Sample Problems for the Final Exam
NOTE: This is not the format of the final – the final exam will have two parts. Part One will
consist of 4 required questions and Part II will consist of 2 questions and you will have to
select one of them.
1.
Suppose that the following production function represents a firm’s ability to
manufacture pencils:
f(L,K) = 3
1/2
K
1/4
L
1/4
.
a)
Show that this production function exhibits decreasing returns to scale.
b)
Assume that the wage rate is equal to 9 and the rental rate on capital is equal to 4.
In addition assume that the firm has a fixed cost of production equal to 16. Find
the compensated factor demands for labor and capital.
Find the cost of the cost
minimizing input bundle (ie find the variable cost curve) and the total cost curve.
c)
Find the marginal cost function and the average cost function.
Graph the
marginal cost function and the average cost function in a single diagram.
Show
that the optimal size of the firm is 2.
What is the minimum value of the average
cost curve?
d)
If this firm is a price taker then what is the firm's supply curve?
e)
Suppose that there is a second firm in the pencil business, which has an identical
total cost function and that these two firms are the only two firms in the industry
then what is the industry supply curve?
f)
If the demand for pencils is given by the inverse market demand curve
P = 100 –
Q
then what is the market clearing price and quantity for the pencil market?
g)
Do you expect that there will be entry or exit in the long run?
What will be the
long run price of pencils? How many units will be traded in the long run?
2. The bolt industry currently consists of 20 producers, all of whom operate with identical total
cost functions given by TC(Q) = 16 + Q
2
. Quantity is measured in tons of bolts.
a)
What is the marginal cost curve associated with this total cost curve? What is the average
cost curve? What is the optimal size of the firm? What is the minimum value of the
average cost curve? Illustrate your answer in a diagram.
b)
What is the individual firm’s supply curve? What is the market supply curve?
Suppose that demand for bolts is given by Q
D
= 132 – P. Price is measured in dollars per ton.
c)
What will be the market clearing price and quantity traded in the shortrun? How many
units will each firm supply to the market?
Will firms be earning normal, supernormal or
subnormal profits? Briefly explain your answer without calculating the firm’s level of
profits.
d)
What is the longrun price of bolts? Do you predict that there will be entry or exit from
this industry?
e)
What is the longrun quantity traded in this market? How many units will each firm
produce in the longrun? How many firms will there be in the longrun?
3.
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 Spring '09
 Elmes
 Microeconomics, Supply And Demand, Bruce trade, HD Chemicals, Sheila `s, Dexinitrite

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