Managerial Economics Homework
PART I: COST ANALYSIS
Please use the following information to answer questions 1 to 7.
The function (in $) is an estimate of the cost of producing Q units of output of a particular product: TC(Q)= 80 + 7Q.
1. What is the fixed cost of producing 10 units of output?
2. Is this a short-run or long-run cost function?
3. What is the variable cost of producing 10 units of output?
4. What is the average total cost of producing 10 units of output?
5. What is the marginal cost of producing the 10th unit of output?
6. What is the average variable cost of producing 10 units of output?
7. Compare the value of the marginal cost of producing 10th unit of output with the value of the average variable cost of producing 10 units of output. Can you infer from the comparison of these 2 values alone (i.e. without referring to the equations of MC and AVC) whether the average variable cost is increasing or decreasing? Or is this comparison insufficient to be able to draw a conclusion? Explain INTUITIVELY, not mathematically (WITHOUT using any of the equations).
8. Suppose marginal cost is flat (i.e. a constant k>0) over a specific output range (say between Q=10 and Q=20), then;
a) marginal cost must equal average total cost over that range
b) marginal cost must equal average variable cost over that range c) total cost must be increasing over that range
d) a and c
e) b and c
f) none of the above
PART II: PERFECT COMPETITION
The following information applies to the next 8 questions: Consider the following information on production capacities for the market for a (commodity) metal and its associated marginal costs (all other costs have been sunk). Please select the correct answer and then explain graphically. Graphs must be accurate and must not be drawn in pen or pencil.
|
Country
|
Annual Production (t)
|
Marginal Cost ($/t)
|
|
Argentina
|
2500
|
25
|
|
Brazil
|
3000
|
30
|
|
Canada
|
2000
|
70
|
|
Congo
|
2000
|
45
|
|
Indonesia
|
1000
|
20
|
|
Russia
|
3000
|
50
|
|
South Africa
|
2000
|
40
|
|
Zimbabwe
|
500
|
45
|
Global annual demand (in t) is given by: QD = 10000 - 50P
9. What is the equilibrium price in this perfectly competitive market?
a) $25/t
b) $30/t
c) $35/t
d) $40/t
e) $45/t
f) $50/t
g) $55/t
h) None of the above
10. How much of the global metal supply will be produced in Africa?
a) Nothing
b) More than 0t but less than 2000t
c) 2000t
d) More than 2000t but less than 4000t
e) 4000t
f) 4500t
11. Suppose the South American countries manage to improve their production processes resulting in a 20% decrease in marginal cost. What will happen to the world equilibrium price?
a) Nothing
b) It will drop by 5%
c) It will drop by 10%
d) It will drop by 20%
e) None of the above
12. Suppose that in addition to all of the above information, Brazil experiences a mining disaster, effectively eliminating 20% of its mining capacity (from 3000t to 2400t initially, but at the 20% lower marginal cost). What will happen to the world equilibrium price?
a) It will be $35/t
b) It will be $40/t
c) It will be $42/t
d) It will be $45/t
e) It will be $50/t
f) It will be $53/t
g) None of the above
Suppose that all of the above information holds with the exception of the information on global demand for the metal. Suppose global demand has increased to QD = 16000 - 40P.
13. What will now happen to the global equilibrium price?
a) It will eventually reach $40/t
b) It will eventually reach $45/t
c) It will eventually reach $50/t
d) It will eventually reach $55/t
e) It will eventually reach $60/t
f) It will eventually reach $65/t
g) It will eventually reach $70/t
h) It will eventually exceed $70/t
14. How much of the metal will now be produced worldwide?
a) 13000t
b) 13200t
c) 14000t
d) 14200t
e) 14400t
f) 14800t
g) 15000t
h) None of the above
The following information applies to the two questions below: You are a manager in a perfectly competitive market. The price in your market is $22. Your total costs are C(Q) = 40 + 2Q + 2Q2.
15. What level of output will you produce in the short-run to maximize profits?
16. How much profit will you make?
PART III: MONOPOLY
The following information applies to the two questions below: You are a strategy consultant to PepsiCo and have estimated that the daily demand for Pepsi-Cola is given by: QP = 10 - 3PP + A + PC + 4PG, where;
QP = the daily volume of Pepsi-Cola sold (in liters)
PP = the price per liter of Pepsi-Cola (in $)
A = the level of advertising of (in $)
PC = the price per liter of Coca-Cola (in $)
PG = the price per liter of Ginger Ale (in $)
One can rewrite the above equation as PP = (10 + 4PG + PC + A - QP)/3 to obtain a typical demand function.
Suppose that the marginal cost of a liter of Pepsi-Cola is constant at $1.
Suppose that currently PP = 4, PC = 2 and PG = 3 and that A=3 and suppose that historically neither Ginger Ale nor Coca-Cola have followed Pepsi-Cola's price hikes or price cuts.
17. What price would you recommend to Pepsi-Cola if its goal is to maximize profits, knowing that Pepsi-Cola has decided to keep advertising expenditures at A=3?
18. What price would you recommend to Pepsi-Cola if its goal is to maximize revenues, knowing that Pepsi-Cola has decided to keep advertising expenditures at A=3?