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