Cost and Production
J.F.O’Connor
Production Function
• Relationship governing the transformation
of inputs or factors of production into
output or product.
• Focus on one variable input. Relationship
between output and the variable input is the
total product (TP) curve.
• An example similar to book’s is as follows:
TotalProductCurve
140
120
Output
100
80
60
40
20
0
0
2
4
6
Labor
8
10
12
Three Questions
• For any given level of employment of the
input:
• How much output is obtained?
• What is the average output per unit of
input?
• If the employment of the input is changed
by one unit what is the change in output?
The Answers
• The Total Product (TP) answers the first.
• The Average Product (AP) of the input
answers the second. It is AP=TP/L.
• The Marginal Product answers the third. It
is the change in total product divided by the
change in the input,
MP = [TP(L1)-TP(L0)]/(L1-L0)
• The relevant quantities for our example are:
In p u t
O u tp u t
A ve ra g e
P ro d u c t
M a rg in a l
P ro d u c t
L
0
1
2
3
4
5
6
7
8
9
10
11
TP
0
40
57
69
80
89
98
106
113
120
126
133
AP
MP
4 0 .0
2 8 .3
2 3 .1
2 0 .0
1 7 .9
1 6 .3
1 5 .1
1 4 .1
1 3 .3
1 2 .6
1 2 .1
2 0 .0
1 4 .1
1 1 .5
1 0 .0
8 .9
8 .2
7 .6
7 .1
6 .7
6 .3
6 .0
The Unit Product Curves
• The average and marginal products are
plotted in the next graph.
• Note that this example has diminishing
marginal product for all ranges of input.
• Since average product is declining, marginal
is less than average at each level of
employment of the input.
Unit Product Curves
80
70
60
Output
50
40
30
AP
20
MP
10
0
0
2
4
6
Labor
8
10
12
Cost of Production
• In order to obtain the information about the
cost of producing various levels of output,
we combine the information from the total
product curve with that of input price.
• The price of the input, labor, is $10 per unit.
• Total variable cost (TVC) is obtained by
multiplying the amount of input required by
the price per unit. See first and third
columns of the next table.
L
Q
0
0.125
0.25
0.5
1
2
3
4
5
6
7
8
9
10
11
TVC
0
14
20
28
40
57
69
80
89
98
106
113
120
126
133
0
1.25
2.5
5
10
20
30
40
50
60
70
80
90
100
110
FC
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
TC
30
31.25
32.5
35
40
50
60
70
80
90
100
110
120
130
140
AVC
0.000
0.088
0.125
0.177
0.250
0.354
0.433
0.500
0.559
0.612
0.661
0.707
0.750
0.791
0.829
AFC
0.000
ATC
0.000
1.500
1.061
0.750
0.530
0.433
0.375
0.335
0.306
0.283
0.265
0.250
0.237
0.226
1.625
1.237
1.000
0.884
0.866
0.875
0.894
0.919
0.945
0.972
1.000
1.028
1.055
MC
0.000
0.177
0.250
0.354
0.500
0.707
0.866
1.000
1.118
1.225
1.323
1.414
1.500
1.581
1.658
Total Costs (Cols 3-5)
• Total variable cost (TVC) gives the
minimum expenditure on variable inputs
required to produce each level of output.
• Fixed cost is the opportunity cost of the
fixed inputs and does not vary with output.
It is $30 in our example.
• Total cost (TC) is the sum of total variable
cost and fixed cost, TC = TVC + FC.
• FC and TC are plotted in the next graph.
TotalCostandFixedCost
TC
140
120
Dollars
100
80
60
40
FC
20
0
0
20
40
60
80
Output
100
120
140
Profit Maximization
• Profit is the difference between total
revenue and total cost. Total revenue is
price of output times quantity of output.
• The price of output is $1 per unit.
• Total revenue is output times $1. We plot
this in the next graph. It is a straight line of
slope one. The vertical difference between
TR and TC is profit. The maximum profit is
at 80 units of output. Profit is $10.
Profit Maximization
TC
140
120
100
Dollars
80
60
40
FC
20
0
0
20
40
60
80
Output
100
120
140
Unit Costs
• It is often more convenient to deal with per
unit costs and revenues rather than the total
quantities. There are four such quantities
• Average variable cost, AVC = TVC/Q
• Average fixed cost, AFC = FC/Q
• Average total cost, ATC = AVC + AFC
• Marginal cost:
MC = (change in TC)/(change in Q)
• All four are given in the Table and plotted:
UnitCosts
1.800
1.600
MC
$/unit
1.400
1.200
ATC
1.000
0.800
AVC
AFC
0.600
0.400
0.200
0.000
0
20
40
60
80
Output
100
120
140
Profit Maximization, Again
• If you are thinking of producing a given
level of output, how do you decide whether
or not you can do better in terms of profit?
• Answer the question:
Would a change in output increase profit?
• For an increase of one unit, is the addition
to total revenue greater than the addition to
total cost? In our case, is price greater than
marginal cost? If so, increase output.
• For an decrease of one unit, is the reduction
in revenue less than than the reduction in
total cost? In our case, is price less than
marginal cost? If so, decrease output.
• Price of output equal to marginal cost is
necessary for profit maximization.
• If we were at 40 units of output, the
addition to revenue is $1 and the addition to
cost is $.5. Increasing output will increase
profit. Continue increasing output until
price = marginal cost, which is at 80 units.
• We would arrive at the same decision by
drawing a price line at $1 in the unit cost
graph and locating the output at which price
= marginal cost, namely, 80 units.