Economics 111
Exam 1
Fall 2006
Prof Montgomery
Answer all questions.
100 points possible.
1) [23 points]
Consider a market with demand function Q
D
= 100 – 2P and supply
function Q
S
= – 40 + 5P where P represents price.
a) Compute the equilibrium price and quantity.
If the current price was 15, would there
be a shortage or a surplus?
How large would this shortage/surplus be?
b) Suppose that supply changes so that Q
S
= –26 + 5P (while the demand function
remains the same as above).
Compute the new equilibrium price and quantity.
c) Given the change in price and quantity from the old equilibrium (part a) to the new
equilibrium (part b), compute the elasticity of demand.
Is the demand curve (in the
region under consideration) elastic or inelastic?
Compute sellers’ revenue for parts (a)
and (b).
In the present example, did the change in price cause revenue to increase or
decrease?
More generally, how does the elasticity of demand affect the relationship
between change in price and change in suppliers’ revenue?
2) [32 points]
A firm’s longrun production function is given by Q = K
1/3
L
1/2
where
Q = quantity of output, K = capital, and L = labor.
However, in the short run, suppose
that capital is fixed at K = 64 while labor remains a variable input.
Thus, the firm’s
shortrun production function becomes Q = (64)
1/3
L
1/2
= 4 L
1/2
= 4
L
.
Further assume
the wage per unit of labor is w = 2 and the price per unit of capital is r = 3.
a) Focusing on the shortrun case, derive the firm’s variable cost, total cost, marginal
cost, and average cost functions.
[HINT: You may answer by constructing a table with a
column for each function, or else compute these functions analytically.
If you construct a
table, you might try increasing quantity by increments of 8.]
b) If the product price is P = 12, what is the optimal quantity (Q*) chosen by the firm?
Compute the firm’s profit (or loss) given production at this optimal quantity.
Plot the
firm’s MC and AC curves.
Using this graph, how is the optimal quantity determined?
What area corresponds to the firm’s profit or loss?
c) Still focusing on the shortrun (with K fixed at 64), suppose the price of capital rises to
r = 5.
(As above, assume w = 2 and P = 12.)
How does this affect the firm’s MC and AC
functions?
Compute the firm’s optimal quantity (Q*) and profit/loss.
d) Conceptually (without doing any numerical computation), how would the firm adapt to
the increase in the price of capital in the longer run?
Illustrate your answer using an
isoquant diagram.
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View Full Document3) [30 points]
Consider a worker who has 1000 total hours per year that may be allocated
between work and leisure.
Thus, letting H = work hours and L = leisure hours, the
worker has a time budget H + L = 1000.
The worker earns w = $30 per hour and has no
nonlabor income.
a) Suppose the government taxes income at a 20% rate.
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 Spring '08
 MONTGOMERY
 Economics, Supply And Demand, pts, New Jersey, optimal quantity

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