cost_production micro economics chapter theory of production

Theory of Production & Cost
BEC 30325
Managerial Economics

2
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?

3
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.

4
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

5
• 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?)

6
• 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’?

7
• 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

8
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)
Units
of
labour
(L)

9
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

10
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

11
Total, average and
marginal product
curves
(with capital fixed at 2
units)

12
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

13
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

14
Short run total costs
Output
(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).

15
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

16
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.

17
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

18
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

19
AVC and AP
• Consider the 100 units of output…
• AVC is calculated by dividing the wage rate by AP

20
SMC and MP
• Consider increase in output from 100 to 200 units…
• SMC is calculated by dividing the wage rate by MP

21
• 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.

22
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?

23
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

24
Production Isoquants
• A curve showing
all possible
combinations of
inputs physically
capable of
producing a
given fixed level
of output.

25
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: ,

26
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

28
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 =

29
Output optimization and cost minimization

30
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

cost_production micro economics chapter theory of production

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