PRODUCTION AND COST

At the beginning of the course, we discussed production possibilities for a society. We had production relations for two goods, and two inputs, or factors of production.

100W*[1 pound per day/W] + 50N*[2 pounds per day/N]

=> 200 pounds of fish per day

The two factors of production, workers and nets, combined to produce fish. In this case, all resources were used to produce fish.

The technology is simple: 1 worker => 1 LB of fish per day

1 net => 2 LB of fish per day

No matter how many workers or nets we use, we always get 1 Lb. of fish per day, and 2 Lb. of fish per day, respectively.

This means, every time we add a worker to the fish-pond, we get one additional pound of fish. Every time we add a net to the fish-pond, we get 2 additional pounds of fish.

This phenomenon is called constant marginal returns. Each additional input [additional worker or additional net], produces the same amount of additional output.

DQ/DW = 1 LB of fish, no matter how many workers are added.

This ratio is called the marginal physical product of labor , the change in output caused by a change in labor employed.    It is constant under constant marginal returns.

Marginal Physical Product of a variable input (DQ/DW): The change in output as one more unit of input is employed.

Average Physical Product (Q/W): Total output divided by the amount of the input employed.

Total Physical Product = Total Output = Q

Economists usually assume that production technologies have diminishing marginal returns, or, diminishing marginal product:

Diminishing Marginal Product: Marginal product declines as additional units of one input are added, and the amounts of all other inputs are held constant.

EXAMPLE
Total Output (Q) Land (acres) Labor (workers) Average Product of Labor (Q/L) Marginal Product of Labor (DQ/DL)
0 Bushels 5 Acres
0
UNDEFINED
 
       
10 Bushels
10 Bushels 5 Acres
1
10 Bushels
 
15 Bushels
25 Bushels  5 Acres
2
12.5 Bushels
12 Bushels 
37 Bushels 5 Acres
3
12.3 Bushels
 
          10 Bushels
47 Bushels 5 Acres
4
11.7 Bushels
 
          8 Bushels
55 Bushels 5 Acres
5
11 Bushels
 
          5 Bushels
60 Bushels 5 Acres
6
10 Bushels
 
          2 Bushels
62 Bushels 5 Acres
7
8.9 Bushels
 
          1 Bushels
63 Bushels 5 Acres
8
7.9 Bushels
 

Graph of total output

Relation of Marginal and Average:

When a marginal outcome is greater than the average outcome, the average is pulled up.

When a marginal outcome is less than the average outcome, the average is pulled down.

All of you deal with marginal and average outcomes each term, when your grade point average for the term causes changes in your grade point average for your career.

Suppose you are a first-year student, take 15 credits this Fall, your first term at Rutgers. You enroll in 5 courses, each of which is worth 3 credits. At the end of the Fall term, you receive three A's and two B's.

9 credits x 4 grade points = 36 grade point credits (gpc for short)

+ 6 credits x 3 grade points = 18 gpc

54 gpc

Grade point average [grade points per credit] for Fall = 54/15 = 3.6

Career Average at the end of your first term = 3.6.

Now, suppose next term you take 15 credits, and get 2 A's and 3 B's. Your GPA for the Spring term will be:

24 gpc + 27 gpc = 51, Spring GPA = 3.47

Career GPA, your average over the Fall and Spring terms: At the end of your first year, you received 54 gpc + 51 gpc = 105 gpc. Your total credits for the two terms is 30.

Therefore, your career GPA at the end of your first year in college is 105gpc/30 credits = 3.5

The lower Spring GPA "Pulled Down" your career average, from 3.6 at the end of the Fall term, to 3.5 at the end of the Spring term.

Your "Marginal Performance", i.e., your performance in Spring, pulled down your average.

If your Spring GPA was higher that your Fall GPA, your Lifetime Average would have risen.
 
 

Similarly, when MPP is below APP, the APP is pulled down. When MPP is above APP, APP is pulled up.

With eventual diminishing marginal returns, APP looks like an upside down bowl. MPP will cross it at its maximum.

Graph of Average product and Marginal Product

COST STRUCTURE

In the example we have above, assume that land rents for $1000 per growing season. The price of one worker per growing season is $3000. What is the cost structure for this type of farm?
Total Output Land Labor Total Cost
0 Bushels 5 acres 0 workers $1000
10 Bushels 5 acres 1 worker $4000
25 Bushels 5 acres 2 workers $7000
37 Bushels 5 acres 3 workers $10,000
47 Bushels 5 acres 4 workers $13,000
55 Bushels 5 acres 5 workers $16,000
60 Bushels 5 acres 6 workers $19,000
62 Bushels 5 acres 7 workers $22,000
63 Bushels 5 acres 8 workers $25,000
       
From this table, we can construct the concepts: Total Cost, Average Cost and Marginal Cost.
Total Output(Q) Total Cost(TC) Average Cost (TC/Q)  Marginal Cost = (DC/DQ)
0 Bushels $1000 Undefined  
      $3000/10 = $300
10 Bushels $4000 $400  
      $3000/15 = $200
25 Bushels $7000 $280  
      $3000/12 = $250
37 Bushels $10,000 $271  
      $3000/10 = $300
47 Bushels $13,000 $276  
      $3000/8 = $375
55 Bushels $16,000 $290  
      $3000/5 = $600
60 Bushels $19,000 $316  
      $3000/2 = $1500
62 Bushels $22,000 $355  
      $3000/1 = $3000
63 Bushels $25,000 $396  

The diminishing marginal product of labor we saw above leads to an increasing marginal cost of production. In fact, the shape of the Total Cost or TC curve is the mirror image of the Total Product , or Q, function. Similarly, Average Cost is the mirror image of Average Product, and Marginal Cost is the mirror image of Marginal Product.

 Graph of Total Cost        Graph of Average Cost and Marginal Cost.

SHORT RUN COSTS

Total costs are composed of two parts, those that must be paid for fixed factors of production, like the rent on land in the example above, and those that must be paid for variable factors of production, like wages of labor.

Total Costs = Fixed Costs + Variable Costs

TC = FC + VC

Just as AC is cost per unit produce,

Average Variable Cost: AVC = VC/Q

Average Fixed Cost: AFC = FC/Q

Therefore,  dividing TC by Q, we get:

    TC/Q = FC/Q + VC/Q
or
     AC = AFC + AVC

Below, we have a table showing all these cost terms for a hypothetical firm.
 
 
 
Q(units of output)
TC($)
MC($ per unit)= DTC/DQ
FC($)
VC($)
AC($/unit)=TC/Q
AFC($/unit)=FC/Q
AVC($/unit)=VC/Q
0
100
 
100
0
 
 
 
 
 
90
 
 
 
 
 
1
190
 
100
90
190
100
90
 
 
80
 
 
 
 
 
2
270
 
100
170
185
50
85
 
 
100
 
 
 
 
 
3
370
 
100
270
123.33
33.33
90
 
 
120
 
 
 
 
 
4
490
 
100
390
122.5
25
97.5
 
 
140
 
 
 
 
 
5
630
 
100
530
126
20
106
 
 
160
 
 
 
 
 
6
790
 
100
690
131.67
16.67
115
 
 
180
 
 
 
 
 
7
970
 
100
870
138.57
14.29
124.29
 
 
200
 
 
 
 
 
8
1170
 
100
1070
148.25
12.5
133.75
Notice that TC is a function of Q, and so is VC. Notice also that MC is also marginal variable cost! On a graph, this means that Total Cost and Variable Cost must have the same slope at each value of Q. This is shown here. FC is the difference between the two curves.

The data in the MC, AC, AVC, and AFC columns of the table must be graphed on a diagram with $/Q on the vertical axis, and Q on the horizontal axis. This diagram represents the a firm's cost structure in the short run, and will help us see how the firm decides on its optimal output.

PROFIT MAXIMIZATION:

We assume that firms have one motive for operating in the short run; they want to maximize profits.

Profit = Total Revenue - Total Cost

These are Economic Profits. This is what we assume firms want to maximize.

There is another type of profit we must mention. As we said above, Total Costs = Fixed Costs + Variable Costs. One of the components of Fixed Costs is the opportunity cost of the owner of the firm, or, of the entrepreneur. These opportunity costs are call normal profits.

If an owner or entrepreneur of a firm does not earn at least as much as he or she could earn in another line of work, he or she will stop operating the firm, and go to that other job. Thus, a firm must earn at least normal profits for the owner to stay in the business. Economic profits are profits in excess of normal profits, i.e., profits above and beyond the payment of all costs, including normal profits.

RULE FOR MAXIMIZING PROFITS: To maximize profits, a firm will choose the quantify of output that sets the marginal revenue equal to marginal cost.

Marginal Revenue is the change in revenue caused by selling an additional unit of output:

MR =DTR/DQ = D[P*Q]/Q
 

OR, MR = P[1 - 1/e] where e = price elasticity of demand
 

The profit maximizing rule says that a firm will sell output at the point where the last unit of output sold creates enough additional revenue to equal the increase in cost that is incurred to make that unit of output; MR = MC.

NOTE: The quantity that maximizes profit will not be the quantity that maximizes revenue, unless all costs are zero!

More on Economic Profit:We can re-write the equation for economic profit many ways, using what we know about average cost, average variable cost, and average fixed costs.

Economic Profit = Total Revenue -Total Cost

                          = P*Q - AC*Q since TC = AC/Q

                          = [P-AC]*Q

Also, Economic Profit = P*Q -[FC + VC] since TC = FC + VC

                                = P*Q - AFC*Q - AVC*Q since AFC = FC/Q and  AVC = VC/Q

                                = [P-AVC]*Q - AFC*Q

                                = [P-AVC]*Q - FC
 

PRICE-TAKING FIRMS:

Some firms have the ability to affect price when they decide how much to produce, and some don't. For the moment, we are going to analyze a case in which a firm has no power over price: It is a price-taking firm. This means that the firm is rather relatively small, so that its output is only a very small part of the total market output.

Specifically, a price taking firm may be in a perfectly competitive industry. Such an industry has the following characteristics:

1. Many, small firms.

2. The firms produce a homogeneous or identical product.

3. There is perfect information, so that all consumers and firms know the good is homogeneous, know the firms are small, and know the market price.

4. There is free entry; anyone who wants to, can get their capital together and start a firm to participate in the industry.

Firms in this situation know that no matter how much output they produce, they will not affect the price of the good they are selling. The demand curve the firm faces for its output is horizontal, perfectly elastic, at the market price.

In this situation, when the firm is a price-taker, the price of the product is also the marginal revenue to the firm. That is, every time the firm sells an additional unit of output, it receives an addition to revenue equal to the market price.

A price-taking or perfectly competitive firm, then, maximizes economic profit by picking the quantity that sets MR = MC.

But, for this type of firm, P = MR. Therefore, the firm will pick the quantity at which P = MC.

We have an example of a price-taking or perfectly competitive below:

Let P = $8. Then, we have:
 
MR TR=PxQ Q TC MC Profit MR-MC
 
0
0
$5
 
-$5
 
$8
 
 
 
$4
 
$4
 
$8
1
$9
 
-$1
 
$8
 
 
 
$1
 
$7
 
$16
2
$10
 
$6
 
$8
 
 
 
$4
 
$4
 
$24
3
$14
 
$10
 
$8
 
 
 
$8
 
0
 
$32
4
$22
 
$10
 
$8
 
 
 
$10
 
-$10
 
$40
5
$32
 
$8
 
$8
 
 
 
$12
 
-$4
 
$48
6
$44
 
$4
 
$8
 
 
 
$16
 
-$8
 
$56
7
$60
 
-$4
 
Notice that P = MR, since P never changes when Q changes.

The quantity that will maximize economic profit must occur where MR = MC, or, where Marginal Profit = MR - MC = 0. This occurs at the quantity Q = 4.

You will notice that maximum profit occurs twice in this example, at Q = 3 and Q = 4. This happens sometimes, but it is always true that the maximum will occur where MR = MC. Use that rule, and you will never go wrong.

On a diagram, our problem and its solution would look as follows.

What would happen if the price rose, to $10, for example. We would have to recalculate the revenue part of the table to determine profit, but the costs side of the table does not change. Our new table would look like the one below.

Let P = $10. Then, we have:
 
 
MR TR=PxQ Q TC MC Profit MR-MC
 
0
0
$5
 
-$5
 
$10
 
 
 
$4
 
$6
 
$10
1
$9
 
$1
 
$10
 
 
 
$1
 
$9
 
$20
2
$10
 
$10
 
$10
 
 
 
$4
 
$6
 
$30
3
$14
 
$16
 
$10
 
 
 
$8
 
$2
 
$40
4
$22
 
$18
 
$10
 
 
 
$10
 
0
 
$50
5
$32
 
$18
 
$10
 
 
 
$12
 
-$2
 
$60
6
$44
 
$16
 
$10
 
 
 
$16
 
-$6
 
$70
7
$60
 
$10
 
Again, we see that P = MR. The quantity that maximizes economic profit in this case is Q = 5, where MR = MC.

Thus, if the price of the good rises, a perfectly competitive firm, a price taker, will increase output. It will always choose the Q where MR = MC.

BREAKEVEN POINT: In a perfectly competitive industry, we have free entry, as we said above. This means that other entrpreneurs will notice is economic profits are being made in an industry, and will be tempted to start a business in that industry. For example, if you know that the computer software business is profitable for the firms now operating in it, you may decided to start your own software company.

As firms enter the industry, the supply of the commodity being sold will rise, and the price in the market will fall. There will be more firms operating in the industry, but each one will be making less economic profits than the typical firm did before entry occurred. This process will continue, until the level of maximum economic profits that can be earned by a firm in the industry become zero.

At this point, all firms in the industry are earning normal profits, so they are willing to stay in the industry, but there are no economic profits being earned, so there is no incentive for new firms to enter any longer. We reach an equilibrium, where each firm is earning maximum economic profits of zero, but making enough to cover all costs, including normal profits or opportunity costs of the entrepreneur.

The quantity where maximum economic profits are zero must occur where MR = MC. Since P = MR for price-taking firms, then P = MC. For the firm to break-even, total revenue must equal total costs. Using one of our alternate equations for profit, we find:

Economic Profit = [P-AC]*Q

For this to be zero, and Q to be positive, we must have P = AC. But, as we said, we must also have P = MC. The only point at which P = MC = AC is at the minimum of the AC curve. So, the break-even point of a price-taking, or perfectly competitive, firm, occurs when the profit maximizing quantity is the quantity at the minimum of the AC curve. If price falls so low that P = MC where MC = min AC, then the firm will maximize economic profits, and break-even. In the diagram below, the point labeled B is the break-even point. The quantity at this point is sometimes called the capacity of the firms production facility.

SHUTDOWN POINT: If the price continues to fall below the break-even level, the firm will start to lose money, even though it is maximizing its profits. In this case, if P < min AC, the firm will have negative maximum economic profits.

How low can the price fall before the owner of the firm will give up and leave the business?

If the firm shuts-down, and stops operating, it will suffer losses equal to its fixed costs, since these must be paid in the short run, where anything is produced or not. So, the owner of the firm knows that as long as he or she is losing less than the value of fixed cost, it pays to operate in the short run.

If maximum economic profits are equal to minus fixed costs, then the firm is no worse off by shutting down then by operating. At what quantity will the firm find the maximum economic profits equal minus fixed costs?

If the firm is maximizing profits, then it is picking Q so that P = MR is set equal to MC. Lets look at one of our alternative equations for profit again.

Economic Profit = [P- AVC]*Q - FC*Q

We can see from this equation, that is P = AVC, then maximum profits will equal -FC, and the firm will face a shutdown decision in the short run. How can this happen?

If can only happen if P = MR = MC where P = AVC. This can only happen where MC = AVC, and, as we saw earlier, MC = AVC at the minimum of AVC.

Therefore, if price in the market falls so low that the quantity which maximizes economic profit is at the minimum of the AVC curve, so that P = MR = MC = min AVC, then,
Max Economic Profit = - FC, and the firm faces a shutdown decision.

SUPPLY CURVE OF A PERFECTLY COMPETITIVE FIRM:

Our discussion of the break even point and the shutdown point shows us something else. Perfectly competitive or price taking firms always choose to produce where P = MC, since they maximize profit, so MR = MC, and P = MR for these kinds of firms. Therefore, if the market establishes a price, the firm will be willing and able to produce the quantity at which P = MC. This is true for any price at or above the shutdown point, i.e., at or above the min AVC. This tells us the following:

The supply curve of a perfectly competitive firm is the marginal cost curve at and above the shutdown point.