Theory of Cost
Topics to be discussed
What is cost
What are the determinants of cost
What is cost function
Actual cost and opportunity cost
What is TC, AC, & MC
Calculation of TC, AC, & MC
Short and long run cost
Fixed and variable cost
What is TFC, TVC, AFC, & AVC
Relationship between TC, TFC, & TVC
Calculation of TFC, TVC, AFC, & AVC
Meaning of Cost:
• Cost refer to the money expenses incurred by a firm in the production process such as
cost of labor, cost of machines, etc.
Determinants of cost
Level of Output: There is a direct relationship between output level and cost. More the
level of output, more is the cost ( i. e., total cost) and vice Versa.
Price of Inputs: There is a direct relationship between price of inputs and cost. As the
price of inputs rises, cost rises and vice versa.
State of technology: More modern and upgraded the technology implies lesser cost
and vice versa.
Raw materials
labor
Cost function
Determinants of a cost function: There are several factors
the influence the cost. Cost function expresses the
relationship between cost and its determinants,
C = f(L, M, R. . . . . . )
Where,
• C = Cost (unit cost or total cost)
• L = Price of labour used in production
• M = Machines
• R= Raw materials
Short and long run cost
Short-run costs: The short-run cost is a period in which the supply of at
least one of the inputs cost cannot be changed by the firm. Eg.
Machinery.
In the short-run, there are both fixed costs and variable costs. The fixed
costs remain unchanged, while variable costs fluctuate with output.
Long-run costs: Long-run costs are costs that can vary with the size of
inputs. In the long-run there are no fixed inputs, i.e. all costs are variable.
Fixed Costs vs. Variable Costs
Fixed Costs Variable Costs
1.
Fixed costs do not vary with quantity 1. Variable costs increases as output
of output. The average fixed cost increases but this increase need not
declines proportionately with be equally proportionate. Its
additions to output proportion first declines, becomes
constant and then starts rising.
2.
They are related with the fixed 2. They are related with the variable
factors. factors.
3.
They do not become zero. They 3. They can become zero when
remain same even when production production is stopped.
is stopped.
4.
A firm can continue production even 4. Production should at least recover
fixed costs are not recovered. the variable cost.
Actual cost and opportunity Cost:
Actual costs: Actual cost means the actual expenditure incurred on
producing of goods and services like the costs of raw material, cost of
labor etc.
Opportunity costs: Opportunity costs or alternative costs are the return
from the second-best use of the firm’s resources which the firm forgoes
in order to avail of the return from the best use of the resources. For
example the inputs which are used to manufacture a car may also be
used in the productions of military equipment.
TC, AC, & MC
Total cost (TC): Total cost represents the money value of the total
resources required for production of goods and services by the firm.
Average cost (AC): Average cost is the cost per unit of output,
assuming that production of each unit of output incurs the same cost.
That is,
AC = TC/Q
where, Q = Total output
Marginal cost (MC): Marginal cost is the incremental or additional costs
incurred when there is addition to the existing output of goods and
services. That is,
MC= ΔTC/ΔQ
MCn = TCn – TCn-1
Units of output Total cost (TC) Average cost (AC) Marginal cost (MC)
0 100 -- --
5 140 28 8
10 170 17 6
15 210 14 8
20 250 12.5 8
25 300 12 10
30 330 11 6
35 350 10 4
Units of output TC AC MC
0 1000 -- --
10 1400 140 40
20 1700 85 30
30 1930 64.3 23
40 2100 52.5 17
50 2400 48 30
60 2900 48.4 50
70 3500 50 60
Relationship between TC, TFC, & TVC
In the above diagram, the horizontal line
shows the output and vertical line
shows the cost. The TFC indicates the
horizontal axis because of fixed cost.
Initially, TVC increases at an increasing
rate because the variable input is
insufficient for the given fixed inputs.
So, an increase in the variable input
results in better utilization of the fixed
inputs, leading to more than
proportionate increase in output.
Thereafter, fixed inputs fall short of the
variable input as a result further
increase in variable input can add
proportionately less to output.
Some formulae
• TC=AC x Q
• AC=TC/Q
• MC= ΔTC/ΔQ
• MCn =TCn – TCn-1
We know that,
• TC=TFC+TVC
• TFC=TC-TVC
• TVC=TC-TFC
• AFC=TFC/Q
• AVC=TVC/Q
TC, AC, MC, TFC, TVC, AFC, AVC
Units of TC TFC TVC AFC AVC AC MC
output (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.) (Rs.)
0 1000 1000 0 - - - -
10 1400 1000 400 100.0 40.0 140.0 400/10=40
20 1700 1000 700 50.0 35.0 85.0 300/10=30
30 1930 1000 930 33.3 31.0 64.3 230/10=23
40 2100 1000 1100 25.0 27.5 52.5 170/10=17
50 2400 1000 1400 20.0 28.0 48.0 300/10=30
60 2900 1000 1900 16.7 31.7 48.4 500/10=50
70 3500 1000 2500 14.3 35.7 50.0 600/10=60
Cont.
Given the total cost function as TC = 1000 + 10Q - 0.9Q2 + 0.04Q3, find the
level of output at which average variable cost is minimum.
TFC = 1000
TVC = 10Q - 0.9Q2 + 0.04Q3
MC = d(TC)/dQ = 10 – 1.8Q + 0.12Q 2
AVC = TVC/Q = (10 – 0.9Q2 + 0.04Q3)/Q
AVC = 10 – 0.9Q + 0.04Q2
The minimum point of AVC occurs at its interaction with MC, (AVC=MC)
10 – 0.9Q + 0.04Q2 = 10 – 1.8Q + 0.12Q2
Rearranging the terms we get 0.9Q – 0.08Q 2 =0
Q(0.9 – 0.08Q) = 0
Dividing both sides by Q we get, 0.9 – 0.08Q = 0
Q = 11.25
Cont.
Alternatively, the minimum point of AVC could be founded by setting the first derivative
of AVC (w.r.t. Q) equal to zero and solving for Q. That is,
d(AVC)/dQ = -0.9 + 0.08Q = 0
0.08Q = 0.9
Q = 11.25
Questions
• What is cost and its determinants?
• Write the difference between actual cost and opportunity cost.
• Find out the value of Average cost (AC) and Marginal cost (MC) from
the given table:
Questions
• What is short run and long run cost?
• Write the difference between fixed cost and variable cost.
• Given the total cost function as TC = 20 + 10Q - 0.18Q2 + 0.4Q3, find the
level of output at which average variable cost is minimum.
• Ans: Q=.225
