Ace Your Exams with the [Managerial Economics,Keat,7e] Test Bank

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.