Analysis of costs
P sivakumarEconomics faculty
Introduction The amount of money spent in
order to produce commodity is known as cost of production
Cost = wages + rent + interest +profit
Cost determines the price, profit, supply of the product
cost function is derived function from production
Types of Cost
Opportunity Cost
Implicit & Explicit CostEconomic Cost
Marginal, Incremental & Sunk CostDirect & Indirect Cost
Fixed & Variable Cost
Cost concepts Total cost = total fixed cost +
total variable cost TFC – the amount of money spent
on fixed factors TVC- the amount of money spent
on variable factors
Output Fixed Costs
Variable Costs
Total Costs
0 10 0 10
1 10 10 20
2 10 18 28
3 10 24 34
4 10 28 38
5 10 32 42
6 10 38 48
7 10 46 56
8 10 62 72
VC
TC
10
20
30
40
50
60
OUTPUT X
Y
COST (Rs.)
70
80
FC
Cost concepts Average cost – the cost per unit AC = TC/Q = AFC + AVCAverage fixed cost is fixed cost per
unitAverage variable cost is variable
cost per unit of output
Marginal cost Addition made to the total cost by
producing one more unit of output MC =TCn – TC(n-1) =ΔTC/ ΔQMC is influenced by variable costMC cuts AC from below at the lowest
point
Short-Run Costs Total Cost = Total Fixed Cost + Total
Variable Cost TC = TFC + TVC Average Fixed Cost (AFC ) = TFC/Q Average Variable Cost (AVC) = TVC/Q Average Cost (AC) = TC/Q = AFC +
AVC Marginal Cost (MC) = TC/Q
Cost and Production Function A cost function determines the
behavior of costs with the change in output.
Cost Function : C = f(Q) Cost function gives the least cost
combination for the production of different levels of output.
Q TC TFC TVC ATC AFC AVC MC
1 120 100 20 120 100 20 --
2 138 100 38 69 50 19 18
3 151 100 51 50.3 33.3 17 13
4 162 100 62 40.5 25 15.5
11
5 175 100 75 35 20 15 13
6 190 100 90 31.7 16.7 15 15
7 210 100 110 30 14.3 15.7
20
8 234 100 134 29.3 12.5 16.8
24
9 263 100 163 29.2 11.1 18.1
29
10 300 100 200 30 10 20 37
Short Run Cost Function
Shot run cost function help in determining the relationship between output and costs
Q
Minimum ATC
E AVC
SATC
MC
O X
Y
Quantity
Costs
AFC
Long Run Cost Function
In the long run, the firm chooses the combination of inputs that minimize the cost of production at a desire level of output.
O X
Y
Quantity
Costs
SAC1
SAC2SAC3
SAC4
SAC5
SAC6
E
LAC
Q
Work out
TC = 10 + 15Q – 2Q2 + 0.1Q3
Find TVC, AC, AVC, MCTotal variable cost = 15Q – 2Q2 + 0.1Q3
AC = TC/Q = (10 + 15Q – 2Q2 + 0.1Q3)
---------------------------------------------
Q = 10/Q + 15 – 2Q +0.1Q2
TFC = 10, AFC = 10/QAVC = TVC/Q =15 - 2Q + 0.1Q2
Marginal cost = δC/ δQ = δ/δQ X (10 + 15Q - 2Q2 + 0.1Q3 ) = 15 – 4Q + 0.3Q2
The minimum point of AC is the BEPof the firm.To find that differentiate AC function with respect to Q& set the equation = 0
= δ(AC) / δQ = δ/δQ X (10/Q +15 – 2Q +0.1Q2) = 0
= -10Q-2 -2 + 0.2Q + 0
Multiplying both sides of the equation by Q2 & dividing by 0.2 we have
Q3 – 10Q2 -50 = 0
Economies of Scale
Economies of Scale
Real Economies
Pecuniary EconomiesProduction
Labor EconomiesTechnical EconomiesInventory EconomiesSelling &
MarketingManagerial Transportation & Storage
Reduction in price or Raw Material
Low wages and salaries
Low rate of InterestLow Advertising Cost
Labor Economies Specialization
Time saving
Automation of production process
Cumulative volume economies
Technical Economies Specialization & excess capacity of
fixed factors Set-up costs- multi purpose
machinery Technical volume/input relations R & D lab
Selling or Marketing Economies
Advertising economies Special arrangements with dealers Model – change economies
Managerial Economies Specialization of management
Decentralization of decision making
Mechanization of managerial functions
Break Even Analysis It studies the inter-relationship among
the firm’s revenues, cost and operating profit at various levels of production.
It measures the effect of changes in selling prices, fixed costs and variable cost on output level.
It is used for determining the financial viability of new marketing plans and product line.
Cont………..
Break Even Analysis It is used for managerial decision
making. It is used for dealing with unknown
variable like demand.
Break Even Analysis
O X
Y
Quantity
Costs
TFC
TR
TC
Q1Q2 Q3
Profit
Loss
A
B
D
C
Maximum Profit at output level Q2
Break Even Point Q1 & Q3
TQ TR TFC TVC TC
0 0 300 0 300
100 400 300 300 600
200 800 300 600 900
300 1200 300 900 1200
400 1600 300 1200 1500
500 2000 300 1500 1800
600 2400 300 1800 2100
TR
TC
1200
300 TQ
TR ,TC
BEP
Formula to find BEP BEP = TFC / P – AVC Target profit Sales = TFC + Profit/ P - AVC
Numerical Example
The fixed cost of a firm is Rs. 2,50,000. The selling price for each unit of product is Rs. 500. The variable cost is Rs. 50. What will be the break-even quantity and revenue.
Solution: Quantity required for break-even = Fixed Cost / P – AVC
= 2,50,000 / 500 – 50= 2,50,000 / 450= 555.56 or 556 Units
Break-even Revenue = Break-even quantity X Selling Price= 556 x 500=Rs. 2,78,000
Merits and Demerits of Break-Even Analysis
Merits a) It is an
inexpensive method.
b) It helps in designing product specification.
c) Break-even point can be estimated
Demeritsa) It assumes
selling price and variable cost per unit is known but it is not real.
b) No proper evaluation of cash flows.
Shut Down Point
In short run if AVC<P then firm has to shut down
In the long run if ATC<P then firm has to shut down
E AVC
ATC
MC
O X
Y
Quantity
Costs, Price
Q1 Q
P1
P
E1