University of South Carolina Arnold School of Public Health HSPM J712 Aug. 2011

Copyright © 1999-2000 Samuel L. Baker

Cost

• Opportunity cost
• Total cost
• Fixed cost
• Variable cost
• Average cost
• Marginal cost

The Economic Problem

• An economic system must make choices about the allocation of resources among the many possible uses.
• The economic system also chooses how the goods and services are distributed -- who gets what.

Cost and the necessity of choice, even in health care

• other kinds of health care, that might give more benefit for the same resources
• other kinds of health-enhancing investments besides health care, such as public health or health education
• consumption goods and services that might enhance our lives more than spending on certain kinds of health care would,
• or as investments outside of health care that might improve our future ability to produce goods and services more than some investments in health might.

Opportunity Cost

The opportunity cost of doing or getting something is:

• what you could have done or gotten instead.

Opportunity cost is what you forgo.

Example: Your opportunity cost for taking this class includes:

• Whatever else you could have bought with your tuition and fee money, plus
• the work, family participation, rest, or recreation that you are not doing because you are spending time doing this.

Opportunity cost is not resources used

Instead, the cost is what else you could have done with those resources.

Resources have value only because you can use them to make goods and services that have value.

Using prices for costs

Dollar costs (prices) are

• easier to determine and
• easier to add up.

Nevertheless, we should not lose sight of opportunity cost.

• saving medical institutional costs by discharging patients early, but
• adding opportunity costs for family members drafted into being home caregivers

Costs and prices

• "Reflect" here means that the ratio of prices of any two goods or services is the opportunity cost of the one in terms of the other.

For this to work properly, you have to have strong competition and savvy consumers. Competition will then force the sellers to be efficient, and provide goods and services at prices in line with costs.

Sound applet
The issue of how well the market works is one to which we will return in a future week, when market concepts are discussed. For an example of what can go wrong, though, consider petroleum and ethanol. OPEC, the oil cartel, manipulates the price of oil. The U.S. government indirectly manipulates the price of ethanol, as does (according to some observers) the Archer Daniels Midland agricultural products company. With all this manipulation going on, it would be astounding if the ratio of gasoline and ethanol prices was anywhere close to the how much ethanol the world would have to give up to get one more gallon of gasoline.

Sound applet
Even if prices don't reflect social opportunity cost, they can reflect an individual's opportunity cost, if the good or service is something you have to buy.  If you have a motor you need to operate, and it can run on gasoline or ethanol, and you cannot make your own gasoline or ethanol, then the opportunity cost of a gallon of gasoline in terms of ethanol really is the the price of a gallon of gasoline divided by the price of a gallon of ethanol.

• That paragraph may have made the concept seem more complicated than it really is.  Suppose a gallon of gasoline costs $4.00, and a gallon of ethanol costs $2.00.  Each gallon of gasoline you buy means you can't buy $4/$2 = 2 gallons of ethanol.  The opportunity cost of a gallon of gasoline is 2 gallons of ethanol.

That completes a chunk of material. Now I'm about to change the subject and talk about specific money cost concepts. This might be a good time to take a break. Use the link near the top of this page to jump back to here when you are ready to resume.

Money cost concepts

The concepts are:

• Total cost
• Fixed cost
• Variable cost
• Marginal cost
• Average cost

Total cost

Total cost = TC(Q)

Total cost at Q = the total cost per unit of time of producing Q units of output per unit of time

Costs are "flows," not "stocks"

All our cost measures

including total cost, fixed cost, variable cost, marginal cost, average cost

For example, a U.S. firm presenting annual budget numbers would use "dollars per year" as its cost units. For a monthly budget, the cost units would be dollars per month.

For brevity, I'll leave "per unit of time" out sometimes, but it's always implicitly there.

Total cost example

The term "Total cost" is used to refer to the whole table, representing the relationship between output flow and cost flow.  It's not just any one number in the table, unless you say something like, "the total cost at an output of 30 per day."

Total cost graphed

Fixed cost

Fixed cost = costs that can't be avoided in the "short run"

"Short run" means a time period in which many costs can't be avoided. (Wait -- isn't that circular?)

Fixed cost is a function of Q (quantity per unit of time) in the trivial sense that it's a constant function.  Fixed cost is the same at all levels of Q.

Fixed cost example

The capital outlay is a stock, really, rather than a flow. To use our cost concepts, we have to convert it to a flow.  We do that by imagining that we borrow the money and then pay back the loan over a period of years at so many dollars per month. That "so many dollars" per month is part of our fixed cost flow.

Sound applet
There are other fixed costs per month.  These are costs that recur monthly independent of how many patients come through.

Other fixed costs per month
Maintenance	$425
Promotion	$250
Accounting	$100
Insurance	$100
Rent	$875
Telephone	$100
Taxes	$750
Clerk/Receptionist salary and benefits	$1,500
Other fixed costs -- total per month	$4,100

Sound applet
Combine the information from the two tables to get the total fixed cost flow per month.

Summary of fixed costs Sound applet
Monthly capital cost	$2,072
Recurring fixed cost	$4,100
Total fixed cost flow per month	$6,172

Fixed cost in the cost table

The fixed cost is the total cost of being open but producing 0.

Total Cost and Fixed Cost graphed

Variable cost

• The variable cost is extra cost of producing Q, above the cost of producing 0.
• The variable cost is a function of Q.

Variable cost example

Variable cost graphed

Marginal cost

• Total cost at output = Q
• minus
• total cost at output = Q-1.

• Or the reduction in cost from producing one less.

Marginal cost example

• "Lumpy" means not continuously variable.
• The technologist is somewhat of a fixed cost over small changes in output rate,
• unless you can hire a part-time technologist. There's no allowance for that in these numbers, so let's assume that you can only hire full-time technologists.

• (There is also the physician's fee, which was $12 per test.  Let's leave that out for now.)

$8.75 is therefore the marginal cost of a screening mammogram
if the technologist is going to be there anyway.

This means:  If a woman walks in unexpectedly and offers $8.76 for a screening mammogram,
and your technologist is not busy,
then you can make $0.01 by doing a mammogram for her.

Marginal cost of larger output changes that mean adding a technologist

Here's our table again, with marginal cost lines added. If we consider only these specific output rates (0, 5, 10, etc.), it simplifies our calculation.

Tests per day Sound applet	0	5	10	15	20	30	40	50
Tests per month	0	100	200	300	400	600	800	1000
Total cost	$6,172	$9,462	$10,337	$13,627	$14,502	$18,667	$20,417	$22,167
Fixed cost	$6,172	$6,172	$6,172	$6,172	$6,172	$6,172	$6,172	$6,172
Technologists needed Sound applet	0	1	1	2	2	3	3	3
Variable cost	$0	$3,290	$4,165	$7,455	$8,330	$12,495	$14,245	$15,995
Marginal cost  from previous output level	Not  applicable	$3,290	$875	$3,290	$875	$4,165	$1,750	$1,750
Corresponding  marginal cost per unit	Not  applicable	$32.90	$8.75	$32.90	$8.75	$20.83	$8.75	$8.75

Sound applet
The lumpiness of the technologist makes the marginal cost jump up or down, depending on whether we do or do not have to add a technologist to achieve the next higher output rate.
The marginal cost is high when we have to add a technologist. It's low otherwise.

Economies of scale

• This is an advantage to size, an "economy of scale" in the jargon.

Marginal cost and the price we can afford to charge

• (Not counting the doctor's $12 fee.)

• Again, not counting the doctor's $12 fee that we'd want to pass through to the patient.

Marginal cost is the concept to use when considering changes.

The difference is the marginal cost of the change.

Compare that with the marginal benefit of the change to decide whether the change is advantageous.

Average cost

• Average cost is sometimes mistakenly used in place of marginal cost. Examples of that come in a later lecture

• Profit = Revenue minus cost.
• So Profit per unit = Revenue/(Units sold) minus Average Cost.

• (in health care, you generally don't.  But, suppose you did.)

• Revenue is the total amount you take in.
• Revenue = Price times Quantity.
• Therefore Price equals Revenue divided by Quantity.

• If Price exceeds Average Cost then your unit profit is positive.
• If the price is less than the average cost, your average profit per unit is negative.

Average Cost and Marginal Cost

Look at the 50 column:

• The marginal cost per test is $8.75
• but the average cost is $22.17.

• Yes, if we don't have to give all our customers that price.

• But if we offer all customers prices just above their marginal costs, we won't cover our fixed costs, so we'll lose money overall.

Price discrimination

• Jargon term for charging different customers different prices.

• Not illegal.
• In health care, often encouraged and expected.

Average cost as the break-even price

• In this example, if our output rate is about 50 per day, we make money overall if our average price for all customers is at least $22.17.

Short-run and long-run decisions

• Even if you lose money overall, you're better off than not selling.

Key cost concepts review

• what you give up to get something

• Total cost -- the dollar value of what you give up by being in business and operating at your current rate.
• Fixed cost -- the dollar value of what you give up by being in business, even if you produce nothing.
• Variable cost -- the dollar value of what you give up to produce at your current rate, over and above your fixed cost.
• Marginal cost -- the dollar value of what you give up to add one unit to your rate of production.
• Average cost -- total cost divided by output rate.

E-mail:

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of South Carolina.