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Practice Problem Set 3
ECON 11
Summer Session C 2010
Microeconomic Theory
Yong Yang
(You may not use calculators in the exam. The exam questions will have simpler numbers.)
1. Consider the production function
Q
=
√
L
.
(a) Find the labor input to need to produce 1 unit.
(b) Find the labor input to need to produce
q
units.
(c) Suppose a unit of labor costs $100. How much does it costs to produce
q
units? Remember
that this is a (short run) cost function.
(d) Compute the marginal cost and the average cost with the cost function obtained in (c). Draw
them with the cost function in the quantitycost space.
(e) Suppose the wage
w
depends on how many units of labor are hired. The labor supply function
is given by
L
= 300

w
. The inverse labor supply function is
w
= 300

L
. How much does
it cost to produce
q
units? Note that you need to obtain the expression in terms of
q
only.
(f) Compute the marginal cost and the average cost with the cost function obtained in (e).
(g) Solve for the quantity where the marginal cost equals the average cost.
(h) Draw the marginal cost and the average cost as well as the total cost (cost function) using
the results in (f) and (g). Note that the total cost has a quartic form.
2. Consider the production function
Q
=
√
LK
.
(a) Find the marginal product of labor and that of capital.
(b) Find the expression for the marginal rate of technical substitution.
(c) Suppose
P
L
= 4 and
P
K
= 9. How many units of
L
and
K
would be minimizing the cost to
produce 30 units?
(d) Calculate the minimum cost in (c). How much portion of the cost was distributed to the
labor? How much portion to the capital?
(e) Suppose now
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 Summer '08
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