cost function managerial economics

COST FUNCTION

Cost function may be defined as the relationship between costs of a product and output.

COST FUNCTION IN SHORT RUN

C = F [Q]

COST

SHORT RUN COST

LONG RUN COST

An analysis in which certain factors are assumed to be fixed during the period analyzed.

In short run output can be increased or decreased by changing only the variable factors.

SHORT RUN COST FUNCTION

+

=

Fixed cost

Variable cost

Total cost

Short run cost

Fixed cost are those cost which do not change with changes in output.

Fixed cost are otherwise called ‘supplementary cost’ or ‘over head costs’.

Eg ; Rent on land and building , Insurance charges, Interest on fixed capital, Salary of permanent employees.

SHORT RUN FIXED COST

Variable cost are those costs which changes with changes in output.

Variable cost are also called ‘prime cost’.

Eg; cost of raw materials, cost of power in production, wages of workers.

SHORT RUN VARIABLE COST

Total cost is defined as the Total actual cost that must be incurred to produce a given quantity of output.

Fixed cost and variable cost are formally called Total fixed cost and Total Variable cost.

SHORT RUN TOTAL COST

TC = TFC + TVC

UNITS OF OUTPUT

TFC[Rs.]

TVC[Rs.]

TC[Rs.]

0 60 60 -60 = 0 60

1 60 100 -60 = 40 100

2 60 120 – 60 = 60 120

3 60 70 130

4 60 100 160

5 60 160 220

6 60 300 360

SHORT RUN TOTAL COST CURVE

.............

TFC being fixed at Rs.60, remains the same at all levels of output . Thus, the TFC- curve is a straight line parallel to the x-axis.

TVC – curve starts from the origin at zero output . It move upwards from left to right.

The shape of TC –curve is the same as TVC-curve.

SHORT RUN AVERAGE COST

AVERAGE FIXED COST

AVERAGE VARIABLE COST

AVERAGE FIXED COST

SHORT RUN AVERAGE

COST

AFC is the per unit fixed cost of producing a commodity. It is obtained by dividing the total fixed cost by the quantity of output [Q].

AVERAGE FIXED COSTS

AFC = TFC Q

AVC is the per unit variable cost of producing a commodity . It is obtained by dividing the total variable cost by the quantity of output.

AVERAGE VARIABLE COST

AVC = TVC

Q

AC is the sum total of AFC and AVC.

AVERAGE TOTAL COST

AC = TC

Q

MARGINAL COST ; Marginal cost is the addition to total cost by the production of an additional unit of output.

; w

SHORT RUN AVERAGE MARGINAL COST CURVE

MCn = TCn - TCn-1

Units of production

TFC[Rs]

TVC[Rs]

TC[Rs]

AFC[Rs]

AVC[Rs]

ATC[Rs]

MC[Rs]

O 60 0 60 - - - -

1 60 40 10 60 40 100 40

2 60 60 120 30 30 60 20

3 60 70 130 20 23.3 43.3 10

4 60 100 160 15 25 40 30

5 60 160 220 12 32 44 60

6 60 300 360 10 50 60 140

SHORT RUN AVERAGE MARGINAL CURVES

The short –run MC curve will at first decline and the ATC and AVC at their minimum points.

The AVC curve will go down , and then go up.

AFC curve will decline as additional units are produced , and continue to decline.

ATC curve initially will decline as the fixed cost are spread over a large number of units , but will go up as MC increase due to the law of diminishing returns.