Production Cost Analysis and Estimation Applied Problems
Please complete the following two applied problems:
Problem 1:
William is the owner of a small pizza shop and is thinking of increasing
products and lowering costs. William’s pizza shop owns four ovens and the cost
of the four ovens is $1,000. Each worker is paid $500 per week.
|
Workers employed |
Qty of pizzas produced per week |
|
0 1 2 3 4 5 6 7 8 |
0 75 180 360 600 900 1140 1260 1360 |
Show all of your calculations and processes. Describe your answer for
each question in complete sentences, whenever it is necessary.
a.
Which inputs are
fixed and which are variable in the production function of William’s pizza
shop? Over what ranges do there appear to be increasing, constant, and/or diminishing
returns to the number of workers employed?
b.
What number of
workers appears to be most efficient in terms of pizza product per worker?
c.
What number of
workers appears to minimize the marginal cost of pizza production assuming that
each pizza worker is paid $500 per week?
d.
Why would
marginal productivity decline when you hire more workers in the short run after
a certain level?
e.
How would
expanding the business affect the economies of scale? When would you have
constant returns to scale or diseconomies of scale? Describe your answer.
Problem 2:
The Paradise Shoes Company has estimated its weekly TVC function from data
collected over the past several months, as TVC = 3450 + 20Q + 0.008Q2 where TVC
represents the total variable cost and Q represents pairs of shoes produced per
week. And its demand equation is Q = 4100 – 25P. The company is currently
producing 1,000 pairs of shoes weekly and is considering expanding its output
to 1,200 pairs of shoes weekly. To do this, it will have to lease another shoe-making
machine ($2,000 per week fixed payment until the lease period ends).
Show all of your calculations and processes. Describe your answer for each item
below in complete sentences, whenever it is necessary.
a.
Describe and
derive an expression for the marginal cost (MC) curve.
b.
Describe and
estimate the incremental costs of the extra 200 pairs per week (from 1,000
pairs to 1,200 pairs of shoes).
c.
What are the
profit-maximizing price and output levels for Paradise Shoes? Describe and
calculate the profit-maximizing price and output.
d.
Discuss whether
or not Paradise Shoes should expand its output further beyond 1,200 pairs per
week. State all assumptions and qualifications that underlie your
recommendation.
