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Cost Function

In Economics we usually talk about two different types of costs, explicit and

implicit. Implicit costs incorporate all opportunity costs and rate of returns into

your cost function. We have already covered these types of costs in

Macroeconomics. We will come back to them later in this course, but for now weare going to focus on Explicit Costs. These are costs that must be paid; anything

that you actually receive a bill for is an explicit cost. Explicit costs are broken

down into two categories; all costs are either Fixed or Variable. Fixed costs are

costs that must be paid regardless of production or output. These can be leases

on cars, salaried employees, buildings, cell phones, copy machines etc. More

times than not these costs are contractual obligations (which is what makes them

unavoidable). Variable costs are costs that change with the level of production,

these are usually costs that are in some way directly associated with output, such

as electricity, paper, steal, packaging etc. Adding together Fixed Costs and

Variable Costs will give you Total Costs.

Fixed + Variable = Total Costs

We also want to find the Average costs; they are Average Fixed Cost, Average

Variable Cost and Average Total Cost. To find the average costs, you divide

Total by the quantity produced at that point.

Average Variable Cost = Total Variable Cost / Quantity

Average Fixed Cost = Total Fixed Cost / QuantityAverage Total Cost = Total Cost / Quantity

EMPHASIS: The average costs can also be found by adding AVC and AFC to

equal ATC. This is nice for checking work. Beware not to round off your answers

too much though, or they wont add correctly. I recommend rounding to 2

decimal places, or cents.

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Quantity Fixed Variable Total MC AFC AVC ATC

0 100 0 100 x x x x

1 100 30 130 30 100 30 130

2 100 55 155 25 50 27.5 77.5

3 100 105 205 50 33.3 35 68.3

4 100 185 285 80 25 46.25 71.255 100 305 405 120 20 61 81

6 100 475 575 170 16.7 79.2 95.8

7 100 705 805 230 14.3 100.7 115

8 100 1005 1105 300 12.5 125.6 138.1

9 100 1385 1485 380 11.1 153.9 165

10 100 1855 1955 470 10 185.5 195.5

Microeconomics is the study of individual people, businesses, and markets. So it

is very important in Micro to discuss and analyze individual changes. To do this

we need to reintroduce the concept called Marginal. We can apply theword/concept to any numeric definition. The term Marginal simply means one

additional. Marginal Cost means the additional cost of producing the next unit of

output, or the cost incurred of producing one additional item. The Marginal Cost

of output #2 would be the difference in cost of output #2 and output #1; it is the

cost of producing that extra unit.

The final categorization of costs we need to address are Sunk Costs. Sunk Costs

can be any type of cost, the distinction is that these are expenses that have

already been paid or obligated to. Sunk Costs are most important in the decisionmaking process, if you have already spent money you generally dont want to

consider that when deciding on future action. If you cant unspend it, we usually

consider it irrelevant in future decisions.

Economies to Scale

In the Long Run, the decision making process with respect to expansion or

contraction occurs using Economies of Scale. Economies of scale tell you how

much return you gain from expansion. Increasing Returns to Scale occurs when

you expand production (increase output) and a lower average cost occurs.

Constant Returns to Scale results when you have expansion and the averagecosts follows by the exact same percentage. Decreasing Returns to Scale

happens when you expand and your average cost per unit increases by more

than production. Negative Returns to Scale occurs when you expand

production and output decreases.

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To calculate the percentages we would use our elasticity set up. This is going to

give us the Elasticity of Supply. Instead of measuring the Percent Change in

Quantity, we can measure the Percent Change in Output. This doesnt change

the way we measure elasticity, it is still a quantity measurement in the top half of

our equation. The bottom half of the equation is still a monetary measurement,

only know we are changing our costs instead of prices or incomes.

The only difference we need to consider is that we now must look at the answer

for each half of the equation, as opposed to using our final E= answer. This is

important because we may find significant information that would be missed

with a single numeric answer.

Types of Economies to Scale:

When % change in Q > % change in Cost is a Increasing Return to Scale(its

becoming relatively cheaper to produce our product with each expansion)

When % change in Q < % change in Cost is a Decreasing Return to Scale(its

becoming relatively more expensive to produce our product with expansion)

If the % change in Q is a negative number and the % change in Cost is a Positive

number we have a Negative Return to Scale (we are spending more money but

getting less output)

If the % change in Q is a positive number and the % change in Cost is a Negativenumber we have Increasing Returns to Scale (we somehow found a way to cut

costs AND produce more of our product at the same time Id argue this is very

rare but if you can find a way to do it you will make a LOT of money)

Example:Quantity Fixed Variable Total MC AFC AVC ATC

3 100 105 205 50 33.3 35 68.3

4 100 185 285 80 25 46.25 71.25

The Returns to Scale from increasing output from 3 units to 4 units is .29 (or 29%)versus a 55% increase in expenses (185 from 105). This gives us Decreasing

Returns to Scale, because the change in cost was greater than the increases in

output that resulted. If we finished our elasticity equation, this would give us a

number between 0 and 1, or in this case an Elasticity of Supply of 0.53.

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If a firm decides to employ a new piece of machinery that will increase costs by

25%, but output only increases 35% this is Increasing Returns to Scale. Our

Elasticity of Supply would be greater than 1, in this case 1.4.

If a firm decides to employ a new production method increasing costs by 8%, but

output decreases by 3%, this is Negative Returns to Scale. The decision resulted

in a net loss in output. Your measurements are moving in opposite directions.

How do you use this?

It is important to understand that this is an area of business where there is no

rule for when you should or should not expand. Like with utility, Economies to

Scale is a comparative measurement tool. In a real world application you would

ideally have a variety of options available and would select the most profitable

option. Even Negative Returns to Scale could be the best option, especially if the

product you are producing is an Inelastic good.