This document provides data on the costs of producing hot dogs per hour for a business. It includes the fixed costs (FC), variable costs (VC), total costs (TC), average fixed costs (AFC), average variable costs (AVC), average total costs (ATC), and marginal costs (MC) for outputs ranging from 0 to 10 hot dogs per hour. It instructs the reader to graph MC in red, ATC in blue, AVC in green, and AFC in black based on this data.

1. Bellringer Mankiw Chapter 13 Costs
1. Calculate the TC, FC, VC, AFC, AVC, ATC, MC
2. on the back of the page graph in red MC, blue ATC,
green AVC, black AFC

2. Hot
dogs
per
hour
FC
VC
0
$3
$0
Total
Cost
AFC
AVC
ATC
MC
Hot
dogs
per
hour
FC
VC
------
0
$3
$0
1
$0.30
1
$0.30
2
$0.80
2
$0.80
3
$1.50
3
$1.50
4
$2.40
4
$2.40
5
$3.50
5
$3.50
6
$4.80
6
$4.80
7
$6.30
7
$6.30
8
$8.00
8
$8.00
9
$9.90
9
$9.90
10
$12.00
10
$12.00
Total
Cost
AFC
AVC
ATC
MC
------

5. 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.
THE COSTS OF PRODUCTION
5

6. Example 1: Farmer Jack’s Production Function
Q
(no. of (bushels
workers) of wheat)
3,000
Quantity of output
L
2,500
0
0
1
1000
2
1800
3
2400
500
4
2800
0
5
3000
THE COSTS OF PRODUCTION
2,000
1,500
1,000
0
1
2
3
4
5
No. of workers
6

7. Marginal Product
 If Jack hires one more worker, his output rises
by the marginal product of labor.
 The marginal product of any input is the
increase in output arising from an additional unit
of that input, holding all other inputs constant.
 Notation:
∆ (delta) = “change in…”

Examples:
∆Q = change in output, ∆L = change in labor
∆Q
Marginal product of labor (MPL) =
∆L
THE COSTS OF PRODUCTION
7

8. EXAMPLE 1: Total & Marginal Product
L
Q
(no. of (bushels
workers) of wheat)
∆L = 1
∆L = 1
∆L = 1
∆L = 1
∆L = 1
0
0
1
1000
2
1800
3
2400
4
2800
5
3000
THE COSTS OF PRODUCTION
MPL
∆Q = 1000
1000
∆Q = 800
800
∆Q = 600
600
∆Q = 400
400
∆Q = 200
200
8

9. EXAMPLE 1: MPL = Slope of Prod Function
Q
(no. of (bushels MPL
workers) of wheat)
0
1
2
3
4
5
0
1000
1800
2400
2800
3000
1000
800
600
400
200
THE COSTS OF PRODUCTION
3,000
MPL
Quantity of output
L
equals the
slope of the
2,500
production function.
2,000
Notice that
MPL
1,500 diminishes
as L increases.
1,000
This explains why
500
the production
function gets flatter
0
as L0increases. 3
1
2
4
5
No. of workers
9

10. Why MPL Is Important
 Recall one of the Ten Principles:
Rational people think at the margin.
 When Farmer Jack hires an extra worker,
 his costs rise by the wage he pays the worker
 his output rises by MPL
 Comparing them helps Jack decide whether he
would benefit from hiring the worker.
THE COSTS OF PRODUCTION
10

11. Why MPL Diminishes
 Farmer Jack’s output rises by a smaller and
smaller amount for each additional worker. Why?
 As Jack adds workers, the average worker has
less land to work with and will be less productive.
 In general, MPL diminishes as L rises
whether the fixed input is land or capital
(equipment, machines, etc.).
 Diminishing marginal product:
the marginal product of an input declines as the
quantity of the input increases (other things equal)
THE COSTS OF PRODUCTION
11

12. EXAMPLE 1: Farmer Jack’s Costs
 Farmer Jack must pay $1000 per month for the
land, regardless of how much wheat he grows.
 The market wage for a farm worker is $2000 per
month.
 So Farmer Jack’s costs are related to how much
wheat he produces….
THE COSTS OF PRODUCTION
12

13. EXAMPLE 1: Farmer Jack’s Costs
L
Q
Cost of
(no. of (bushels
land
workers) of wheat)
Cost of
labor
Total
Cost
0
0
$1,000
$0
$1,000
1
1000
$1,000
$2,000
$3,000
2
1800
$1,000
$4,000
$5,000
3
2400
$1,000
$6,000
$7,000
4
2800
$1,000
$8,000
$9,000
5
3000
$1,000 $10,000
$11,000
THE COSTS OF PRODUCTION
13

14. EXAMPLE 1: Farmer Jack’s Total Cost Curve
0
$12,000
Total
Cost
$1,000
1000
$3,000
1800
$5,000
2400
$7,000
2800
$9,000
3000
$10,000
Total cost
Q
(bushels
of wheat)
$11,000
THE COSTS OF PRODUCTION
$8,000
$6,000
$4,000
$2,000
$0
0
1000
2000
3000
Quantity of wheat
14

15. Marginal Cost
 Marginal Cost (MC)
is the increase in Total Cost from
producing one more unit:
∆TC
MC =
∆Q
THE COSTS OF PRODUCTION
15

16. EXAMPLE 1: Total and Marginal Cost
Q
Total
(bushels
Cost
of wheat)
∆Q = 1000
∆Q = 800
∆Q = 600
∆Q = 400
∆Q = 200
0
$1,000
1000
$3,000
1800
$5,000
2400
$7,000
2800
$9,000
3000 $11,000
THE COSTS OF PRODUCTION
Marginal
Cost (MC)
∆TC = $2000
$2.00
∆TC = $2000
$2.50
∆TC = $2000
$3.33
∆TC = $2000
$5.00
∆TC = $2000
$10.00
16

17. EXAMPLE 1: The Marginal Cost Curve
0
TC
MC
$1,000
1000
$3,000
1800
$5,000
2400
$7,000
2800
$9,000
3000 $11,000
$2.00
$2.50
$3.33
$10
Marginal Cost ($)
Q
(bushels
of wheat)
$12
$8
MC usually rises
as Q rises,
as in this example.
$6
$4
$2
$5.00
$10.00
THE COSTS OF PRODUCTION
$0
0
1,000
2,000
3,000
Q
17

18. Why MC Is Important
 Farmer Jack is rational and wants to maximize
his profit. To increase profit, should he produce
more or less wheat?
 To find the answer, Farmer Jack needs to
“think at the margin.”
 If the cost of additional wheat (MC) is less than
the revenue he would get from selling it,
then Jack’s profits rise if he produces more.
THE COSTS OF PRODUCTION
18

19. Fixed and Variable Costs
 Fixed costs (FC) do not vary with the quantity of
output produced.
 For Farmer Jack, FC = $1000 for his land
 Other examples:
cost of equipment, loan payments, rent
 Variable costs (VC) vary with the quantity
produced.
 For Farmer Jack, VC = wages he pays workers
 Other example: cost of materials
 Total cost (TC) = FC + VC
THE COSTS OF PRODUCTION
19

20. EXAMPLE 2
 Our second example is more general,
applies to any type of firm
producing any good with any types of inputs.
THE COSTS OF PRODUCTION
20

21. EXAMPLE 2: Costs
Q
FC
VC
$800
$700
TC
FC
VC
$0 $100
1
100
70
170
$500
2
100 120
220
3
100 160
260
4
100 210
310
5
100 280
380
6
100 380
480
7
100 520
620
TC
$600
Costs
0 $100
$400
$300
$200
$100
$0
0
1
2
3
4
5
6
7
Q
THE COSTS OF PRODUCTION
21

22. EXAMPLE 2: Marginal Cost
TC
0 $100
1
170
2
220
3
260
4
310
5
380
6
480
7
620
MC
$70
50
40
50
70
100
140
$200
Recall, Marginal Cost (MC)
is $175change in total cost from
the
producing one more unit:
$150
∆TC
MC =
∆Q
$100
Usually, MC rises as Q rises, due
$75
to diminishing marginal product.
Costs
Q
$125
$50
Sometimes (as here), MC falls
$25
before rising.
$0
(In other examples, MC may be 7
0 1 2 3 4 5 6
constant.)
Q
THE COSTS OF PRODUCTION
22

23. EXAMPLE 2: Average Fixed Cost
Q
FC
0 $100
$200
Average fixed cost (AFC)
is fixed cost divided by the
$175
quantity of output:
$150
AFC
n/a
100
$100
2
100
50
3
100 33.33
4
100
25
5
100
20
6
100 16.67
7
100 14.29
Costs
1
AFC
$125
= FC/Q
$100
Notice that AFC falls as Q rises:
$75
The firm is spreading its fixed
$50
costs over a larger and larger
$25
number of units.
$0
0
1
2
3
4
5
6
7
Q
THE COSTS OF PRODUCTION
23

24. EXAMPLE 2: Average Variable Cost
Q
VC
$200
Average variable cost (AVC)
is variable cost divided by the
$175
quantity of output:
$150
AVC
$0
n/a
1
70
$70
2
120
60
3
160
53.33
4
210
52.50
5
280
56.00
6
380
63.33
7
520
74.29
Costs
0
THE COSTS OF PRODUCTION
AVC
$125
= VC/Q
$100
As Q rises, AVC may fall initially.
$75
In most cases, AVC will
$50
eventually rise as output rises.
$25
$0
0
1
2
3
4
Q
5
6
7
24

25. EXAMPLE 2: Average Total Cost
Q
TC
0 $100
ATC
AFC
AVC
n/a
n/a
n/a
1
170
$170
$100
$70
2
220
110
50
60
3
260 86.67 33.33
53.33
4
310 77.50
25
52.50
5
380
76
20
56.00
6
480
80 16.67
63.33
7
620 88.57 14.29
Average total cost
(ATC) equals total
cost divided by the
quantity of output:
74.29
THE COSTS OF PRODUCTION
ATC = TC/Q
Also,
ATC = AFC + AVC
25

26. EXAMPLE 2: Average Total Cost
TC
0 $100
1
170
$200
ATC
Usually, as in this example,
$175
the ATC curve is U-shaped.
n/a
$150
$170
110
Costs
Q
$125
2
220
3
260 86.67
4
310 77.50
$50
5
380
76
$25
6
480
80
$0
7
620 88.57
THE COSTS OF PRODUCTION
$100
$75
0
1
2
3
4
5
6
7
Q
26

27. EXAMPLE 2: Why ATC Is Usually U-Shaped
As Q rises:
$200
Initially,
falling AFC
pulls ATC down.
$175
Costs
Eventually,
rising AVC
pulls ATC up.
$150
Efficient scale:
The quantity that
minimizes ATC.
$125
$100
$75
$50
$25
$0
0
1
2
3
4
5
6
7
Q
THE COSTS OF PRODUCTION
27

28. EXAMPLE 2: The Various Cost Curves Together
$200
$175
Costs
ATC
AVC
AFC
MC
$150
$125
$100
$75
$50
Check mark?
Bowed up L shape
Smile
Bowed down L shape
$25
$0
0
1
2
3
4
5
6
7
Q
THE COSTS OF PRODUCTION
28

29. EXAMPLE 2: ATC and MC
When MC < ATC,
ATC
MC
$200
ATC is falling.
$175
$150
ATC is rising.
$125
The MC curve
crosses the
ATC curve at
the ATC curve’s
minimum.
Costs
When MC > ATC,
$100
$75
$50
$25
$0
0
1
2
3
4
5
6
7
Q
THE COSTS OF PRODUCTION
29

31. Cost Round up
 If MC is higher than AVC, does MC increase or
decrease?
 Why does the AFC curve slope down forever as a firm
produces more?
 Which curve looks like a check mark?
 Which curve has the most extreme upward slope?
 Which is the only average curve that decreases over
time?
 Which curve is the above the other average curves?

32. Costs assignment
1
2