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Managerial Economics (ARE) 100A
University of California, Davis, Spring 2008
Dr. John H. Constantine
Final Exam
Thursday, June 12, 1:00 p.m. – 3:00 p.m. (Exam “W”)
120 TOTAL POINTS
NOTE:
All work must be shown to receive any credit.
Quadratic Formula
:
a
2
ac
4
b
b
2
There are 11 pages and 7 problems.
Please
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1
Problem 1 (22 points)
:
Problem 1 is continued on the following page.
The market for product Q has many identical firms, each having the short-run total cost function:
STC(q) = 900 + 10q + q
2
,
where q is the firm’s annual output.
We also know that the market demand curve for Q is given by:
Q = 287.5 – 0.25P,
where P is the market price.
Each firm is currently earning zero economic profit.
(a)
Calculate numeric values for:
(15 points.)
(i)
the market price,
(ii)
each firm’s output,
(iii)
the number of firms in the market.
Since each firm is earning zero economic profit, we can find where P = SATC or min ATC.
In
either case:
q = 30 and P = 70.
This the yields the market level demand to be:
Q = 287.5 – 0.25(70)
Q = 270.
Finally, the number of firm is given by:
Number of firms = Q/q = 270/30
Number of firms = 9
(b)
State the equation for the market-level supply curve.
(7 points.)
Each firm’s MC curve is given by:
P = MC = 10 + 2q.
We need to sum this equation across all 12 firms, but to do so, we need to state the equation in q-
dependent form:
q = – 5 + (1/2)P.
Q = 9q = 9[– 5 + (1/2)P]
Q = – 45 + 4.5P