Which inputs are fixed and which are variable in the production function of William’s pizza shop?

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.

  1. 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?
  2. What number of workers appears to be most efficient in terms of pizza product per worker?
  3. What number of workers appears to minimize the marginal cost of pizza production assuming that each pizza worker is paid $500 per week?
  4. Why would marginal productivity decline when you hire more workers in the short run after a certain level?
  5. 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.

  1. Describe and derive an expression for the marginal cost (MC) curve.
  2. Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes).
  3. What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output.
  4. 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.
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