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


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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

 

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 & 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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