Theory of Production & Cost

BEC 30325Managerial Economics

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Fundamental questions…

• How can production be optimized?• How can cost be minimized?• How does output behave when quantity of inputs is

increased?• How can the least-cost combination of inputs be

achieved?• What does happen to the rate of return when more

plants are added? • How does technology matter in reducing the cost of

production?

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Why production and cost???

• Profit through managing the revenue is more interesting and exciting.

• Managers may enjoy time spent on revenue decisions.

• In a competitive market scenario;– Profitability fairly depends on optimization of

production and minimization of costs.– Managers may find internalization of profitability

is easier than externalization.

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Some basic concepts of production theory…

• Fixed and variable inputs– Fixed inputs (Ex: buildings, machinery)• Economic sense – supply is inelastic in the short run• Technical sense – remains constant for a certain level of

output• Quasi-fixed inputs - unlike the fixed inputs, this can be

avoided and cost is zero if the firm chooses to produce nothing

– Variable inputs (Ex: raw materials, labour, fuel)• Economic sense – supply is elastic in the short run• Technical sense – changes with the change in output

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Some basic concepts of production theory…

• Short run and long run– Short run • Refers to a period of time in which the level of usage of

at least one input is fixed• Changes in the output must be accomplished by

changes in variable inputs• Short run production function;

• Other variable inputs (such as materials, fuel) are omitted in the production function. (Why?)

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Some basic concepts of production theory…

• Short run and long run– Long run• Refers to the time in the future when all inputs are

variable• Output changes with changes in both labour and capital• Long run production function;

• Long run consists of all possible short run situations (all possible choices of capital usage)• What is the ‘very long run’?

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Some basic concepts of production theory…

• Technical and economic efficiency– Technical efficiency• Production of the maximum level of output that can be

obtained from a given combination of inputs

– Economic efficiency• Production of a given amount of output at the lowest

possible cost

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Production in the short run

0 1 2 3 4 5 6 7 8 9 10

0 0 0 0 0 0 0 0 0 0 0 0

1 0 25 52 74 90 100 108 114 118 120 121

2 0 55 112 162 198 224 242 252 258 262 264

3 0 83 170 247 303 342 369 384 394 400 403

4 0 108 220 325 400 453 488 511 527 535 540

5 0 125 258 390 478 543 590 631 653 663 670

6 0 137 286 425 523 598 655 704 732 744 753

7 0 141 304 453 559 643 708 766 800 814 825

8 0 143 314 474 587 679 753 818 857 873 885

9 0 141 318 488 609 708 789 861 905 922 935

10 0 137 314 492 617 722 809 887 935 953 967

Units of capital (K)

Uni

ts o

f lab

our (

L)

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Total, Average & Marginal Product of Labour (with capital fixed at 2 units)

No. of workers (L)

Total product (TP)

Average product (AP = Q/L)

Marginal product(MP = ∆Q/∆L)

0 0 - -

1 52 52 52

2 112 56 60

3 170 56.7 58

4 220 55 50

5 258 51.6 38

6 286 47.7 28

7 304 43.4 18

8 314 39.3 10

9 318 35.3 4

10 314 31.4 -4

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Average & Marginal Products• Average product of labor

• Marginal product of labor

• When AP is rising, MP is greater than AP• When AP is falling, MP is less than AP• When AP reaches it maximum, • Law of diminishing marginal product– As usage of a variable input increases, a point is reached

beyond which its marginal product decreases

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Total, average and marginal product curves (with capital fixed at 2 units)

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Law of Diminishing Marginal Product

• Number of units of the variable input increases, a point will be reached beyond which the marginal product decreases

• Other inputs held constant• Increasing, diminishing and negative marginal

product situations

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Short run cost of production

• Economic cost of using resources;Total economic (opportunity) cost =

Explicit costs of market supplied resources + Implicit costs of owner supplied resources

• Total cost consists of total fixed and variable costs

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Short run total costsOutput

(Q)Total fixed cost

(TFC)Total variable cost

(TVC)Total cost

(TC = TFC + TVC)0 $ 6,000 $ 0 $ 6,000

100 6,000 4,000 10,000

200 6,000 6,000 12,000

300 6,000 9,000 15,000

400 6,000 14,000 20,000

500 6,000 22,000 28,000

600 6,000 34,000 40,000

• TVC changes with the output but depends on the usage of variable inputs (labour).

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Short run average and marginal costs

Output(Q)

Average fixed cost

(AFC = TFC/Q)

Average variable cost (AVC =

TVC/Q)

Average total cost

(ATC = TC/Q)

Short run marginal cost

(SMC = ∆TC/∆Q)

0 - - - -

100 $ 60 40 $ 100 $ 40

200 30 30 60 20

300 20 30 50 30

400 15 35 50 50

500 12 44 56 80

600 10 56.7 66.7 120

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Short run average and marginal cost curves

• SMC curve crosses AVC and ATC curves at their respective minimum points.

• So, AVC and ATC falling when SMC is less than those.

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Relationship between short run production and costs

Short run production Short run costs

Labour(L)

Output(Q)

Total variable cost(TVC = wL)

Total fixed cost(TFC = rK)

Total cost(TC = wL + rK)

0 0 0 $ 6,000 $ 6,000

4 100 $ 4,000 6,000 10,000

6 200 6,000 6,000 12,000

9 300 9,000 6,000 15,000

14 400 14,000 6,000 20,000

22 500 22,000 6,000 28,000

34 600 34,000 6,000 40,000

• Assumptions Wage rate (w) = $ 1,000 per worker, Cost of capital (r) = $ 2,000 per unit

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Average and marginal relations between cost and production

Short run production Short run costs

L Q AP MP AVC SMC

0 0 - - - -

4 100 25 25 $ 40 $ 40

6 200 33.33 50 30 20

9 300 33.33 33.33 30 30

14 400 28.57 20 35 50

22 500 22.73 12.50 44 80

34 600 17.65 8.33 56.67 120

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AVC and AP• Consider the 100 units of output…

• AVC is calculated by dividing the wage rate by AP

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SMC and MP• Consider increase in output from 100 to 200 units…

• SMC is calculated by dividing the wage rate by MP

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• Assume a wage rate of $21 • First consider the product and cost

curves over the range of 0 to 500 units of labour.• MP lies above AP, so AP is rising. • Because, SMC is inversely related to

MP (SMC = w/MP) and AVC is inversely related to AP (AVC = w/AP)

• MP is maximized (9 units of output) and SMC is minimized to $ 2.33 (21/9) at the usage of 500 units of labour and 3,250 units (6.5 x 500) of output.

• Now consider the product and cost curves over the range of 500 to 800 units of labour.• As MP falls SMC rises. • But, AP rises as MP is still greater

than AP and AVC falls as SMC is still less than AVC.

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Implications for managers…

• Relations between production and cost curves in the short run involves the effect of the law of diminishing marginal product on the marginal cost of production.

• In the above example;– At 800 units of labour and 5,600 units of output, both SMC

and AVC are equal ($3) and AVC reaches its minimum. – Beyond this point AP begins to decrease but never

becomes negative. However, MP eventually becomes negative.

• So…what’s your decision?

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Production and cost in the long run

• Increase in the scale of operations– Need to increase the amount of capital employed– Variability of all factors of production with the output

change• Economies of scale• Economies of scope – Reduce the cost of one good by becoming the

producer of other related goods in production• Related diversification• Mergers and acquisitions

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Production Isoquants

• A curve showing all possible combinations of inputs physically capable of producing a given fixed level of output.

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Marginal Rate of Technical Substitution

• MRTS– The rate at which one input is substituted another

along an isoquant

• Relation of MRTS to marginal products

Ex: ,

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Isocost Curves

• Shows various combinations of inputs that may be purchased for a given level of expenditure at given input prices .

• Slope of the isocost curve is the negative of the input price ratio

• Intercept is – Represents amount of capital that may be

purchased if zero labor is purchased

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Isocost Curves

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Optimal combination of inputs

• Minimize total cost of producing by choosing the input combination on the isoquant for which is just tangent to an isocost curve.– Two slopes are equal in equilibrium– Implies marginal product per dollar spent on last

unit of each input is the same

= or =

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Output optimization and cost minimization

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Optimization and cost

• Expansion path gives the efficient (least-cost) input combinations for every level of output– Derived for a specific set of input prices– Along expansion path, input-price ratio is constant

& equal to the MRTS

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Expansion path