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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
Hot dogs per hour
FC VC Total
Cost
AFC AVC ATC MC
0 $ 3 $ 0 ------
1 $0.30
2 $0.80
3 $1.50
4 $2.40
5 $3.50
6 $4.80
7 $6.30
8 $8.00
9 $9.90
10 $12.00
Hot dogs per hour
FC VC Total
Cost
AFC AVC ATC MC
0 $ 3 $ 0 ------
1 $0.30
2 $0.80
3 $1.50
4 $2.40
5 $3.50
6 $4.80
7 $6.30
8 $8.00
9 $9.90
10 $12.00
THE COSTS OF PRODUCTION 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 6
0
500
1,000
1,500
2,000
2,500
3,000
0 1 2 3 4 5
No. of workers
Qu
anti
ty o
f o
utp
ut
Example 1: Farmer Jack’s Production Function
30005
28004
24003
18002
10001
00
Q (bushels of wheat)
L(no. of
workers)
THE COSTS OF PRODUCTION 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
Marginal product of labor (MPL) = ∆Q∆L
THE COSTS OF PRODUCTION 8
30005
28004
24003
18002
10001
00
Q (bushels of wheat)
L(no. of
workers)
EXAMPLE 1: Total & Marginal Product
200
400
600
800
1000
MPL
∆Q = 1000∆L = 1
∆Q = 800∆L = 1
∆Q = 600∆L = 1
∆Q = 400∆L = 1
∆Q = 200∆L = 1
THE COSTS OF PRODUCTION 9
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.
0
500
1,000
1,500
2,000
2,500
3,000
0 1 2 3 4 5
No. of workers
Qu
anti
ty o
f o
utp
ut
EXAMPLE 1: MPL = Slope of Prod Function
30005200
28004400
24003600
18002800
100011000
00
MPLQ
(bushels of wheat)
L(no. of
workers)
THE COSTS OF PRODUCTION 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 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 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 13
EXAMPLE 1: Farmer Jack’s Costs
$11,000
$9,000
$7,000
$5,000
$3,000
$1,000
Total Cost
30005
28004
24003
18002
10001
$10,000
$8,000
$6,000
$4,000
$2,000
$0
$1,000
$1,000
$1,000
$1,000
$1,000
$1,00000
Cost of labor
Cost of land
Q(bushels of wheat)
L(no. of
workers)
THE COSTS OF PRODUCTION 14
EXAMPLE 1: Farmer Jack’s Total Cost Curve
Q (bushels of wheat)
Total Cost
0 $1,000
1000 $3,000
1800 $5,000
2400 $7,000
2800 $9,000
3000 $11,000
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
0 1000 2000 3000
Quantity of wheat
To
tal c
ost
THE COSTS OF PRODUCTION 15
Marginal Cost Marginal Cost (MC)
is the increase in Total Cost from producing one more unit:
∆TC∆Q
MC =
THE COSTS OF PRODUCTION 16
EXAMPLE 1: Total and Marginal Cost
$10.00
$5.00
$3.33
$2.50
$2.00
Marginal Cost (MC)
$11,000
$9,000
$7,000
$5,000
$3,000
$1,000
Total Cost
3000
2800
2400
1800
1000
0
Q(bushels of wheat)
∆Q = 1000 ∆TC = $2000
∆Q = 800 ∆TC = $2000
∆Q = 600 ∆TC = $2000
∆Q = 400 ∆TC = $2000
∆Q = 200 ∆TC = $2000
THE COSTS OF PRODUCTION 17
MC usually rises as Q rises, as in this example.
EXAMPLE 1: The Marginal Cost Curve
$11,000
$9,000
$7,000
$5,000
$3,000
$1,000
TC
$10.00
$5.00
$3.33
$2.50
$2.00
MC
3000
2800
2400
1800
1000
0
Q(bushels of wheat)
$0
$2
$4
$6
$8
$10
$12
0 1,000 2,000 3,000Q
Mar
gin
al C
ost
($)
THE COSTS OF PRODUCTION 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 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 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 21
EXAMPLE 2: Costs
7
6
5
4
3
2
1
620
480
380
310
260
220
170
$100
520
380
280
210
160
120
70
$0
100
100
100
100
100
100
100
$1000
TCVCFCQ
$0
$100
$200
$300
$400
$500
$600
$700
$800
0 1 2 3 4 5 6 7
Q
Co
sts
FC
VC
TC
THE COSTS OF PRODUCTION 22
Recall, Marginal Cost (MC) is the change in total cost from producing one more unit:
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.)
EXAMPLE 2: Marginal Cost
6207
4806
3805
3104
2603
2202
1701
$1000
MCTCQ
140
100
70
50
40
50
$70
∆TC∆Q
MC =
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
THE COSTS OF PRODUCTION 23
EXAMPLE 2: Average Fixed Cost
1007
1006
1005
1004
1003
1002
1001
14.29
16.67
20
25
33.33
50
$100
n/a$1000
AFCFCQ Average fixed cost (AFC) is fixed cost divided by the quantity of output:
AFC = FC/Q
Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units.
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
THE COSTS OF PRODUCTION 24
EXAMPLE 2: Average Variable Cost
5207
3806
2805
2104
1603
1202
701
74.29
63.33
56.00
52.50
53.33
60
$70
n/a$00
AVCVCQ Average variable cost (AVC) is variable cost divided by the quantity of output:
AVC = VC/Q
As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises.
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7Q
Co
sts
THE COSTS OF PRODUCTION 25
EXAMPLE 2: Average Total Cost
88.57
80
76
77.50
86.67
110
$170
n/a
ATC
6207
4806
3805
3104
2603
2202
1701
$1000
74.2914.29
63.3316.67
56.0020
52.5025
53.3333.33
6050
$70$100
n/an/a
AVCAFCTCQ Average total cost (ATC) equals total cost divided by the quantity of output:
ATC = TC/Q
Also,
ATC = AFC + AVC
THE COSTS OF PRODUCTION 26
Usually, as in this example, the ATC curve is U-shaped.
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
EXAMPLE 2: Average Total Cost
88.57
80
76
77.50
86.67
110
$170
n/a
ATC
6207
4806
3805
3104
2603
2202
1701
$1000
TCQ
THE COSTS OF PRODUCTION 27
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
EXAMPLE 2: Why ATC Is Usually U-ShapedAs Q rises:
Initially, falling AFC pulls ATC down.
Eventually, rising AVC pulls ATC up.
Efficient scale:The quantity that minimizes ATC.
THE COSTS OF PRODUCTION 28
EXAMPLE 2: The Various Cost Curves Together
AFCAVCATC
MC
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
Check mark?Bowed up L shapeSmileBowed down L shape
THE COSTS OF PRODUCTION 29
EXAMPLE 2: ATC and MC
ATCMC
$0
$25
$50
$75
$100
$125
$150
$175
$200
0 1 2 3 4 5 6 7
Q
Co
sts
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.
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?
Costs assignment1
2
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