04/19/23 ©2000Claudia Garcia-Szekely 1

Short Run Costs

Costs when the plant size is fixed

Expenses that do not change with the number of units produced

Rent

Interest Payments

Secretaries

Property Taxes

Insu

ranc

e

Managers

Fixed Cost

Expenses that change with the number of units produced

Variable Cost

Variable Cost

Rent

Interest Payments

SecretariesProperty Taxes

Insu

ranc

e

ManagersFixed Cost

4

Some labor costs are fixed.

Management Salaries are a fixed cost, because they do not change with the

firm’s output.

Production Function

Quantity Produced (Q)

$ C

ost

s

Labor (L)

Quanti

ty P

roduce

d

(Q)

Cost Function

Fixed Costs: Do not change with Q

Q

FC =40000

Q=500 Q=10,000

$40,000

FC = 40000FC =40000

Q=0

Rent

Interest Payments

SecretariesProperty Taxes

Insu

ranc

e

ManagersFixed Cost

Variable Costs increase with Output

Output

Starts at the Origin

VC

Variable Cost

Total Costs = FC+VC

Output

Starts at FC

FCStarts at the Origin

TC

VC

9Output

FCFC

FC

FC

VC

TC

Distance between the TC and VC = FC

Distance between the TC and VC = FC

10

Output

500

600

400

1000 2000

VC=?

VCTC

FC

11

Output

500

600

400

1000 2000

VC = 400

TC = 600

FC =200

VC = 300

TC = 500

FC =200VC = 300

From MP to MCL Q MP VC MC0 0 01 5 5 50 10.002 15 10 100 5.003 30 15 150 3.334 50 20 200 2.505 67 17 250 2.946 82 15 300 3.337 95 13 350 3.858 107 12 400 4.179 117 10 450 5.0010 125 8 500 6.2511 131 6 550 8.3312 136 5 600 10.00

MP

Incr

ease

s

MC

Decr

ease

s

MP d

ecr

ease

s

MC Incr

ease

s

From MP to MCL Q MP VC MC0 0 01 5 5 50 10.002 15 10 100 5.003 30 15 150 3.334 50 20 200 2.505 67 17 250 2.946 82 15 300 3.337 95 13 350 3.858 107 12 400 4.179 117 10 450 5.0010 125 8 500 6.2511 131 6 550 8.3312 136 5 600 10.00

MP

Incr

ease

s

MC

Decr

ease

s

MP d

ecr

ease

s

MC Incr

ease

s

Wage =$50/da

y

Assume that labor is the

ONLY variable cost

1 worker = $50

2 workers = $100

3 workers = $150

From MP to MCL Q MP VC MC0 0 01 5 5 50 10.002 15 10 100 5.003 30 15 150 3.334 50 20 200 2.505 67 17 250 2.946 82 15 300 3.337 95 13 350 3.858 107 12 400 4.179 117 10 450 5.0010 125 8 500 6.2511 131 6 550 8.3312 136 5 600 10.00

MP

Incr

ease

s

MC

Decr

ease

s

MP d

ecr

ease

s

MC Incr

ease

s

Marginal CostL Q MP VC MC0 0 01 5 5 50 10.002 15 10 100 5.003 30 15 150 3.334 50 20 200 2.505 67 17 250 2.946 82 15 300 3.337 95 13 350 3.858 107 12 400 4.179 117 10 450 5.0010 125 8 500 6.2511 131 6 550 8.3312 136 5 600 10.00

MP

Incr

ease

sM

P d

ecr

ease

s

MC Incr

ease

s

MC = VC/Q

$50/5=$10$50/10=$5

$505units

$5010units

MC = wage/MP

$50/15=$3.3$50/20=$2.5$50/17=$2.9$50/15=$3.3$50/13=$3.8

MP Wage

From MP to MCL Q MP VC MC0 0 01 5 5 50 10.002 15 10 100 5.003 30 15 150 3.334 50 20 200 2.505 67 17 250 2.946 82 15 300 3.337 95 13 350 3.858 107 12 400 4.179 117 10 450 5.0010 125 8 500 6.2511 131 6 550 8.3312 136 5 600 10.00

MP

Incr

ease

s

MC

Decr

ease

s

MP d

ecr

ease

s

MC Incr

ease

s

MC = wage/MP

Increasing MP=Decreasing

MC

Wage is the same

Decreasing MP

=Increasing MC

Wage is the same

MC = VC/Q

From MP to MCL Q MP VC MC0 0 01 5 5 50 10.002 15 10 100 5.003 30 15 150 3.334 50 20 200 2.505 67 17 250 2.946 82 15 300 3.337 95 13 350 3.858 107 12 400 4.179 117 10 450 5.0010 125 8 500 6.2511 131 6 550 8.3312 136 5 600 10.00

MP

Incr

ease

s

MC

Decr

ease

s

MP d

ecr

ease

s

MC Incr

ease

s

MP

MP

Labor

Units of Output

MC

As th

e M

P incr

ease

s

The MC decreases

MC

As the MP decreases

The M

C incr

ease

s

When the MP is at its Maximum

The MC is at its Minimum

Diminishing Returns to Labor set in

Diminishing Returns to Labor set in

Q0

L0

From VC to TC: add FCL Q MP VC MC FC TC MC0 0 0 50,0001 5 5 50 10.00 10.002 15 10 100 5.00 5.003 30 15 150 3.33 3.334 50 20 200 2.50 2.505 67 17 250 2.94 2.946 82 15 300 3.33 3.337 95 13 350 3.85 3.858 107 12 400 4.17 4.179 117 10 450 5.00 5.0010 125 8 500 6.25 6.2511 131 6 550 8.33 8.3312 136 5 600 10.00 10.00 19

TC = FC + VC50,000 = FC + VC50,000 = FC + 0FC = 50,000

TC = FC + VC50,000 = FC + VC50,000 = FC + 0FC = 50,000

Variable cost of producing

zero units = 0

Total cost of producing zero units = 50,000

50,00050,00050,00050,00050,000

20

Marginal Cost

Cost of “the last” unit produced.– When one more unit is produced, the

fixed cost does not change.– Is the cost of labor, raw materials and

other variable expenses incurred when producing an additional unit.

Marginal Cost FormulaMC = TC/Q MC = (FC +VC) /Q

Because TC = VC when one more unit is produced, we can also write:

MC = VC/Q Marginal cost is the additional Variable

Cost of producing one more unit

FC = 0

MC is the slope of both the TC and the slope of the VC

MC = rise/runMC = slopeMC = rise/runMC = slope

TC and VC have the exact same slope

TC and VC have the exact same shape

22

L Q MP VC MC FC TC MC0 0 0 50,000 50,0001 5 5 50 10.00 50,000 50,050 10.002 15 10 100 5.00 50,000 50,100 5.003 30 15 150 3.33 50,000 50,150 3.334 50 20 200 2.50 50,000 50,200 2.505 67 17 250 2.94 50,000 50,250 2.946 82 15 300 3.33 50,000 50,300 3.337 95 13 350 3.85 50,000 50,350 3.858 107 12 400 4.17 50,000 50,400 4.179 117 10 450 5.00 50,000 50,450 5.0010 125 8 500 6.25 50,000 50,500 6.2511 131 6 550 8.33 50,000 50,550 8.3312 136 5 600 10.00 50,000 50,600 10.00

Total Cost = Fixed Cost + Variable Cost

23

L Q MP VC MC FC TC0 0 0 50,000 50,0001 5 5 50 10.00 50,000 50,0502 15 10 100 5.00 50,000 50,1003 30 15 150 3.33 50,000 50,1504 50 20 200 2.50 50,000 50,2005 67 17 250 2.94 50,000 50,2506 82 15 300 3.33 50,000 50,3007 95 13 350 3.85 50,000 50,3508 107 12 400 4.17 50,000 50,4009 117 10 450 5.00 50,000 50,45010 125 8 500 6.25 50,000 50,50011 131 6 550 8.33 50,000 50,55012 136 5 600 10.00 50,000 50,600

Total Cost = Fixed Cost + Variable Cost

L Q MP VC MC FC TC MC

0 0   0  5000

05000

0  

1 5 5 505000

05005

0

2 15 10 1005000

05010

0

3 30 15 1505000

05015

0

4 50 20 2005000

05020

0

5 67 17 2505000

05025

0

6 82 15 3005000

05030

0

7 95 13 3505000

05035

0

8 107 12 4005000

05040

0

9 117 10 4505000

05045

0

10 125 8 5005000

05050

0

11 131 6 5505000

05055

0

12 136 5 6005000

05060

0

MC can be calculated using the VC or the

TC

TC50

VC50

MCVC/QMCVC/Q

MCTC/QMCTC/Q

10.0010.00

5.00 5.00

TC50

VC50

L Q MP VC MC FC TC MC

0 0   0  5000

05000

0  

1 5 5 5010.0

05000

05005

010.0

0

2 15 10 100 5.005000

05010

0 5.00

3 30 15 150 3.335000

05015

0 3.33

4 50 20 200 2.505000

05020

0 2.50

5 67 17 250 2.945000

05025

0 2.94

6 82 15 300 3.335000

05030

0 3.33

7 95 13 350 3.855000

05035

0 3.85

8 107 12 400 4.175000

05040

0 4.17

9 117 10 450 5.005000

05045

0 5.00

10 125 8 500 6.255000

05050

0 6.25

11 131 6 550 8.335000

05055

0 8.33

12 136 5 60010.0

05000

05060

010.0

0

MCVC/Q MCTC/Q

Marginal Cost

Tells you how the Variable cost changes as more output is produced

It is the slope of the Variable Cost

26

MCVC/Q

Variable Cost

Output

Increasin

g functi

on

The MC decreases

MC

The M

C incr

ease

sSteps get smaller

MC

Steps

get

larg

er

Q VC0 05 50

15 10030 15050 20067 25082 30095 350107 400117 450125 500

131 550136 600

MC decrease

Steps get s

maller

MC In

crea

se

Steps

get

larg

erStarts at the Origin

Marginal CostTells you how the Variable cost changes as more output is produced

Tells you how the Total cost changes as more output is produced

Both the VC and the TC change by the SAME amount.

28

MCVC/Q

MCTC/Q

Total Costs

Output

Starts at FC

FC

The MC decreases

MC

The M

C incr

ease

sSteps get smaller

MC

Steps

get

larg

er

Starts at the Origin

TC

VC

TC has the same slope

(shape)as the VC

04/19/23 ©2000Claudia Garcia-Szekely 30

Per Unit Costs

Average Costs

Average (per unit) Costs

TC = FC + VCTo get per unit costs, divide by Q (Units Produced)TC/Q = FC/Q + VC/Q

ATC = AFC + AVC

31

32

Fixed Costs

Fixed Costs do not change with the level of output (Q)

We show this by drawing a horizontal line.

Fixed Costs

Q

FC =40Kwhen Q=2

Q=2 Q=10

40K

FC = 40Kwhen Q=10

33

Average Fixed Costs

QQ=2 Q=10

4

20

AFC

Ave

rag

e F

ixed

Cost

AFC =20when Q=2

AFC = 4when Q=10

FC = 40Q = 2 AFC = 40/2 = 20

AFC = 40/10 = 4 AFC = 40/5 = 8

8

Q=5

Q = 5Q = 10

Even though FC remains the same: 40k

Even though FC remains the same: 40k

The Average Fixed Cost

Decrease as output increase

Variable Costs

Output

AVC = VC / Q

AVC = Slope of ray from

origin

AVC = rise / run

Minimum AVC

AVC

Q

VC

As Q increase, slope decrease: AVC decrease

Variable Costs

Output

AVC = Slope of ray from

origin

Minimum AVC

As Q increase, slope increase: AVC increase

AVC

TC

ATC = Slope of ray from

origin

Minimum ATC

As Q increase, (slope) ATC decrease

Output (Q)

ATC

ATC = TC / Q

As Q increase, (slope) ATC decreasereaches a minimum and then increase

37Q=2 Q=10

9

AVC = 1515

AVC

ATC = AVC + AFC

AFC

AFC =20

29

20

AFC = 44

ATC

19

AVC =9

ATC =29

ATC = 19

AVC

AFC

ATC

Q=2 Q=10

915

AVC

AV

C,

AF

C,

AT

C

29 ATC

19AFC

AFC AFCAFCDistance between the ATC and AVC =

AFC

Distance between the ATC and AVC = AFC

The Relationship between Average and Marginal costs

If MC > Average Cost, the Average Cost increase.If MC < Average Cost, the Average Cost decrease.If MC = Average Cost, the Average Cost does not increase or decrease: it is maximum.

39

AVC or ATCAVC or ATC

AVC or ATCAVC or ATC

AVC or ATCAVC or ATC

Q

MC

MC <

AVC

AVC

ATC

MC >

AVC,

MC <

ATC,

MC

> A

TC

,

MC = AVC, AVC minimum

MC = ATC, ATC minimum

AVC

decrease AVC in

crea

se

ATC

in

crea

se A

TC

decrease

MP AP

MP, AP

L

MC AVC

Q

MC, AC

AP is max

MP is max

AVC is min

MC is min

42

MC cuts the ATC and the AVC at their MINIMUM points

ATC

,AV

C,

MC

AVC

MCATC

Reach Minimum at differentOutput levels

Min AVC

Min ATC

Min MC: Diminishing returns to labor set in

From Average Costs to Total Costs

ATC = TC/QAVC = VC/QAFC = FC/Q

TC =ATC x Q

VC = AVC x Q

FC = AFC x Q

Rearrange as

44

Per unit Costs

MC

AVC

ATC

ATCAVC

Q

VCTC AVC x Q = VC

AFC x Q = FC

ATC x Q = TC

AFC =ATC - AVC

FC

MC

Cost of producing the LAST unit

10

120

TC = 120*20FC = 120*(20-10)

VC = 120*10

For Q = 120

ATC = 20

AVC = 10

Cost of producing the120th unit

2020

AFC=20 -10= 10

46

10

2024

40

50 120 300

44

For Q = 300

TC = 300*24

FC = 300*(24-20)

VC = 300*20