0. 7 Production and Cost in the Firm How do economists calculate profit?
What is a production function? What is marginal product? How are they related?
What are the various costs, and how are they related to each other and to output?
How are costs different in the short run vs. the long run?
What are “economies of scale”?

1. Total Revenue, Total Cost, Profit
We assume that the firm’s goal is to maximize profit.
Profit = Total revenue – Total cost
the amount a firm receives from the sale of its output
the market value of the inputs a firm uses in production

2. Costs: Explicit vs. Implicit
Explicit costs – actual cash payments for resources, such as paying wages to workers
Implicit costs – opportunity cost of using owner-supplied resources, such as the opportunity cost of the owner’s time
Remember: The cost of something is the value of the next best alternative.
This is true whether the costs are implicit or explicit. Both matter for a firm’s decisions.

3. Explicit vs. Implicit Costs: An Example
Suppose you need $100,000 to start your business. The interest rate is 5%.
Case 1: borrow $100,000
explicit cost =
Case 2: use $40,000 of your savings, borrow the other $60,000
implicit cost =

4. Economic Profit vs. Accounting Profit
Accounting profit
= total revenue minus total explicit costs
Economic profit
= total revenue minus total costs (including BOTH explicit and implicit costs)
Accounting profit ignores implicit costs, so it will be greater than economic profit.

5. A C T I V E L E A R N I N G 2: Economic profit vs. accounting profit
The equilibrium rent on office space has just increased by $500 per month.
Compare the effects on your firm’s accounting profit and economic profit if
a. you rent your office space
b. you own your office space 5

6. Production in the Short Run
Some resources are considered to be variable and some are considered to be fixed.
It depends on how quickly the level can be altered to change the rate of output.
In the short run, at least one resource is fixed.
In the long run, all resources are variable.

7. The Production Function
A production function shows the relationship between the quantity of inputs used to produce a good, and the quantity of output of that good.
It can be represented by a table, equation, or graph.
Example 1:
Farmer Jack grows wheat.
He has 5 acres of land.
He can hire as many workers as he wants.

8. EXAMPLE 1: Farmer Jack’s Production Function
500
1,000
1,500
2,000
2,500
3,000 1 2 3 4 5
# of workers
Quantity of output
Q (bushels of wheat)
L (# of workers)
1,000 1
1,800 2
2,400 3
2,800 4
3,000 5

9. Marginal Product
The marginal product of any input is the increase in output arising from an additional unit of that input, holding all other inputs constant.
If Farmer Jack hires one more worker, his output rises by the marginal product of labor.
Marginal product of labor (MPL) = ∆Q ∆L

10. EXAMPLE 1: Total & Marginal Product
3,000 5
2,800 4
2,400 3
1,800 2
1,000 1
Q (bushels of wheat)
L (# of workers)
MPL
∆Q = 1,000
∆L = 1
∆Q = 800
∆L = 1
∆Q = 600
∆L = 1
∆Q = 400
∆L = 1
∆Q = 200
∆L = 1

11. EXAMPLE 1: MPL = Slope of Prod. Function
500
1,000
1,500
2,000
2,500
3,000 1 2 3 4 5
No. of workers
Quantity of output
L (# of workers)
Q (bushels of wheat)
MPL
MPL equals the slope of the production function.
Notice that MPL diminishes as L increases.
This explains why the production function gets flatter as L increases.
1,000 1
1,000
800 2
1,800
600 3
2,400
400 4
2,800
200 5
3,000

12. Why MPL Is Important
Recall from Chapter 1: Rational people choose actions for which the expected marginal benefit exceeds the expected marginal cost.
When Farmer Jack hires an extra worker,
his costs rise by the wage he pays the worker
his output rises by MPL
Comparing the wage and the change in his output helps Jack decide whether he would benefit from hiring the worker.

13. EXAMPLE 2: A “Fold-It” Factory
We are going to create a factory that produces a product known as a “fold-it”
Resources:
factory
paper
stapler
staples
labor

14. Why MPL Diminishes
The Law of Diminishing Marginal Returns: the marginal product of a variable resource eventually falls as the quantity of the resource used increases (other things equal)
If we increases the # of workers but not the # of staplers or the desk area, each add’l worker has less to work with and will be less productive.
In general, MPL diminishes as L rises whether the fixed resource is land (as would be the case with Jack the wheat farmer) or capital (our desk and stapler).

15. EXAMPLE 1: Farmer Jack’s Costs
Farmer Jack must pay $1,000 per month for the land, regardless of how much wheat he grows.
The market wage for a farm worker is $2,000 per month.
So Farmer Jack’s costs are related to how much wheat he produces….

16. EXAMPLE 1: Farmer Jack’s Costs
L (# of workers)
Q (bushels of wheat)
Cost of land
Cost of labor
Total Cost 1
1,000 2
1,800 3
2,400 4
2,800 5
3,000

17. EXAMPLE 1: Farmer Jack’s Total Cost Curve
Q (bushels of wheat)
Total Cost
$1,000
1,000
$3,000
1,800
$5,000
2,400
$7,000
2,800
$9,000
3,000
$11,000

18. Marginal Cost
Marginal Cost (MC) is the increase in Total Cost from producing one more unit:
∆TC ∆Q
MC =

19. EXAMPLE 1: Total and Marginal Cost
$11,000
$9,000
$7,000
$5,000
$3,000
$1,000
Total Cost
3,000
2,800
2,400
1,800
1,000
Q (bushels of wheat)
Marginal Cost (MC)
∆Q = 1000
∆TC = $2000
$2.00
∆Q = 800
∆TC = $2000
$2.50
∆Q = 600
∆TC = $2000
$3.33
∆Q = 400
∆TC = $2000
$5.00
∆Q = 200
∆TC = $2000
$10.00

20. EXAMPLE 1: The Marginal Cost Curve
Q (bushels of wheat) TC MC
MC usually rises as Q rises, as in this example.
$1,000
$10.00
$5.00
$3.33
$2.50
$2.00
1,000
$3,000
1,800
$5,000
2,400
$7,000
2,800
$9,000
3,000
$11,000

21. Why MC Is Important
Farmer Jack is rational and wants to maximize his profit. To increase profit, should he produce more wheat or less?
To find the answer, Farmer Jack needs to “think at the margin.”
If the cost of an additional bushel of wheat (MC) is less than the revenue he would get from selling it, Jack’s profits rise if he produces more.
(In the next chapter, we will learn more about how firms choose Q to maximize their profits.)

22. EXAMPLE 3
Our third example is more general, and applies to any type of firm producing any good with any types of resources.

23. EXAMPLE 3: Costs Q FC VC TC 100 $100 520 380 280 210 160 120 70 $0 1 2
$800 FC Q FC VC TC VC
$700
100
$100
520
380
280
210
160
120 70 $0 TC
$600 1
$500 2
Costs
$400 3
$300 4
$200 5
$100 6 $0 7 1 2 3 4 5 6 7 Q

24. EXAMPLE 3: Marginal CostQ TC MC
Recall, Marginal Cost (MC) is the change in total cost from producing one more unit:
$100
$70 1
170
∆TC ∆Q
MC = 50 2
220 40 3
260
Usually, MC rises as Q rises, due to diminishing marginal product.
Sometimes (as here), MC falls before rising.
(In other examples, MC may be constant.) 50 4
310 70 5
380
100 6
480
140 7
620

25. EXAMPLE 3: Average Fixed CostQ FC
AFC
Average fixed cost (AFC) is fixed cost divided by the quantity of output:
AFC = FC/Q
$100
---- 1
100 2
100 3
100
Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units. 4
100 5
100 6
100 7
100

26. EXAMPLE 3: Average Variable CostQ VC
AVC
Average variable cost (AVC) is variable cost divided by the quantity of output:
AVC = VC/Q $0
---- 1 70 2
120 3
160
As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises. 4
210 5
280 6
380 7
520

27. EXAMPLE 3: Average Total Cost
Average total cost (ATC) equals total cost divided by the quantity of output:
ATC = TC/Q Q TC
ATC
74.29
14.29
63.33
16.67
56.00 20
52.50 25
53.33
33.33 60 50
$70
$100
----
AVC
AFC
$100 1
170 2
220 3
260
Also,
ATC = AFC + AVC 4
310 5
380 6
480 7
620

28. EXAMPLE 3: Average Total Cost$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs Q TC
ATC
Usually, as in this example, the ATC curve is U-shaped.
$100
---- 1
170
$170 2
220
110 3
260
86.67 4
310
77.50 5
380 76 6
480 80 7
620
88.57

29. EXAMPLE 3: The Cost Curves Together$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs
ATC
AVC
AFC MC

30. A C T I V E L E A R N I N G 3: Costs
Fill in the blank spaces of this table. Q VC TC
AFC
AVC
ATC MC
$50
----
----
----
$10 1 10
$10
$60.00 2 30 80 30 3
16.67 20
36.67 4
100
150
12.50
37.50 5
150 30 60 6
210
260
8.33 35
43.33 30

31. EXAMPLE 3: Why ATC Is Usually U-shaped$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs
As Q rises:
Initially, falling AFC pulls ATC down.
Eventually, rising AVC pulls ATC up.

32. EXAMPLE 3: ATC and MC When MC < ATC, ATC ATC is falling.$0
$25
$50
$75
$100
$125
$150
$175
$200 1 2 3 4 5 6 7 Q
Costs
When MC < ATC,
ATC is falling.
When MC > ATC,
ATC is rising.
The MC curve crosses the ATC curve at the ATC curve’s minimum.
ATC MC
A student’s GPA is like ATC. The grade she earns in her next course is like MC. If her next grade (MC) is less than her GPA (ATC), then her GPA will fall. If her next grade (MC) is greater than her GPA (ATC), then her GPA will rise.
You run a pizza joint. You’re producing 100 pizzas per night, and your cost per pizza (ATC) is $3. The cost of producing one more pizza (MC) is $2. If you produce this pizza, what happens to ATC? Most students will understand immediately that ATC falls (albeit by a small amount). Instead, suppose the cost of producing one more pizza (MC) is $4. Then, producing this additional pizza causes ATC to rise.
Point out that the same relationship exists between AVC and MC.

33. Costs in the Long Run Short run: Some inputs are fixed
Long run: All inputs are variable (firms can build new factories, or remodel or sell existing ones)
In the long run, ATC at any Q is cost per unit using the most efficient mix of inputs for that Q (the factory size with the lowest ATC).

34. EXAMPLE 4: LRAC with 3 Factory Sizes
Firm can choose from 3 factory sizes: S, M, L.
Each size has its own SRATC curve.
The firm can change to a different factory size in the long run, but not in the short run. Q
Cost
($)
ATCS
ATCM
ATCL

35. EXAMPLE 4: LRAC with 3 Factory SizesQ
Cost
($)
ATCS
ATCM
ATCL
LRATC QA QB

36. A Typical LRAC Curve
In the real world, factories come in many sizes, each with its own SRATC curve.
So a typical LRAC curve looks like this: Q
Cost
LRAC

37. How LRAC Changes as the Scale of Production Changes
Economies of scale: LRAC falls as Q increases.
Constant returns to scale: LRAC stays the same as Q increases.
Diseconomies of scale: LRAC rises as Q increases. Q
Cost
LRAC