# Why would marginal productivity decline when you hire more workers in the short run after a certain level?

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 9 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.

Required Text

Douglas, E. (2012). Managerial Economics (1st ed.). San Diego, CA: Bridgepoint Education.

Guidance: (1) what is fixed? (what is there a limited number of that doesn’t change throughout the scenario); (2) what is variable (opposite of fixed, this input does change, it is “scalable”); (3) how is efficient defined? How does it apply to each additional worker, do they help/ hurt production (4) perform your analysis, calculate what the marginal product (MP) for each successive worker/pizza employee; (5) Look at the definitions of the different types of “economies of scale” explain how this relates to increasing the scale of your pizza operation (6) Lastly, recall that minimizing marginal cost = maximizing marginal product.

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.

Describe your answer for each question in complete sentences, whenever it is necessary.)

Guidance: (1) The marginal cost (MC) is the additional cost to a firm of producing one more unit of a good or service. You can derive the marginal cost (MC) curve or function from the TVC function, using differentiation, MC = dTVC/dQ, (2) The incremental costs of the extra 200 pairs of shoes per week from 1,000 pairs to 1,200 pairs of shoes are the difference between TVC at 1,200 and TVC at 1,000; (3) You can obtain the profit-maximizing price and output levels by solving the profit maximization condition, MR = MC; (4) Decide whether Paradise Shoes should expand its output further beyond 1,200 pairs per week…..can it attain its profit maximization goal of MR = MC? Further, what assumptions is this based on?

Required Text

Douglas, E. (2012). Managerial Economics (1st ed.). San Diego, CA: Bridgepoint E

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