Tag: Marginal cost

Solved Problem: Mickey v. Cost Curves

Supports: Microeconomics and Economics, Chapter 11, Section 11.5, and Essentials of Economics, Chapter 8, Section 8.5

Image generated by ChatGTP-4o showing the costs of inputs to a factory.

Mickey, the Econ Pup, sometimes struggles with drawing and interpreting cost curves. Examine the cost curves shown in images a. and b. and let Mickey know if you find any errors.

a.

b.

Solving the Problem
Step 1: Review the chapter material. This problem is about drawing and interpreting cost curves, so you may want to review Chapter 11, Section 11.5, “Graphing Cost Curves.”

Step 2: Answer part a. by explaining whether there are any errors in the cost curves shown in the image in a. No wonder Mickey is confused! This figure has multiple errors:

  1. It’s an error to have the ATC and AVC curves cross. The unlabeled curve at the bottom is supposed to be AFC. We know that if a firm has fixed costs, then the ATC and AVC curves will get closer and closer as the quantity increases and AFC becomes smaller and smaller. But because AFC will never decline to zero, ATC and AVC can’t be equal at any quantity.
  2. The second error is related to the first error. We know that the MC and ATC curves should intersect at the quantity at which ATC is at a minimum. In this figure, the MC curve intersects the ATC curve at a quantity that is larger than the quantity at which ATC recaches a minimum.
  3. The third error is related to the first two errors. The relationship between the three average cost curves should be ATC = AVC + AFC at every quantity. In this figure the relationship doesn’t hold at any quantity.
  4. Finally, there is a dotted line from the point where the (unlabeled) AFC curve intersects with the MC curve down to the Q-axis. But that point has no economic significance.

Step 3: Answer part b. by explaining whether there are any errors in the cost curves shown in image b. Mickey can rest easy with these cost curve because, although the figure seems to be only partially finished, all of the cost curves are correctly drawn. The MC curve correctly intersects the AVC curve at the quantity at which the AVC curve is at a minimum. The instructor could finish the figure by labeling the bottom curve as AFC and by drawing an ATC curve above the AVC curve, with the ATC curve intersecting the MC curve at the quantity at which the ATC curve is at a minimum.

Solved Problem: Do Firms Always Raise Their Prices When Their Costs Go Up?

Supports: Microeconomics and Economics, Chapter 12,  and Essentials of Economics, Chapter 9.

The entrance to the Lincoln Tunnel, which connects New Jersey to Midtown Manhattan. (Photo from the Associated Press via the New York Times.)

This spring, New York City will begin charging an additional fee—referred to as a congestion price or congestion toll—on vehicles entering the borough of Manhattan below 60th Street. The purpose of the fee is to reduce the congestion and pollution that additional vehicles cause when driving in that part of the city. (Note that the fee can be thought of as Pigovian tax because it is intended to address a negative externality caused by driving a vehicle. We discuss Pigovian taxes in Microeconomics and Economics, Chapter 5, Section 5.3, and in Essentials of Economics, Chapter 4, Section 4.5.)

Trans-Bridge Lines operates buses between the Lehigh Valley in Pennsylvania and Manhattan. The firm will have to pay a fee of $24 each time one of its buses enters Manhattan. An article in the (Allentown, PA) Morning Call quotes the president of Trans-Bridge Lines as objecting to the fee: “It doesn’t make sense and punishes bus operators who are part of the solution to the congestion problem.” However, the article also notes that “Trans-Bridge is not considering fare increases at this time.”

If Trans-Bridge’s cost of providing bus service between the Lehigh Valley and Manhattan increases by $24 per bus, shouldn’t the firm raise the price it charges passengers? Does the failure of Trans-Bride to raise ticket prices following the enactment of the fee mean that the firm isn’t its maximizing profit? Briefly explain. 

Solving the Problem

Step 1:  Review the chapter material.This problem is about what costs firms take into account when determining the profit-maximizing price to charge in the short run, so you may want to review Microeconomics or Economics, Chapter 12, Section 12.2, “How a Firm Maximizes Profit in a Perfectly Competitive Market” (Essentials of Economics, Chapter 9, Section 9.2)

Step 2: Answer the two questions by explaining what type of cost the $24 fee is and whether the fee should affect the profit-maximizine price Trans-Bridge Lines should charge passengers for a ticket on a bus going to Manhattan. The fee is a flat $24 per bus and, so, it doesn’t change with the number of passengers on a bus. Therefore, the fee is a fixed cost to Trans-Bridge. Trans-Bridge should set the price of a ticket so that the last ticket sold on a bus increases the firm’s marginal cost and marginal revenue by the same amount. Because the $24 fee doesn’t change the marginal cost (or the marginal revenue) to the firm of transporting another passenger, the fee doesn’t change the firm’s profit-maximizing price. The answer to the first question in the problem is that an increase (or decrease) in a firm’s fixed cost won’t cause the firm to change its profit-maximizing price in the short run. The answer to the second question follows from the answer to the first question: That Trans-Bridge isn’t raising the price of a ticket following the enactment of the doesn’t mean that the firm isn’t maximizing profit.

Extra credit: Note that in the answer we refer to Trans-Bridge’s decision in the short run. It’s possible that the $24 fee will cause Trans-Bridge to suffer an economic loss on at least some of the bus trips it offers during different times during the day. As we discuss in Microeconomics and Economics, Chapter 12, Section 12.4 (Essentials of Economics, Chapter 9, Section 9.4), in that case, Trans-Bridge will continue to offer those bus trips in the short run, but, if nothing else changes, it will stop offering the trips in the long run.

The Effect on a Firm’s Costs of Using a Generative AI Program

Supports: Microeconomics, Chapter 11, Section 11.5; Economics, Chapter 11, Section 11.5; and Essentials of Economics, Chapter 8, Section 8.5

Photo from the Wall Street Journal.

Imani owns a firm that sells payroll services to companies in the Atlanta area. Her largest cost is for labor. She employs workers who use software to prepare payroll reports and to handle texts and calls from client firms. She decides to begin using a generative AI program, like ChatGPT, which is capable of quickly composing thorough answers to many questions and write computer code. She will use the program to write the additional computer code needed to adapt the payroll software to individual client’s needs and to respond to clients seeking advice on payroll questions. Once the AI program is in place, she will need only half as many workers. The number of additional workers she needs to hire for every 20 additional firms that buy her service will fall from 5 to 1. She will have to pay a flat monthly licensing fee for the AI program; the fee will not change with the number of firms she sells her services to. Imani determines that making these changes will reduce her total cost of providing services to her current 2,000 clients from $2,000,000 per month to $1,600,000 per month

In answering the following questions, assume that, apart from the number of workers, none of the other inputs—such as the size of her firm’s office, the number of computers, or other software—change as a result of her leasing the AI program.

a. Briefly explain whether each of the following statements about the cost situation at Imani’s firm after she begins using the AI program is correct or incorrect.

  1. Her firm’s average total cost, average variable cost, and average fixed cost curves will shift down, while her firm’s marginal cost curve will shift up.
  2. Her firm’s average total cost, average variable cost, average fixed cost and marginal cost curves will all shift up.
  3. Her firm’s average total cost, average variable cost, and marginal cost curves will shift down, while her average fixed cost curve will shift up.
  4. Her firm’s average total cost, average variable cost, average fixed cost, and marginal cost curves will all shift down.
  5. Her firm’s average fixed cost curve will shift up, but her other cost curves will be unchanged.

b. Draw a graph illustrating your answer to part a. Be sure to show the original average total cost, average variable cost, average fixed cost, and marginal cost curves. Also show the shifts—if any—in the curves after Imani begins using the AI program.

Solving the Problem

Step 1:  Review the chapter material. This problem requires you to understand definitions of costs, so you may want to review the sections “The Difference between Fixed Costs and Variable Costs,” “Marginal Costs,” and “Graphing Cost Curves”

Step 2:  Answer part (a) by explaining whether each of the five listed statements is correct or incorrect. The cost of the AI program is fixed because it doesn’t change with the quantity of her services that Imani sells. Her firm will have greater fixed costs after licensing the AI program but she will have lower variable costs because she is able to produce the same level of output with fewer workers. Her marginal cost will also decline because she needs to hire fewer workers as the quantity of services she sells increases. We know that the average total cost per month of providing her service to 2,000 clients has decreased because we are given the information that it changed from ($2,000,000/2,000) = $1,000 to ($1,600,000/2,000) = $800.

  1. This statement is incorrect because her average fixed cost curve will shift up as a result of her total fixed cost having increased by the amount of the AI program license and because her marginal cost curve will shift down, not up.
  2. This statement is incorrect because all of her cost curves, except for average fixed cost, will shift down, not up.
  3. This statement is correct because it describes the actual shifts in her cost curves. 
  4. This statement is incorrect because her average fixed cost curve will shift up, not down.
  5. This statement is incorrect because her rather than being unaffected, her average total cost, average variable cost, and marginal cost curves will shift down.

Step 3:  Answer part (b) by drawing the cost curves for Imani’s firm before and after she begins using the AI program. Your graph should look like the following, where the curves representing the firm’s costs before Imani begins leasing the AI program are in blue and the costs after leasing the program are in red.