## Answered: - ECON 520 Instructor: Yang Jiao Assignment 4 for Chapter 7 (Due

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

teams required.

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 &amp; 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,

MPK=5L.

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

engine?

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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