Production and Costs

The Short-Run Production Function

Imagine a bakery with 3 ovens that, when in use, can make 50 loaves an hour. One baker using all three ovens will probably only make around 40 loaves; she's too busy running back and forth. If you add a second baker, production jumps to 100, because they can share the work. A third baker gets you to 140 loaves, and a fourth only to 155. This is because at that point the bakers don't all have ovens to work with. The way production increases quickly at first, then slows down, is the short-run production function.

"Short run" in economics means at least one thing can't be changed immediately. The bakery can't suddenly get a fourth oven tomorrow morning; the lease is signed and the oven is installed. Labor is the thing the manager can change quickly.

Total Product (TP) is just the total amount of stuff made for a given number of workers. Marginal Product (MP) is how much extra is made by adding one more worker. The second baker added 60 loaves (MP = 60), the third 40 (MP = 40), and the fourth just 15 (MP = 15).

Initially, marginal product (MP) increased because of the benefits of specialization, but then it went down because the ovens (which couldn't be changed) became the limiting factor. This pattern of increasing and then decreasing MP is what determines the shape of all the cost curves we will look at in this section.

The Law of Diminishing Marginal Returns

The Law of Diminishing Marginal Returns isn't just a theory; it's a real limit on what you can achieve when you add more and more of one thing (like workers) to a fixed amount of something else (the ovens, the workspace).

The word "eventually" is important in the sentence above. At first, adding more workers increases MP because they can each do different parts of the job. For example, two people on an assembly line, one wiring and the other soldering, will do better than two people each doing the entire job by themselves. A third person to check quality could increase output per person even more. During this specialization period, MP goes up.

But if you put twenty people on that same assembly line with three stations, they'll be literally getting in each other's way waiting to use the equipment.

The relationship to costs is straightforward. If the eighth worker adds 15 items, but the ninth only adds 10, then those 10 last items needed more work per item and therefore were more expensive to make. Diminishing marginal returns make marginal cost (MC) increase, and that's why the MC curve eventually slopes upward — and the College Board likes to test if you can make that connection from production to costs.

From Production to Cost Curves

Production and cost curves are like looking in a mirror. As MP increases, MC decreases. As MP decreases, MC increases. Once you understand that connection, cost curves become much easier to understand.

Total Cost (TC) has two parts: Total Fixed Cost (TFC), which includes things like rent, insurance and equipment leases — bills you have to pay whether you make nothing or ten thousand items; and Total Variable Cost (TVC), which includes wages, materials, and the electricity used in the factory. TVC goes up and down with the amount you produce.

TC = TFC + TVC

Four per-unit cost curves are on the standard graph on almost every AP exam. Marginal Cost (MC) is the change in TC divided by the change in Quantity. Average Total Cost (ATC) is TC divided by Q. Average Variable Cost (AVC) is TVC divided by Q. Average Fixed Cost (AFC) is TFC divided by Q. You absolutely need to know all four, and how they're connected.

AFC keeps going down, and for a mathematical reason. A $5,000 per month lease on a building is $50 per item if you make 100 items. If you make 1,000 items, it's $5 per item. It never stops decreasing, or reverses. And as you make a huge number of items, ATC and AVC get closer and closer together because the AFC part of the difference between them gets smaller and shrinks toward zero.

MC Crosses ATC and AVC at Their Minimums

MC crosses both ATC and AVC at their lowest points.

The analogy to your Grade Point Average is really the best way to understand this. If your GPA this semester is lower than your overall GPA, your overall GPA goes down. If it's higher, your overall GPA goes up. The marginal (semester) GPA pulls the average (overall) toward itself.

Costs work with the same math. When MC is lower than ATC, each extra item is cheaper than the current average, pulling ATC down. As soon as MC goes above ATC, each new item is more expensive than the average, and ATC begins to rise. Therefore MC must cross ATC at ATC's lowest point. The same is true for AVC — MC crosses AVC at AVC's lowest point.

One detail for the exam: AVC reaches its lowest point at a lower level of production than ATC does. This is just about how the numbers work. ATC = AVC + AFC. Even after AVC has begun to increase, AFC is still decreasing (and it always decreases). That decreasing AFC continues to pull ATC down for a while longer, so ATC doesn't reach its lowest point until later, when you are producing a larger quantity than where AVC was lowest. I've noticed students frequently lose points on Free Response Questions because they get the order of these minimums wrong on their graphs, so make sure your graphs show the correct sequence.

Economies and Diseconomies of Scale

Economies and diseconomies of scale are concepts relating to the long run, and in the long run a firm isn't limited by what it currently has. It can completely change things: triple the size of the factory, get all new machinery, even relocate to another state. The question then becomes not "how many employees should we hire?" but "how big should the entire business be?"

The long-run average total cost (LRATC) curve illustrates the answer across three distinct sections.

The left, downward-sloping part of LRATC represents economies of scale. Think of Toyota making 500,000 Camrys a year. They can afford automated welding that a place making only 5,000 cars a year couldn't possibly justify, get cheaper steel because they're buying in huge quantities, and spread a $1.8 billion research and development budget over many more cars. As the scale of production grows, the cost per car falls.

Diseconomies of scale are shown on the right, upward-sloping part. A company with 200,000 people often gets bogged down in too many levels of management, repeating departments, and a lot of meetings to plan more meetings. Communication becomes slower, decisions take a very long time, and the cost per item starts to rise again.

The flat part in the middle is constant returns to scale — doubling all inputs doubles output and the average cost doesn't change. The point on the LRATC where it first reaches this lowest point is the minimum efficient scale. In some industries, this minimum efficient scale is huge (building semiconductor fabrication plants costs $20 billion or more, and Boeing spent approximately $32 billion on the 787) and that's why only a few companies exist, since no one else can get to the size needed to compete on price.

Connecting Costs to Market Structure

All of a firm's decisions about how much to produce relate back to these cost curves. A firm in perfect competition will produce where Price equals Marginal Cost (P = MC), and a monopoly will produce where Marginal Revenue equals Marginal Cost (MR = MC). But importantly, Marginal Cost is the foundation of the production decision, no matter the type of market.

However, there's a second question: should the firm produce anything at all?

If the price is above Average Total Cost (ATC), the firm will make a profit. If the price is below ATC but above Average Variable Cost (AVC), the firm is losing money, but it's still better to continue operating because the revenue from sales will cover the variable costs and lessen the amount of the fixed costs. Shutting down would mean no revenue, and those fixed costs (rent, insurance) will still be due. It's when the price falls below AVC that things become really bad; each additional item made will actually increase the total losses, more than simply closing. This is the shutdown point, and it's something students on the AP exam frequently get confused with the break-even point.

Putting it all together for a perfectly competitive firm: it produces along its Marginal Cost curve, but only at prices that are at or above the minimum Average Variable Cost. If the price is below that, the amount they supply is zero. Therefore, the short-run supply curve is the part of the Marginal Cost curve that is above the Average Variable Cost curve. This is a typical multiple-choice question; a version of it appeared on the 2019 AP Micro exam.

Worked Example

A screen-printing shop pays $120 a day for rent and equipment. They printed 8 shirts today at a total cost of $280.

Total Variable Cost (TVC) = TC − TFC = $280 − $120 = $160. This $160 is for the ink, the blank shirts, and the wages of the people doing the printing.

Here's the breakdown of cost per shirt:
- Average Fixed Cost (AFC) = $120 / 8 = $15 a shirt
- Average Variable Cost (AVC) = $160 / 8 = $20 a shirt
- Average Total Cost (ATC) = $280 / 8 = $35 a shirt

And to check: AVC + AFC = $20 + $15 = $35 = ATC. This will always be true. If your figures don't add up, something is wrong.

Now, the shop prints a ninth shirt, and it costs $42 to produce that additional one. So Marginal Cost (MC) = $42. What happens to ATC?

The new Total Cost is $280 + $42 = $322. The new ATC is $322 / 9 = $35.78. ATC increased from $35 to $35.78 because the Marginal Cost of $42 was greater than the previous ATC of $35, and that pulls the average upward. This is the idea of marginal cost influencing the average, shown with real numbers.

Let's look at it the other way around. If making that ninth shirt only cost $28 (the marginal cost or MC is $28, and that's less than the average total cost or ATC of $35), the new ATC becomes $308 / 9 = $34.22. The average cost comes down. When the MC is below the ATC it lowers it, and when the MC is above the ATC it raises it. This push and pull is precisely why the MC and ATC lines intersect at the very lowest point of the ATC.