Identify the range of output exhibiting increasing returns (increasing MP), and the range exhibiting diminishing returns (decreasing MP).

Section Overview: Chapters 8 and 9 provide the theoretical analysis of firm production; how much output the firm is able to produce and at what cost. The cost curves achieve two purposes: it provides a simple representation of how the production process behaves, and the few curves within it give us important information about fixed and variable expenses as well as marginal cost (which will be used in optimal decision-making). Chapter 8 describes short-run production and cost, and 9 describes long-run production and cost.
Learning Goals: Upon completing this section, we will understand why economists differentiate between the short run and the long run, and how this impacts firm decision making. We will recognize the relationship between a firm’s production and its costs, and be able to construct and interpret the various production and cost curves. We will develop tools of long-run optimization (isoquants and isocost lines). Finally, we will utilize some of our earlier tools (regression, calculus) in analyzing these topics.

1. Your HR Manager comes to you about an employee whose performance reviews have been declining recently, and asks your advice about whether to keep the employee or let him go. To provide some balance, the manager mentions that the company has spent a considerable amount of time and effort in training this employee on company-specific procedures and that, in the manager’s words, “it would be a shame to let that money go to waste.” How would you respond?

2. You have collected the following data on output and total variable costs:

Q TVC ($)
1 50
2 100
3 140
4 170
5 190
6 200
7 220
8 250
9 290
10 340
Identify the range of output exhibiting increasing returns (increasing MP), and the range exhibiting diminishing returns (decreasing MP).
Current fixed costs for the company equal $150. Draw two graphs, both with Q on the horizontal axis: one graph shows TVC and TC, and the other shows AVC, AC, and MC.
Suppose that the government imposes a $30 property tax hike on all businesses; how will that affect your two graphs; i.e., which cost curves will be affected and how?
Suppose instead that the government considers your production process to be polluting, and imposes a $7 tax per unit produced. How does this tax increase compare to the property tax increase, in terms of the effect on your company’s cost curves?
Your boss says “either of these taxes is going to force us to change our production levels.” Given what you know about optimization analysis, how would you respond?

3. Your work for a company that supplies parts to a manufacturer, and have a standing order to produce 5,400 parts per day. You currently hire employees at $50 per day, and each additional employee produces 200 more parts per day (i.e., MP is constant and equal to 200). Your company is considering implementing one new machine that can produce 3,000 more parts per day at a cost of $600 per day.
a. Would your company save money in the production of the 5,400 parts by purchasing the new machine and reducing its demand for labor?
b. After news of the technologically-advanced machine spreads, along with news of fast-food automated kiosks replacing human employees, your employees improve their performance such that each additional employee now produces 300 more parts per day (MP is constant and equal to 300). If the other values remain the same (wage is $50, machine is $600 and machine’s output is 3,000), would the company save money in the production of the 5,400 parts by purchasing the machine and reducing labor demand?

4. You work for a company that is being accused of monopoly behavior, given its large size. Comparisons are made to the industry standard, where each establishment has on average about 16.2 employees. Your company is bigger than that, but you want to provide evidence against the monopoly charges.
a. You’ve collected data at different times in your company’s history, when you had different amounts of capital.
In 2003, SRATC = 2.5Q2 – 61Q + 480
In 2008, SRATC = 2.5Q2 – 16Q + 150
In 2014, SRATC = 2.5Q2 – 40Q + 250
Plot these three different SRATC curves (have Q go from 0 to 20), and discuss how (and possibly why) your company has changed since 2003 in terms of its size.
b. Make another column labeled “LRATC” that includes three points: 2008’s SRATC when Q = 1; 2014’s SRATC when Q = 8, and 2003’s SRATC when Q = 15. Plot these three points on your graph (be sure to show, don’t hide, the dots) and add a 2nd-degree polynomial trendline to represent your company’s LRATC.
c. In a more competitive industry with smaller firms, typical LRATC curves follow LRATC = 6Q2 – 36Q + 147. Using all available information in this question, present an argument that could be used to justify your company’s size.

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