curve is given by:
QD = 5000 - 10 P
Find equations for:
a. Total revenue
b. Marginal revenue
Answer:
a. TR = P ∗ Q = (500 - 1/10 Q)Q = 500Q - 1/10 Q2
b. MR = 500 - 1/5Q
2) The demand curve is given by:
QD = 5000 - 10P
Find the price and quantity at which total revenue is maximized and the maximum
revenue.
Answer:
MR = 500 - 1/5 Q
0 = 500 - 1/5 Q
,Q = 2500
P = 250
TR = $625,000
3) For each of the following sets of supply and demand curves, calculate equilibrium
price and quantity.
a. QD = 1000 - P; QS = P
b. QD = 1500 - 2P; QS = 100 + 2P
c. QD = 2000 - 3P; QS = -300 + 3P
Answer:
a. Q = 500, P = 500
b. Q = 800, P = 350
c. Q = 850, P = 383.33
,4) For each of the following cost functions, find MC, AC, and AVC.
a. TC = 40,000 + 20 Q
b. TC = 1000 + 2Q + 0.1 Q2
Answer:
a. MC = 20
AC = (40,000/Q) + 20
AVC = 20
b. MC = 2 + 0.2Q
AC = (1000/Q) + 2 + 0.1Q
AVC = 2 + 0.1Q
5) For each of the following cost functions, if possible, find minimum AC and minimum
AVC.
a. TC = 40,000 + 20 Q
b. TC = 1000 + 2Q + 0.1 Q2
Answer:
a. Set MC = AC.
20 = (40,000/Q) + 20
In this case, AC is decreasing everywhere, and thus there is no minimum average cost
(although it will approach $20).
Set MC = AVC.
20 = 20
Q = 0, and at that point, AVC = $20.
b. Set MC = AC.
2 + 0.2Q = (1000/Q) + 2 + 0.1Q
, Q = 100, and at that point, AC = $22.
Set MC = AVC.
2 + 0.2Q = 2 + 0.1Q
Q = 0, and at that point, AVC = $2.
(Online Only) Review of Mathematical Concepts Used in Managerial Economics
Analytical Questions
1) The demand curve is given by:
QD = 5000 - 10 P
Find equations for:
a. Total revenue
b. Marginal revenue
Answer:
a. TR = P ∗ Q = (500 - 1/10 Q)Q = 500Q - 1/10 Q2
b. MR = 500 - 1/5Q
2) The demand curve is given by:
QD = 5000 - 10P
Find the price and quantity at which total revenue is maximized and the maximum
revenue.
Answer:
MR = 500 - 1/5 Q
0 = 500 - 1/5 Q
,Q = 2500
P = 250
TR = $625,000
3) For each of the following sets of supply and demand curves, calculate equilibrium
price and quantity.
a. QD = 1000 - P; QS = P
b. QD = 1500 - 2P; QS = 100 + 2P
c. QD = 2000 - 3P; QS = -300 + 3P
Answer:
a. Q = 500, P = 500
b. Q = 800, P = 350
c. Q = 850, P = 383.33
,4) For each of the following cost functions, find MC, AC, and AVC.
a. TC = 40,000 + 20 Q
b. TC = 1000 + 2Q + 0.1 Q2
Answer:
a. MC = 20
AC = (40,000/Q) + 20
AVC = 20
b. MC = 2 + 0.2Q
AC = (1000/Q) + 2 + 0.1Q
AVC = 2 + 0.1Q
5) For each of the following cost functions, if possible, find minimum AC and minimum
AVC.
a. TC = 40,000 + 20 Q
b. TC = 1000 + 2Q + 0.1 Q2
Answer:
a. Set MC = AC.
20 = (40,000/Q) + 20
In this case, AC is decreasing everywhere, and thus there is no minimum average cost
(although it will approach $20).
Set MC = AVC.
20 = 20
Q = 0, and at that point, AVC = $20.
b. Set MC = AC.
2 + 0.2Q = (1000/Q) + 2 + 0.1Q
, Q = 100, and at that point, AC = $22.
Set MC = AVC.
2 + 0.2Q = 2 + 0.1Q
Q = 0, and at that point, AVC = $2.
