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MGT 404 – Economics 2016 Professor Kevin Williams PROBLEM SET 2: PRODUCTION – COSTS – COMPETITION – MONOPOLY 1. True False and Uncertain (20 points)…

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MGT 404 – Economics
Professor Kevin Williams
2016
PROBLEM SET 2: PRODUCTION – COSTS – COMPETITION – MONOPOLY
1.
True False and Uncertain
(20 points)
You need to explain your answer in order to obtain full credit. No more than three sentences
a.
(5 points) If the wage rates a firm must pay increase, it may end up with lower total costs
for a given level of output.
b.
(5 points) A firm should always produce at an output at which long-run average cost is
minimized.
c.
(5 points) The ratio of a monopolist’s optimal price to its marginal cost is larger when the
market elasticity of demand is greater in absolute value (i.e., more elastic).
d.
(5 points) A monopolist will always want to produce in the more elastic segment of its
demand curve.
2.
Production
(10 points)
A firm produces output using capital (K) and labor (L) according to the following production
function:
q= L
a
K
b
,
where L and K are measured in hours.
We assume that a = ½ and b = ½.
An hour of labor costs
\$1 and an hour of capital can be rented at a cost of \$4 (or alternatively has an opportunity cost of
\$4 in terms of other products the firm could produce with that capital).
a.
(2 points) Does this production function exhibit constant returns to scale? (EXPLAIN
b.
(2 points)
Solve for a general expression for the marginal product of labor and the
Hint: Note
that for example MP_L =1/2L
-.5
K
.5
from the notes but use the fact that L=q
2
/K
(rearranging the production function) to greatly simplify the MP_L expression. Use the
same trick to solve for MP_K.
c.
(1 points) What it the marginal rate of technical substitution?
d.
(5 points) Assume that the firm wishes to produce 10 units of output at minimum cost.
Write down the two equations (but you do not need to solve) that would tell us the
optimal L and K to choose.

MGT 404 – Economics
Professor Kevin Williams
2016
3.
Cost Functions
(20 points)
The local store Ted’s Tunes is the best music store in town.
The cost function for the store is:
TC = 20 + 4q + 3q
2
+ 2q
3
(Where q is number of records sold.)
Please make sure to write out all answers to this question as equations: graphs are not sufficient.
a.
(5 points) What are the fixed costs of Ted’s Tunes?
Give an example of a fixed cost.
b.
(5 points) What is the average fixed cost function?
Explain what happens (and why it
happens) to average fixed costs as quantity increases.
c.
(5 points) What is the average (total) cost function of the firm?
d.
(5 points) What is the variable cost function?
Give an example of a variable cost.
4.
The Schott App.
(30 points)
Peter Schott starts a new company that has a monopoly on a cool new app that gives answers to
SOM econ problem sets. His total cost function is:
TC = 80 + 3Q + 3Q
2
which means that MC = 3 + 6Q. The fixed cost of 80 is not a sunk cost.
Demand for the app is:
Q = 10 – (1/8)P.
a)
(10 points) If Peter is a monopolist, what price does Peter set and what output is
produced? Calculate profit and consumer surplus. What is the deadweight loss when
Peter is a monopolist?
b)
(10 points) Sharon Oster is tired of the Schott App users being taken advantage of by a
monopolist Peter. She proposes that government sets a maximum price for the app of
\$45. Calculate quantity, change in consumer surplus and Peter’s profits at this maximum
price.
c)
(10 points) Judy Chevalier suggests that consumers need even more relief from greedy
monopolists. She proposes a maximum price of \$25. What do you think Judy is trying to
do? What result would her proposal have upon Peter?