The Firm and Cost

Overheads

Costs in the short runTotal cost

— everything they must give upin order to produce output

A firm’s total cost of production is theopportunity cost of the owners

Explicit and implicit costs

Explicit costs

1. purchase of expendable inputs including labor time

2. purchase of capital services (usually rent or lease)

Implicit costs

1. value of produced expendables(feed for a cattle producer)

2. value of services provided by owned capital including financial capital

Operating costs and allocated overhead

1. Costs of all expendables are often allocated to the generic group OPERATING COSTSOPERATING COSTS

2. All other costs are allocated to the group ALLOCATED OVERHEADALLOCATED OVERHEAD

Data for the hay hauling problem

Cost of labor per hour = w1 = $6.00

Cost of tractor-wagon per hour = w2 = $20.00

Total fixed cost (TFC)

The cost of all inputs that are fixedin the short run are called total fixed costs

Assume that wagons hours is fixed at 1

For this example, then TFC = $20.00

Fixed Cost Curve

0

20

40

60

80

100

0 400 800 1200 1600 2000 2400

Co

st

Output - y

TFC

Graphical representation

x1 x2 TPP APP A MPP MPP TFC TVC TC AFC AVC ATC AMC MC0.00 1.00 0.00 0.00 20.0 0.00 20.00

Data on hay hauling

1.0 1.0 38.0 38.00 38.00 74.0 20.0 6.00 26.00 0.526 0.158 0.684 0.158 0.081

2.0 1.0 144.0 72.00 106.00 136.0 20.0 12.00 32.00 0.139 0.083 0.222 0.057 0.044

3.0 1.0 306.0 102.00 162.00 186.0 20.0 18.00 38.00 0.065 0.059 0.124 0.037 0.032

Fixed cost stays the same -- variable cost is rising

x1 x2 TPP APP A MPP MPP TFC TVC TC AFC AVC ATC AMC MC0.00 1.00 0.00 0.00 20.0 0.00 20.00

Data on hay hauling

1.0 1.0 38.0 38.00 38.00 74.0 20.0 6.00 26.00 0.526 0.158 0.684 0.158 0.081

2.0 1.0 144.0 72.00 106.00 136.0 20.0 12.00 32.00 0.139 0.083 0.222 0.057 0.044

3.0 1.0 306.0 102.00 162.00 186.0 20.0 18.00 38.00 0.065 0.059 0.124 0.037 0.0324.0 1.0 512.0 128.00 206.00 224.0 20.0 24.00 44.00 0.039 0.047 0.086 0.029 0.0275.0 1.0 750.0 150.00 238.00 250.0 20.0 30.00 50.00 0.027 0.040 0.067 0.025 0.0246.0 1.0 1008.0 168.00 258.00 264.0 20.0 36.00 56.00 0.020 0.036 0.056 0.023 0.0237.0 1.0 1274.0 182.00 266.00 266.0 20.0 42.00 62.00 0.016 0.033 0.049 0.023 0.0238.0 1.0 1536.0 192.00 262.00 256.0 20.0 48.00 68.00 0.013 0.031 0.044 0.023 0.0239.0 1.0 1782.0 198.00 246.00 234.0 20.0 54.00 74.00 0.011 0.030 0.042 0.024 0.02610.0 1.0 2000.0 200.00 218.0 200.0 20.0 60.00 80.0 0.010 0.030 0.040 0.028 0.03011.0 1.0 2178.0 198.00 178.0 154.0 20.0 66.00 86.0 0.009 0.030 0.039 0.034 0.03912.0 1.0 2304.0 192.00 126.0 96.0 20.0 72.00 92.0 0.009 0.031 0.040 0.048 0.06313.0 1.0 2366.0 182.00 62.0 26.0 20.0 78.00 98.0 0.008 0.033 0.041 0.097 0.23114.0 1.0 2352.0 168.00 -14.0 -56.0 20.0 84.00 104.0 0.009 0.036 0.044

Total variable cost (TVC)

Remember that the cost of all the inputs that are variable

in the short run is called total variable cost

For our example TVC(38) = $6.00

TVC Σn1

i 1wixi

And TVC (306) = $18.00

Data on hay hauling

x1 x2 TPP APP A MPP MPP TFC TVC TC AFC AVC ATC AMC MC0.00 1.00 0.00 0.00 20.0 0.00 20.00 1.0 1.0 38.0 38.00 38.00 74.0 20.0 6.00 26.00 0.526 0.158 0.684 0.158 0.0812.0 1.0 144.0 72.00 106.00 136.0 20.0 12.00 32.00 0.139 0.083 0.222 0.057 0.0443.0 1.0 306.0 102.00 162.00 186.0 20.0 18.00 38.00 0.065 0.059 0.124 0.037 0.032

Data on hay haulingx1 x2 TPP APP A MPP MPP TFC TVC TC AFC AVC ATC AMC MC0.00 1.00 0.00 0.00 20.0 0.00 20.00 1.0 1.0 38.0 38.00 38.00 74.0 20.0 6.00 26.00 0.526 0.158 0.684 0.158 0.0812.0 1.0 144.0 72.00 106.00 136.0 20.0 12.00 32.00 0.139 0.083 0.222 0.057 0.0443.0 1.0 306.0 102.00 162.00 186.0 20.0 18.00 38.00 0.065 0.059 0.124 0.037 0.0324.0 1.0 512.0 128.00 206.00 224.0 20.0 24.00 44.00 0.039 0.047 0.086 0.029 0.0275.0 1.0 750.0 150.00 238.00 250.0 20.0 30.00 50.00 0.027 0.040 0.067 0.025 0.0246.0 1.0 1008.0 168.00 258.00 264.0 20.0 36.00 56.00 0.020 0.036 0.056 0.023 0.0237.0 1.0 1274.0 182.00 266.00 266.0 20.0 42.00 62.00 0.016 0.033 0.049 0.023 0.0238.0 1.0 1536.0 192.00 262.00 256.0 20.0 48.00 68.00 0.013 0.031 0.044 0.023 0.0239.0 1.0 1782.0 198.00 246.00 234.0 20.0 54.00 74.00 0.011 0.030 0.042 0.024 0.02610.0 1.0 2000.0 200.00 218.0 200.0 20.0 60.00 80.0 0.010 0.030 0.040 0.028 0.03011.0 1.0 2178.0 198.00 178.0 154.0 20.0 66.00 86.0 0.009 0.030 0.039 0.034 0.03912.0 1.0 2304.0 192.00 126.0 96.0 20.0 72.00 92.0 0.009 0.031 0.040 0.048 0.06313.0 1.0 2366.0 182.00 62.0 26.0 20.0 78.00 98.0 0.008 0.033 0.041 0.097 0.23114.0 1.0 2352.0 168.00 -14.0 -56.0 20.0 84.00 104.0 0.009 0.036 0.044

Graphical representation of TVC

Total Variable Cost

0

20

40

60

80

100

0 400 800 1200 1600 2000 2400

Co

st

Output - y

TVC

Total cost (TC)

The cost of all inputs used by the firm is called total costs

TC = TFC + TVC

TC Σn

i 1wixi

Specifically, the sum of fixed and variable costs is called total costs

Cost function

C(y ,w , x̄ ) FC(x̄ , w) C(y , w)

Graphical representation of total cost (TC)

Total Cost Curves

0

20

40

60

80

100

0 400 800 1200 1600 2000 2400

Co

st

Output - y

TFC

TVC

TC

Average cost (AC)

Average cost is just a total cost figure divided by theassociated output level

AC represents the average per unit costof a given level of output

There are average costs associated with eachlevel of total costs

Average fixed cost is given by

AFC FCy

TFCy

Average variable cost is given by

AVC VCy

TVCy

Average (total) cost is given by

ATC AC TCy

Cy

Data on hay haulingx1 x2 TPP(y) APP A MPP MPP TFC TVC TC AFC AVC ATC AMC MC0.00 1.00 0.00 0.00 20.0 0.00 20.00 1.0 1.0 38.0 38.00 38.00 74.00 20.0 6.00 26.00 0.526 0.158 0.684 0.158 0.0812.0 1.0 144 72.00 106.0 136.0 20.0 12.0 32.0 0.139 0.083 0.222 0.057 0.0443.0 1.0 306.0 102.00 162.00 186.00 20.0 18.00 38.00 0.065 0.059 0.124 0.037 0.0324.0 1.0 512.0 128.00 206.00 224.00 20.0 24.00 44.00 0.039 0.047 0.086 0.029 0.0275.0 1.0 750.0 150.00 238.00 250.00 20.0 30.00 50.00 0.027 0.040 0.067 0.025 0.0246.0 1.0 1008.0 168.00 258.00 264.00 20.0 36.00 56.00 0.020 0.036 0.056 0.023 0.0237.0 1.0 1274.0 182.00 266.00 266.00 20.0 42.00 62.00 0.016 0.033 0.049 0.023 0.0238.0 1.0 1536.0 192.00 262.00 256.00 20.0 48.00 68.00 0.013 0.031 0.044 0.023 0.0239.0 1.0 1782.0 198.00 246.00 234.00 20.0 54.00 74.00 0.011 0.030 0.042 0.024 0.02610.0 1.0 2000.0 200.00 218.0 200.00 20.0 60.00 80.0 0.010 0.030 0.040 0.028 0.03011.0 1.0 2178.0 198.00 178.0 154.00 20.0 66.00 86.0 0.009 0.030 0.039 0.034 0.03912.0 1.0 2304.0 192.00 126.0 96.00 20.0 72.00 92.0 0.009 0.031 0.040 0.048 0.06313.0 1.0 2366.0 182.00 62.0 26.00 20.0 78.00 98.0 0.008 0.033 0.041 0.097 0.23114.0 1.0 2352.0 168.00 -14.0 -56.00 20.0 84.00 104.0 0.009 0.036 0.044

AFC 20144

.1388 ATC 32144

.2222

Average Fixed Cost

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 400 800 1200 1600 2000 2400

Co

st

Output - y

AFC

AVC

Average Variable Cost

0.00

0.05

0.10

0.15

0.20

0 400 800 1200 1600 2000 2400

Co

st

Output - y

Note that ATC = AVC + AFC

Average Cost Curves

0.00

0.10

0.20

0.30

0.40

0 400 800 1200 1600 2000 2400

Co

st

Output - y

AVC

ATC

AFC

Marginal costMarginal cost is the increment, or addition, to costMarginal cost is the increment, or addition, to costthat results from producing one more unit of outputthat results from producing one more unit of output

The increase in total cost is the increase in variable cost

In discrete or average terms marginal cost is given by

MC ΔC(y,w)Δy

ΔTC(y,w)Δy

Marginal cost is just the derivative of the cost function with respect to y

MC dC(y,w)dy

Example calculation

MC ΔC(y,w)Δy

x1 x2 y TFC TVC TC AVE MC0.0 1.0 0.0 20.0 0.00 20.00 1.0 1.0 38.0 20.0 6.00 26.00 0.1582.0 1.0 144.0 20.0 12.00 32.00 0.0573.0 1.0 306.0 20.0 18.00 38.00 0.0374.0 1.0 512.0 20.0 24.00 44.00 0.0295.0 1.0 750.0 20.0 30.00 50.00 0.0256.0 1.0 1008.0 20.0 36.00 56.00 0.023

(38 32)(306 144)

6162

0.037

Graphical representation of Marginal Cost

0.00

0.05

0.10

0.15

0.20

0 400 800 1200 1600 2000 2400

Co

st

Output - y

AVE MC

Relationship between MC & MPP (1 variable input)

When MPP rises, MC falls

When MPP falls, MC rises

Marginal Cost Curve

0.00

0.05

0.10

0.15

0.20

0 400 800 1200 1600 2000 2400

Co

st

Output - y

AVE MC

Marginal Product of Input 1

-50

0

50

100

150

200

250

300

2 4 6 8 10 12 14

Input - x1

Ou

tpu

t -

y

MPP 1

4. The marginal cost curve will intersect AVCand ATC at their minimum points

Average and marginal costs1. When marginal cost is below the average cost, the average cost curve is falling

2. When the marginal and average costs are equal,the average cost curve does not change(is at minimum point)

3. When the marginal cost is greater thanaverage cost, average cost is rising

Average and Marginal Cost Curves

0.0

0.1

0.2

0.3

0 400 800 1200 1600 2000 2400

Co

st

Output - y

AVC

ATC

AVE MC

AFC

FC

Cost curves for alternative functionC(y) 100 6y .4y 2 .02y 3

050100150200250300350400450500

0 10 20 30 40

Output - y

Co

st

VC

TC

AVCATC

AFC

Average and Marginal Cost Curves

0481216202428323640

0 10 20 30

Output - y

Co

st

AMC

The End