William is the owner of a small pizza shop and is thinking of increasing products and lowering costs

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. 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 shoemaking 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. Carefully review the Grading Rubric for the criteria that will be used to evaluate your
assignment.


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