DYNAMIC STRATEGIC PLANNING
MIDSEMESTER QUIZ October, 1998
NOTE CAREFULLY!
The questions on the quiz test different capabilities. Furthermore, each question generally proceeds from easier to more difficult concepts. Examinees should therefore allocate their time optimally, by responding first to the questions that are easiest, and setting aside until the end the questions which are more difficult for them.
For your guidance, the points associated with each question are marked in parentheses alongside the question. They are calibrated with the time it should take to answer the question  one point possible per minute.
The total number of points possible = 90
Name: _________________________________________
Question 
Section 
Maximum points 
Actual points 
1 
A 
3 

B 
3 


C 
3 


D 
3 


2 
A 
6 

B 
3 


C 
4 


D 
7 


E 
6 


F 
7 


3 
A 
4 

B 
6 


C 
4 


D 
2 


E 
5 


F 
8 


G 
10 


H 
6 


Total 

90 

QUESTION 1
Answer the following questions:
a) (3pts) Define the production function
b) (3pts) What is the difference between technical efficiency and economic efficiency?
c) (3pts) Define an isoquant
d) (3pts) Define the Internal Rate of Return  Is it always uniquely define?
QUESTION 2
Given the production function:
Z = X^{0.2} Y^{0.3}
Given the input cost function:
C = X + 0.2 Y^{0.5}
a) (6pts) What are the marginal products ?
b) (3pts) Are returns to scale increasing?
c) (4pts) What is the marginal rate of substitution at (X=1; Y=1)?
d) (7 pts) State the conditions for optimal design as they apply to this case.
e) (6pts)Write the equation defining the expansion path. Explain the meaning of the expansion path?
f) (7pts) Find the cost function and costeffectiveness function associated with this technology. Are there economies of scale?
QUESTION 3
As a junior consultant, you are advising a major oil company on how to develop a newly discovered oil field. According to geological experts, the capacity of this oil field is either 10M barrels or 5M barrels. These two possibilities (high reserves and low reserves) appear equally likely.
The investment costs required to develop this field and bring the oil to the market would normally be 90M$, which enable you to extract a constant flow of 1M barrel per year, (up to the capacity of the field), starting at the end of the first period.
Alternatively, a smaller investment of 70M$could be made, but then it would only be possible to extract 0.5M barrel per year.
Assuming that the price of oil will be 20M$ per barrel, that the variable costs of extraction are negligible and that the discount rate is equal to 10%, answer the following questions:
a) (4 pts) Evaluate the NPV of the 90M$ investment assuming high reserves. Give the details of the computation. You can use the following information:
number of periods 
Series present value at 

5% 
10 % 
15 % 

3 
2.72 
2.49 
2.28 
5 
4.33 
3.79 
3.35 
8 
6.46 
5.33 
4.49 
10 
7.72 
6.14 
5.02 
15 
10.4 
7.61 
5.85 
20 
12.5 
8.51 
6.26 
b) (6 pts) Do the same for the three other possible situations and summarize your results in the following table. (not necessary to give the details this time)

High reserves: 10M barrels 
Low reserves: 5M barrel 
NPV Big investment 


NPV Small investment 


c) (4 pts) Draw the decision tree, indicating all data
d) (2 pts) What investment decision would you advise?
e) (5 pts) An exploration firm proposes you to collect additional information. What in practice is the most you be ready to pay for exploring the field?
f) (8 pts) During the course of your investigations, you learn that it is possible to estimate the size of the reserves by analyzing oil samples at no cost. This estimation has proven in the past to be 70% reliable. What is the probability of exploiting important reserves if the samples indicate that it is an important reserve? What if they indicate the contrary?
g) (10 pts) What is the expected value of the test described in question f?
h) (6pts) If the true cost if conducting the test described in question f were to be to delay the extraction of oil by 4 months (so that it were to occur at the end of 16 months instead of 12 months), is it worthwhile conduct the test? Show calculations.