Cost theory and analysis

1. COST THEORY AND
ANALYSIS
MANAGERIAL ECONOMICS

2. Costs Theory and Analysis
 Short run – Diminishing marginal returns results from adding successive
quantities of variable factors to a fixed factor
 Long run – Increases in capacity can lead to increasing, decreasing or
constant returns to scale

3. Short Run Production Costs
 Total variable cost (TVC)
 Total amount paid for variable inputs
 Increases as output increases
 Total fixed cost (TFC)
 Total amount paid for fixed inputs
 Does not vary with output
 Total cost (TC)
 TC = TVC + TFC

4. Short-Run Total Cost Schedules
Output (Q) Total fixed cost
(TFC) taka
Total variable cost
(TVC) Taka
Total Cost Taka
TC=TFC+TVC)
0 6,000
100 6,000
200 6,000
300 6,000
400 6,000
500 6,000
600 6,000
0
14,000
22,000
4,000
6,000
9,000
34,000
6,000
20,000
28,000
10,000
12,000
15,000
40,000

5. Total Cost Curves

6. Average Costs

TVC
AVC
Q

TFC
AFC
Q
  
TC
ATC AVC AFC
Q
• ( AFC )
Average fixed cost
• ( ATC )
Average total cost
( AVC )
Average variable cost
•

7. Short Run Marginal Cost
 Short run marginal cost (SMC) measures rate of change in total cost (TC)
as output varies
 
 
 
TC TVC
SMC
Q Q

8. Average & Marginal Cost Schedules
Output
(Q)
Average
fixed cost
(AFC=TFC/Q)
Average
variable cost
(AVC=TVC/Q)
Average total
cost
(ATC=TC/Q=
AFC+AVC)
Short-run
marginal cost
(SMC=TC/Q)
0
100
200
300
400
500
600
--
15
12
60
30
20
10
--
35
44
40
30
30
56.7
--
50
56
100
60
50
66.7
--
50
80
40
20
30
120

9. Average & Marginal Cost Curves

10. Short Run Average & Marginal Cost Curves

11. Short Run Cost Curve Relations
 AFC decreases continuously as output increases
 Equal to vertical distance between ATC & AVC
 AVC is U-shaped
 Equals SMC at AVC’s minimum
 ATC is U-shaped
 Equals SMC at ATC’s minimum

12. Short Run Cost Curve Relations
 SMC is U-shaped
 Intersects AVC & ATC at their minimum points
 Lies below AVC & ATC when AVC & ATC are
falling
 Lies above AVC & ATC when AVC & ATC are
rising

13.  In the case of a single variable input, short-run costs
are related to the production function by two
relations
Relations Between Short-Run Costs &
Production
 
w w
AVC SMC
MP MP
and
w
Where is the price of the variable input
A

14. Short-Run Production & Cost Relations

15. Relations Between Short-Run Costs &
Production
 When marginal product (average product)
is increasing, marginal cost (average cost) is
decreasing
 When marginal product (average product)
is decreasing, marginal cost (average
variable cost) is increasing
 When marginal product = average product
at maximum AP, marginal cost = average
variable cost at minimum AVC

16. Isocost
 The combinations of
inputs that cost the
producer the same
amount of money
 For given input prices,
isocosts farther from the
origin are associated with
higher costs.
 Changes in input prices
change the slope of the
isocost line
K
L
C1
C0
L
K
New Isocost Line
for a decrease in the
wage (price of
labor).

17. Cost Minimization
 Marginal product per dollar spent should be equal for all inputs:
 Expressed differently
r
MP
w
MP K
L

r
w
MRTSKL 

18. Cost Minimization
Q
L
K
Point of Cost
Minimization
Slope of Isocost
=
Slope of
Isoquant

19. 19
The Firm’s Expansion Path
 An Expansion curve is formally defined as the set of
combinations of capital and labor that meet the efficiency
condition MPL/w = MPK/r, where w and r are wage rate and
interest rate respectively.
 The firm can determine the cost-minimizing combinations
of K and L for every level of output
 If input costs remain constant for all amounts of K and L the
firm may demand, we can trace the locus of cost-minimizing
choices
 called the firm’s expansion path

20. 20
The Firm’s Expansion Path
L per period
K per period
q00
The expansion path is the locus of cost-minimizing
tangencies
q0
q1
E
The curve shows
how inputs increase
as output increases

21. Equation for Expansion Path
 Production Function
Q = 100K0.5L0.5
The marginal product functions are
MPL =50
MPK = 50
Efficiency Condition is MPL/ MPK = w/r
Solving for K
K = (w/r).L
The production function re-written as
Q = 100((w/r)L)0.5 L0.5
Or Q = 100L(w/r)0.5

22. Example
 Determine the efficient input combination for producing 1000 units of
output if w = 4, r = 2.
 Answer: 1000 = 100L(4/2)0.5
 Or L = 7.07
 K = (4/2) 7.07 = 14.14
 The input combination ( K=14.14 and L = 7.07) is the most efficient way to
produce 1000 units of output.

23. 23
The Firm’s Expansion Path
 The expansion path does not have to be a straight
line
 the use of some inputs may increase faster than others
as output expands
 depends on the shape of the isoquants
 The expansion path does not have to be upward
sloping
 if the use of an input falls as output expands, that
input is an inferior input

24. Revenue
 Total revenue – the total amount received
from selling a given output
 TR = P x Q
 Average Revenue – the average amount
received from selling each unit
 AR = TR / Q
 Marginal revenue – the amount received from
selling one extra unit
of output
 MR = TRn – TR n-1 units

25. Profit
 Profit = TR – TC
 The reward for enterprise
 Profits help in the process of directing resources to alternative uses in free
markets
 Relating price to costs helps a firm to assess profitability in production

26. Profit
 Normal Profit – the minimum amount
required to keep a firm in its current line of
production
 Abnormal or Supernormal profit – profit
made over and above normal profit
 Abnormal profit may exist in situations where firms
have market power
 Abnormal profits may indicate the existence of
welfare losses
 Could be taxed away without altering resource
allocation

27. Profit
 Sub-normal Profit – profit below normal profit
 Firms may not exit the market even if sub-normal profits made if they are
able to cover variable costs
 Cost of exit may be high
 Sub-normal profit may be temporary (or perceived as such!)

28. Profit
 Assumption that firms aim to maximise profit
 May not always hold true –
there are other objectives
 Profit maximising output would be where MC = MR

29. Profit Why?
Cost/Revenue
Output
MR
MR – the addition
to total revenue as
a result of
producing one
more unit of
output – the price
received from
selling that extra
unit.
MC MC – The cost of
producing ONE
extra unit of
production
100
Assume output is at
100 units. The MC of
producing the 100th
unit is 20.
The MR received from
selling that 100th unit
is 150. The firm can
add the difference of
the cost and the
revenue received from
that 100th unit to
profit (130)
20
150
Total
added
to
profit
If the firm decides to
produce one more unit –
the 101st – the addition
to total cost is now 18,
the addition to total
revenue is 140 – the firm
will add 128 to profit. –
it is worth expanding
output.
101
18
140
Added to
total
profit
30
120
Added
to total
profit
The process continues
for each successive
unit produced.
Provided the MC is
less than the MR it
will be worth
expanding output as
the difference
between the two is
ADDED to total profit
102
40
145
104
103
Reduces
total
profit by
this
amount
If the firm were to
produce the 104th unit,
this last unit would cost
more to produce than it
earns in revenue (-105)
this would reduce total
profit and so would not
be worth producing.
The profit maximising
output is where MR =
MC

30. Example
 A micro-entrepreneur produces caps and hats for
women. The output-cost data of the business is
reproduced below:
Output Total
Cost
50 870
100 920
150 990
200 1240
250 1440
300 1940
350 2330
a. Estimate the total cost function and then use
that equation to determine the average and
marginal cost functions. Assume a cost
function.
b. Determine the output rate that will minimize
average cost and the per-unit cost at that rate of
output.
c. The current market price of caps and hats per
unit is Tk. 9.00 and is expected to remain at
that level for the foreseeable future. Should the
firm continue its production?

31. Getting an Idea about the form of the equation
0
500
1000
1500
2000
2500
50 100 150 200 250 300 350
Output-Cost

32. Estimate of Example
 First we assume the cost function as
TC = c0+c1Q + c2Q2 +c3Q3
 Results
TC= 954.29 -2.46Q +0.02Q2 -.0002Q3
(5.9) (-0.75) (1.04) (-0.07)
R2 = 0.99 F = 197.78
 Comments: t-statistics are not acceptable though R2 and F are good.
 Second, we assume the cost function as
TC = c0+c1Q + c2Q2
Results
 TC = 944.29 -2.24Q + 0.02Q2
t Stat (12.51) (-2.58) (8.45)
R2 = 0.99 F = 394.86
 Comments: t-statistics are acceptable and R2 and F are good.

33. Answer to Question (a)
 a. The t-statistics, shown in the parenthesis of the second
estimation, indicate that the coefficient of each of the
independent variables are significantly different from zero. The
value of the co-efficient of determination means that 99 percent
of the variation in total cost is explained by changes in the rate
of output.

34. Answer (a) contd.

35. Answer (b)
 The output rate that results in minimum per-unit cost
is found by taking the first derivative of the average
cost function, setting it equal to zero, and solving for
Q.

36. Answer (b) contd.
Sign mistake

37. Answer (c)
 Because the lowest possible cost is Tk. 6.45 per unit, which is above the
market price of Tk. 9.00, the production should be continued.

38. Exercise
Output Total Cost
25 700
100 920
150 990
200 1240
280 1440
360 1940
460 2330
600 3500