Managerial Economics
Moon Oulatta, Ph.D.
Final Exam
0.1 Uncertainty and Consumer Behavior
1. Equation (1) denotes Blake’s utility for income
u(I) =
√
I (1)
(i) What is Blake’s preference towards risk? Show your work (see the
conditions derived in class), discuss what happens to Blake’s marginal
utility of income as income rises. (ii) Blake is thinking about getting
a new job and leaving his current job that pays him some guaranteed
income. However, with the new gig, there is a 20% probability of obtaining
$150,000 annually and a 80% of probability of earning $350,000. Given
the risk associated with the new job, If Blake decides to take the new
job, he would be willing to buy insurance to guarantee that he gets the
expected income for certain. How much would Blake be willing to pay
for that insurance? (find the risk premium). (iv) Plot Blake’s preference
towards risk: show the risk premium, expected income, risky incomes, and
expected utility.
0.2 Production and Costs
1. The production function for a product is given as follows
q
0
= K
α
L
β
(2)
where q
0
denotes a given desired level of output (production isoquant)
α represents the output elasticity of capital and β represents the output
elasticity of labor. K denotes the capital stock and L denotes the amount
of labor. The price of labor (the real wage) is given by w and the rental
rate of capital is given by r.(i) write down the cost minimization problem.
(ii) Then express the Lagrangian for the cost minimization problem (don’t
solve it yet). (iii) Rely on the Lagrangian method to solve for the optimal
demands for capital (K
∗
) and labor (L
∗
): if you remember these formulas
from class, then you do not need to rely on the Lagrangian method, just
write them down.
(iv) In class, I showed that an increase in price of labor increases the
optimal demand for capital and reduces the optimal demand for labor.
Then, I showed that an increase in the price of capital increases the de-
mand for labor and reduces the demand for capital. This was to show the
concept of input substitution. Here, discuss how an increase in production
(a positive shift in the isoquant) impacts the optimal demands for capital
and labor? you can show this mathematically (rely on the derivative ap-
proach) or you can rely on a diagram that shows one shift in the isoquant
(for simplicity, assume constant returns to scale when you are drawing, see
Figure 6.10 in your book for reference).(v) Assume that the firm desires
1
to produce 100 units of output. If α = β = 1/2, w = $5, and r = $10,
find the minimum cost of producing 100 units of output.
0.3 Monopoly Versus Perfect Competition
You have the following information about a monopolist
p = 40 − 2q (3)
MR = 40 − 4q (4)
AC = M C = 30 (5)
where equation (3) is the demand curve, equation (4) is the marginal revenue
function, and equation (5) denotes the marginal cost function (let’s assume that
the competitive firm and the monopolist share a similar cost structure).
1. Under the perfect competitive outcome, what would be the profit-maximizing
level of output (Q
C
) and price (P
C
)?
2. Under the monopoly outcome, what would be the profit-maximizing level
of output (Q
M
) and price (P
M
)?
3. Use the data obtained from questions (i) and (ii) to solve for the dollar
value of the deadweight loss of monopoly power. Provide a brief definition
explaining the deadweight loss from monopoly power and how this problem
can be addressed by policymakers.
4. Use the appropriate market mechanism diagram (supply and demand) to
show the estimated deadweight loss, including the profit maximizing level
of output and price derived under the perfectly competitive outcome and
the monopolist outcome. Label your axis and curves properly (show all
values).
0.4 Duopoly Models
1. Two firms produce a homogeneous good. Both firms have a constant
marginal cost of zero and a fixed cost of $2. The market demand curve is
given by
p = 100 − q (6)
where q = q
1
+ q
2
. Here, assume that Firm (2) is the Stackelberg leader
[i.e., makes its output decisions before firm (1)]. For simplicity, the marginal
revenue functions for the leader (MR
2
) and and the follower (MR
1
) are
given as follows
MR
1
= 100 − 2q
1
− q
2
(7)
MR
2
= 50 − q
2
(8)
(i) Write down the Stackelberg problem (you need to derive the reaction
function of the follower before doing this). (ii) Derive profit for each
firm?(iii) Discuss the importance of having the first mover advantage for
firm (2).
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