MBA Program
Managerial Economics
CP4:
Show all your calculations and explain how you reached the
answers for all parts:
Managerial Decisions in Competitive Markets
1. Ajax
Corporation is a price-taking firm in a competitive industry that employs only
one variable input, labor, to produce a product that sells for $2 per unit. The
wage rate is $8 per unit of labor and total fixed costs are $1,000. Fill in the
blanks in each column of this table as instructed by the questions below:
(1) (2) (3) (4) (5) (6) (7) (8)
Units of Labor
Output
Marginal Product Marginal
Revenue Product
Average Product Average
Revenue Product
Marginal Cost
Profit
0 0 xx xx xx xx xx ______
1 400 ______ ______ ______ ______ ______ ______
2 950 ______ ______ ______ ______ ______ ______
3 1,250 ______ ______ ______ ______ ______ ______
4 1,350 ______ ______ ______ ______ ______ ______
5 1,370 ______ ______ ______ ______ ______ ______
6 1,373 ______ ______ ______ ______ ______ ______
7 1,369 ______ ______ ______ ______ ______ ______
8 1,364 ______ ______ ______ ______ ______ ______
a. Fill inthe blanks in columns 3 and 5. Marginal product
begins to diminish beyond ________ units of labor. Marginal product is negative
beyond _________ units of labor.
b. Compute
marginal and average revenue products and fill in the blanks in columns 4 and
6. The sixth unit of labor __________________ (increases, decreases) total
revenue by $__________. Decreasing labor usage from four to three units
_______________ (increases, decreases) total revenue by $_________.
c. The
manager can maximize total revenue by hiring ________ units of labor. The
maximum possible value of total revenue is $____________.
d. The
manager hires ________ units of labor and produces ___________ units of output
in order to maximize profit. At this level of labor usage, ARP = _____________
which is ______________ (greater, less) than MRP.
e. Compute
marginal cost and fill in the blanks in column 7. At first, marginal cost
___________ (rises, falls) as marginal product rises, then marginal cost
_____________ (rises, falls) as marginal product falls.
f. The
profit-maximizing level of output is ______ units because this is the last
level of output for which _____________ exceeds _____________, or equivalently, _____________ exceeds _____________ .
g. Compute
profit and fill in the blanks in column 8. The optimal level of labor
employment and the optimal level of output both result in an identical maximum
profit level of $_____________.
h. Now
suppose total fixed cost increases to $5,000. Recalculate profit at each level
of labor usage (and output) and fill in the blanks in column 9 below. When
total fixed cost is $5,000, the optimal level of labor usage is _______ units
of labor, and the optimal level of output is ________ units. How high must
total fixed costs rise in order for it to be optimal for this firm to shut
down? Explain briefly.
(1) (2) (9)
Units of Labor
Output Profit
TFC = $5,000
0 0 ______
1 400 ______
2 950 ______
3 1,250 ______
4 1,350 ______
5 1,370 ______
6 1,373 ______
7 1,369 ______
8 1,364 ______
Decisions under Risk and Uncertainty
Star Products, Inc. faces uncertain demand conditions in
2015. Management at Star Products is considering three different levels of
output for 2015: 1, 1.5, or 2 million units. Management has determined that the
following profit levels will occur under weak and strong demand conditions:
Profit
(in $millions) if Demand is
Output Level Weak Strong
1 million units 60 175
1.5 million units 50 200
2.0 million units â50 400
1. Using
each of the four rules for decision making under uncertainty, determine the
output level of 2015.
Maximax rule ______________
units of output
Maximin rule ______________
units of output
Minimax regret rule ______________
units of output
Equal probability rule ______________
units of output
2. Now
suppose that management believes the probability of weak demand in 2015 is 25%
and the probability of strong demand is 75%. Compute the expected profit,
variance, standard deviation, and coefficient of variation for each level of
output:
Output E( )
1 million units ________ ________ ________ ________
1.5 million units ________ ________ ________ ________
2.0 million units ________ ________ ________ ________
3. Based on
the expected value rule, Star Products should produce ________ units in 2015.
4. Using
mean-variance analysis, which level of output should be chosen? Explain your answer.
5. Using the
coefficient of variation rule, Star Products should produce ______ units in
2015. Explain briefly.
6. Suppose
the managerâs utility function for profit is U( ) = 100 . Calculate the
expected utility of profit for each of the three output decisions:
Output E[U( )]
1 million units __________
1.5 million units __________
2.0 million units __________
To maximize the expected utility of profit, the manger
should choose to produce ___________ units in 2015. Explain why this decision
is the same as the decision in question 3 above.