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ECON 520 Instructor: Yang Jiao
Assignment 4 for Chapter 7 (Due April 7 in class)
1. (10?) you manage a plant that mass-produces engines by teams of workers using
assembly machines. The technology is summarized by the production function
q = 5 KL.
Where q is the number of engines per week, K is the number of assembly machines and L
is the number of labor teams. Each assembly machine rents for r = $10,000 per week, and
each team costs w = $5000 per week. Your plant has a fixed installation of 5 assembly
machines (or K=5) as part of its design.
In the SHORT RUN:
a. Write the expression of production function in the short run, in terms of Labor
b. What is the short run cost function for your plant ? namely, how much would it
cost to produce q engines?
c. How many Labor teams are required to produce 250 engines? What is the average
cost per engine?
In the LONG RUN (both L & K are variable now):
d. You are asked to make recommendations for the design of a new production
facility. What is the condition for cost minimization, given that the MPL=5K,
e. For output q=500, how many L and K should you use in order to minimize cost?
f. What is the minimum cost of production for q=500? What is the average cost per
g. This firm has economies of scale, diseconomies of scale, or constant return to
scale? Briefly explain.
h. If w is increased to $10,000 per week, given the new wage rate, how many L and
K should you use in order to minimize cost for output q=500?
2. a.The production function is written as q=L+K. Both MPL
and MPK equal to 1, implying 1 labor for 1 capital. If wage is
$2000 and rental rate for capital is $3000, what is the lowest
cost of labor and capital usage for this firm to produce 50
units of output?
b.Now the production function becomes q=L+2K. And MPL
=1 and MPK=2, which implies 2 labor substitutes for 1
unit of capital. What is the optimal labor and capital usage
for this firm to produce 50 output?
ECON 520 Instructor: Yang Jiao
2. (2?) suppose a firm has the following production technology: one worker is required
to operate on one machine (capital) More than one worker on the same machine will
have a zero MPL. One worker operating on two more machines will also have zero
MPK. If wage is $100 and rental rate for capital is $500, what is the lowest cost of
labor and capital usage for this firm to produce 300 output? (Hint: this is the case
when labor and capital are perfectly complements)
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