Cost3

To begin the process of understanding the firm's output choice, we might as well start at the beginning with the production process. At a very abstract level we can think of a firm as a place where inputs are transformed into outputs. Harvard is where faculty expertise is transformed into education, while at the Nissan plant in Smryna, TN, labor, machines, and raw materials are transformed into automobiles. In the remainder of our analysis we will examine the important concepts with the help of two sets of examples based on RIU. The first set will be viewed from the perspective of the university president who is deciding on the appropriate size of the university. The second will be viewed from the perspective of Chris, a student in an introductory ECN course. Here we will look at the concepts through the eyes of Chris, but you are encouraged to work your way through the situation at the university level. In the Questions of the Day we will look at a third example - a jewelry business where we will be looking to determine how many guards to hire.

As we continue, you will note the importance of the time horizon. We will distinguish between the short-run, a period of time short enough so that capital (machines and facilities) cannot be changed, and the long-run, a period of time sufficient to allow for changes in all inputs - long enough, for example, to build a new plant.

At this time we will look only at the short-run relationship between output and input, in this case between the hours spent with a tutor (input) and the grades earned in ECN (output). The key piece of the analysis is the production function - the conceptual link between inputs and outputs. In our analysis we will be looking at the relationship between output level (grades) and input use (hours). In more traditional analysis the focus would be on the relationship between output and labor, the primary variable input in the short-run. The relationship between the input and output is presented in the table below. For those wanting a visual representation of the analysis, you should check out the graphs section at the end of this unit.

Inputs Hours	Total Product (Grades)	Average Product (Grades per hour)	Marginal Product
1	10	10
2	22	11	12
3	36	12	14
4	46	11.5	10
5	54	10.8	8
6	60	10	6

How do you read the table? The first column contains information on the number of units of the input, in this case hours of studying. In other settings you would think of the figures as representing the number of workers, the number of hours, the number of weeks, or any other unit for labor input. In the second column we have output, the grades that would be achieved in ECN. If our analysis were of the automobile industry, these would be the number of automobiles produced, while if we were talking about a hospital, output may be the number of patients treated / cured.

In our example, when two hours are spent studying with the tutor, the ECN grade is 22. If Chris uses five hours of tutorial help, his grade is 54. This confirms what you would have expected, more inputs produce more output. If you study more, your grade improves. The graph of the relationship between the level of output (grades) and the number of inputs (hours) is the total product curve and it is positively sloped. You should check out the graph to see what this relationship looks like because it is the graphical version which most of your friends will be seeing in their classes.

In the third column you will find the average product which measures the average grade produced by each hour. When Chris uses five hours of a tutor's time, his grade would be 54 which means that each hour on average produces 10.8 points [54/5]. This figure is computed by dividing the units of output by the units of input. This figure of average productivity is what the US government measures with its published labor productivity figures.

When the hours spent studying expands from 1 to 2, output increases from 10 points to 22 points. If Chris expanded his tutorial time from 2 to 3 hours, grades would increase from 22 to 36. As we will see later, the relationship between the change in inputs and the change in output - the marginal product of labor - is very important in our analysis of profit maximizing behavior. In this example, the marginal product of the 2nd hour would be 12. [MP = Doutput/Dinput = (22-10)/(2-1) - 12/1 = 12.

Before leaving our simple example, you should note one feature of the Marginal Product column. Once we expand beyond the third hour the marginal product of the tutor begins to decline. It turns out that this is a general feature of production relationships, if you keep adding units of an input to an operation with a fixed facility, eventually the additional output produced by the additional input will begin to decline. Once this happens we have diminishing marginal product. If you happen to be looking at the graphs, you will find that we are talking about a marginal product graph with a negative slope. Once again this should not surprise you. As you study longer your grade will improve, but at some point each additional hour will improve your grade by a smaller amount. In this instance we would say that you are experiencing diminishing returns to your study. You could work so long through the night that your grade actually falls - a negative marginal product [so don't use the cramming approach!].

It is now time to shift gears to an analysis of cost. Below you will find a table of cost data for the production of grades. [We have not derived the relationship between the cost and production relationship, but we will talk later about it] The first thing to note in the table are the column headings. These are the key cost concepts you will be dealing with throughout the remainder of our work and it is worthwhile familiarizing yourself with them. You will be hearing a lot about Total Cost, Average Cost, Fixed Cost, Variable Cost, and Marginal Cost before you are done.

The appearance of fixed cost indicates we are talking about the short-run since in the long-run everything is variable. In this short-run period there are some inputs which will not vary with the level of output. We call the costs associated with these inputs that cannot be changed fixed costs. Another way of looking at fixed cost would be the cost that does not vary with the level of output. The costs that will vary with the level of output are called variable costs. We will see later that industries differ substantially in terms of the mix between fixed and variable costs. The steel, automobile, and airline industries, because of their enormous capital costs (capital intensive), have high levels of fixed costs while jewelry, textiles, and health care are very labor intensive industries and have substantial variable costs.

To better understand the distinction between the cost concepts let's return to RIU where we see Chris trying to get through that intro course. The tutor that Chris hires will charge $5.00 an hour, but because the tutor works on the other side of the Bay, it will cost $3 in bridge tolls and gas to get to and from the meeting. Once Chris has decided to use the tutor and arrived at the office, the $3.00 would be considered a fixed cost because it will not change as the number of hours with the tutor changes. Now let's look at the cost of 3 hours of tutoring help that will give Chris a grade of 36. The total cost of the 36 points would be $18.00. The fixed cost, the cost of getting there and back, is $3.00. The variable cost, which is simply the $5 per hour for 3 hours, is $15. Total cost is simply the addition of fixed and variable costs.

The complete relationship between grades and the cost of tutorial time spent with Tammy's Tutors appears in the table below.

Inputs Hours	Total Product (Grades)	Variable Cost	Fixed Cost	Total Cost	Average Cost	Marginal Cost
1	10	$5	$3	$8	$.80
2	22	$10	$3	$13	$.59	$.42
3	36	$15	$3	$18	$.50	$.36
4	46	$20	$3	$23	$.50	$.5
5	54	$25	$3	$28	$.52	$.63
6	60	$30	$3	$33	$.55	$.83

A second set of cost concepts that you will find useful will be average cost and marginal cost that appear in the last two columns. Average total cost of 3 points, what you will hear shortened to average cost, would be $.50. When you spend three hours with the tutor, each point in your grade costs you fifty cents ($.50). The $.50 figure is derived by dividing total cost by total number of points [total cost / output]. To convince yourself of your command of the average cost concept, you should make sure your computations show average variable cost of 60 points to be $.5 and the average fixed cost would be $.05

The last cost concept, but certainly not the least important, is marginal cost. As with all marginal cost concepts, here we are talking about the relationship between changes - something computed as the ratio of changes in two variables. In this case we are talking about marginal cost of producing an additional unit of output (grade point average) which is defined as DCost / DOutput. The marginal cost of moving from the third to fourth unit of input - from a grade of 36 to one of 46 - is $.50 [ $.50 = (23-18)/(46-36]. Once again you are encouraged to check out the graphs to see what these cost relationships look like. What you see here are very typical cost curves. The TC (total cost) curve is positively sloped, the MC (marginal cost) and AC (average cost) curves are U shaped, and the AFC (average fixed cost) curve is downward sloping.

It is now time to extend our analysis in a few important ways. First, we will look at the relationship between the cost and product - more specifically, between marginal cost and marginal product. Second, we will look at the situation in the long run. Third, we will look at the peculiar nature of economic costs as we reintroduce the concept of opportunity cost. The final extension will be an examination of the conditions for optimal choice of inputs. In our simple example we would be interested in the rules to guide us as we decide on the best use of time.

Up to this point we have looked at the production and cost relationships separately even though they are closely related. To see the nature of the relationship we can return to the original tutoring problem and combine the production and cost tables. If you were to graph these relationships you would find there is a definite relationship between marginal cost and marginal product. What we find is that diminishing marginal product and increasing marginal costs are mirror images of each other - when we have one, we have the other. In this example diminishing marginal product begins with the 4th hour of tutoring when the grade reaches 46, the same level of output at which marginal cost begins to increase.

Inputs Hours	Total Product (Grades)	Average Product (Grades per hour)	Marginal Product	Total Cost	Average Cost	Marginal Cost
1	10	10		$8	$.80
2	22	11	12	$13	$.59	$.42
3	36	12	14	$18	$.50	$.36
4	46	11.5	10	$23	$.50	$.5
5	54	10.8	8	$28	$.52	$.63
6	60	10	6	$33	$.55	$.83

How do things differ when we take the long-term perspective? At least when we look at the graphs there is little difference. The total cost curve is positively sloped and the average and marginal cost curves tend to be U-shaped. The major difference is we have no fixed costs, and at each level of output the firm has chosen the cost minimizing combinations of inputs. For example, in the long-run Chris will be able to weigh the costs of a new computer with the cost of hours spent being tutored. The grades achieved will be dependent upon the level of these two inputs (hours of tutoring and computer). The basis for the choice is discussed in the unit on input choice.

In the analysis of the long run there is an important new concept which you are likely to hear mentioned frequently. The concept is economies of scale. In the previous discussion of the short-run, we examined the change in output associated with an input change on the assumption all other inputs remained unchanged. We looked at the relationship between grades and the hours spent with a tutor, assuming that no other inputs were changed. The three possibilities were diminishing, constant, and increasing marginal product, and they correspond to increasing, constant, and decreasing marginal cost.

In the long-run, however, all inputs can be varied and the returns to scale concept provides a measure of the relationship between the inputs and output. More specifically, returns to scale describe the impact on output of a proportional change in all inputs. The three possibilities defined below are increasing, constant, and decreasing returns to scale.

Not surprisingly, there is the cost equivalent of the returns to scale. Just as there is a relationship between diminishing marginal product and increasing marginal cost in the short run, there is a relationship between decreasing returns to scale and increasing average cost in the long run. The three long-run cost concepts are:

What are the conditions that are likely to generate economies of scale (decreasing cost industries)? The primary factor would be a high level of fixed costs so that these costs can be spread over more buyers. A dam for water power might be an example here. It might be that scale allows for a finer division of labor that produces greater efficiencies. In later units we will examine the implications of these differences which have figured heavily in the structure of American industry and the government's antitrust and regulation policies.

You should also know about economies of scope defined in the Dictionary of Economics as: "A situation in which the same investment can support multiple profitable projects or activities less costly together than separately. For example, an airline selling round trips from New York to Los Angeles can produce air transportation less expensively than one selling only one way-routes." Another example would be where trucks and auto production can be produced by the same company.

The economies of scale and scope can be demonstrated with the simple table that appears below. Let's assume that a firm is considering the production of goods X and Y. After a review of their production situation, the firm's managers came up with the following cost matrix. If you were to produce only X and chose 40 as the level of output, then production costs would be 301. Similarly, if you were to produce only Y and chose 40 as the level of output, then production costs would be 302. Total production costs for the two isolated operations would be 603. But what if you produced both in the same operation. The cost of production of 4 units of each would be 349, a substantial savings from the 603. This is an example of economies of scope.

		Amount of Y
		0	10	20	30	40
Amount of X	0	*102*	*154*	*206*	*257*	*301*
	10	*159*	*198*	*239*	*274*	*317*
	20	*204*	*230*	*275*	*293*	*326*
	30	*255*	*277*	*297*	*312*	*334*
	40	*302*	*316*	*329*	*333*	*349*

To examine economies of scale, meanwhile, you would want to examine a column or row in the table. For example, what happens to the unit cost of production of X as we increase production from 20 to 40? It rises from 206 to 301. The doubling of output was accomplished with less than a doubling of cost so the cost per unit fell from 10.4 to 6.5 - an example of increasing returns to scale.

How do we measure costs? To many the answer seems obvious, but as you will recall from our earlier analysis of the cost of a year's education, obvious is not always correct. When economists talk about costs they are always concerned with economic cost which can be very different from accounting cost. The first example of where this would be relevant to a firm's choice was the situation facing Stephen Works, the owner of a rapidly expanding computer services business. In this example we saw that economic profit could be negative even when the accountant's books indicated a profit.

Differences between economic and accounting profit would also surface in situations where a business had money tied up in the business. For example, let's look at Tammy's Tutoring, a for-profit tutoring service. To run her business Tammy must maintain a balance of $1,000 a day in her company checking account. The accountant would not consider this money that sits in a checking account as a cost of doing business and it would therefore not enter the books. An economist, meanwhile, would look at the money and ask: what else could be done with the money? If we assume that a reasonably safe investment would produce a return of 8 percent, then the economic cost of these funds being tied up would be $80 [.08*$1,000]. By staying in the tutoring business, Tammy is losing the opportunity to earn $80 a year with her $1,000 cash and economists would have this reflected in the 'economic' books. Economic profit would be $80 lower than accounting profit.

For a third example of the differences between the two costs we could look at the books of Gene's Graphics. Gene was a very successful Silicon Valley engineer making $100,000 a year working for a software company. The problem is that Gene wanted to try something new, wanted to get on the entrepreneurial bandwagon and form a start-up company. The company was Gene's Graphics and the product was tutorial software for ECN courses. At the end of the first year's operation Gene had an accountant and economist review the year. The accountant's review of the books indicated that Gene had drawn a salary of $60,000 and that the company's total revenues had exceeded costs by $20,000. The accountant reported that the company earned Gene a profit of $20,000.

The economist, however, reported back that Gene had lost $20,000. As the economist saw it, Gene had the ability to earn $100,000 a year and the cost of Gene's labor on the books should be $100,000 rather than the $60,000 salary. If we computed costs on this basis, then total costs of operation would have risen $40,000 and the $20,000 profit would have become a $20,000 loss.

These examples clearly demonstrate that economic and accounting profits are not the same since economic and accounting costs are not the same. In all of the diagrams and tables you will see in our analysis of firms we will always be talking about economic cost and economic profit. Once we decide to focus on economic costs, however, we must recognize what the existence of economic profit means. The existence of economic profit in some business simply means that some resource is earning more in that business than it could in its best alternative use and, as we will see later, this will act as a signal to owners of that resource to move the resource into that industry.

In the case of Gene, if the salary drawn at Gene's Graphics had been $140,000, then other engineers are likely to have followed Gene's lead and leave their companies to form start ups where they could make substantially more money. As it is, where the owners of the start-ups are actually making less than they had as engineers, you would be likely to see exits from the start-ups and people returning to their engineering jobs.

Now it is time to move to the revenue side of the firm's finances and then combine the revenue and cost information to examine the choices made by firms. First, however, you might want to check out the graphs.

We have now looked at the relationship between outputs and inputs using a simple example of a tutoring "business." Here we will look at the graphs that go with this example. Each one of these graphs corresponds to a column in one of the tables so you will see the same information, its simply presented in a different way. We will look first at the production relationship where we will be able to "see" diminishing marginal product. This will be followed by the cost curves where we will "see" increasing marginal cost.

Total (physical) product: amount of output obtained from given input. The positive slope indicates that output increases as the input increases.

Average (physical) product: amount of output obtained per unit of input. This is calculated by dividing total output by number of units of inputs.

Marginal (physical) product: additional output obtained by 1 more unit of input. You will note the marginal product curve has a negative slope after 3 units of input are used which indicates that if you keep adding labor to an operation with a fixed facility, eventually the additional output produced by the additional labor will begin to decline. When this happens we enter a situation in which we have diminishing marginal product.

One of the features of the graph is that the MP curve cuts through the maximum point on the AP curve.

When you see cost curves they tend to come in two sets. The first set includes some combination of the total cost concepts - Total Cost, Variable Cost, and Fixed Cost. The second set would include some combination of the average and marginal cost concepts - Average Total Cost, Average Variable Cost, Average Fixed Cost, and Marginal Cost. The reason there are two very distinct sets of graphs is the two sets have very different orders of magnitude. Total costs may be in millions of dollars, while average or marginal costs may be in terms of dollars. In our example the orders of magnitude are not that different, but the ranges for the total cost variables are different from the range for the average, and marginal variables.

You will find there is a relationship between average and marginal cost curves. The marginal cost curve and average cost curves tend to be U-shaped and the marginal cost curve cuts through the average cost curves at their minimum points.