Ram Kumar Phuyal presents on production theory and costs. He discusses production functions with one and two variable inputs and the concept of returns to scale. He explains the production function and differentiates between fixed and variable inputs. Total, average, and marginal products are defined for a single variable input. There are three stages of production as marginal product first increases, then decreases and becomes negative. Short-run costs include total fixed, variable, and total costs. Average and marginal costs are also analyzed.

1. Ram Kumar Phuyal, Ph.D.Ram Kumar Phuyal, Ph.D.
MicroeconomicsMicroeconomics
Kathmandu UniversityKathmandu University
Theory of Production and CostsTheory of Production and Costs

2. Contents:
This presentation includes about
production function with one and two
variable input(s), returns to scale, and
short run and long run costs functions.

3. The Production FunctionThe Production Function
 TheThe production functionproduction function refers to the physical relationshiprefers to the physical relationship
between the inputs or resources of a firm and theirbetween the inputs or resources of a firm and their
output of goods and services at a given period of time,output of goods and services at a given period of time,
ceteris paribus.ceteris paribus.
 The production function isThe production function is dependentdependent on differenton different
time frames. Firms can produce for a brief or lengthytime frames. Firms can produce for a brief or lengthy
period of time.period of time.

4. Firm’s InputsFirm’s Inputs
 Inputs - are resources that contribute in theInputs - are resources that contribute in the
production of a commodity.production of a commodity.
 Most resources are lumped into three categories:Most resources are lumped into three categories:
 Land,Land,
 Labor,Labor,
 CapitalCapital
 OrganizationOrganization
 Raw materials and etc.Raw materials and etc.

5. Fixed vs. Variable InputsFixed vs. Variable Inputs
 Fixed inputs -resources used at a constant amount inFixed inputs -resources used at a constant amount in
the production of a commodity.the production of a commodity.
 Variable inputs - resources that can change in quantityVariable inputs - resources that can change in quantity
depending on the level of output being produced.depending on the level of output being produced.
 The longer planning the period, the distinction betweenThe longer planning the period, the distinction between
fixed and variable inputs disappears, i.e., all inputs arefixed and variable inputs disappears, i.e., all inputs are
variable in the long run.variable in the long run.

6. Production Analysis with One Variable InputProduction Analysis with One Variable Input
 Total product (Q)Total product (Q) refers to the total amount of outputrefers to the total amount of output
produced in physical units (may refer to, kilogramsproduced in physical units (may refer to, kilograms
of sugar, sacks of rice produced, etc)of sugar, sacks of rice produced, etc)
 TheThe marginal product (MP)marginal product (MP) refers to the rate of changerefers to the rate of change
in output as an input is changed by one unit, holdingin output as an input is changed by one unit, holding
all other inputs constant.all other inputs constant.
L
L
TP
MP
L
∆
=
∆

7. Total vs. Marginal ProductTotal vs. Marginal Product
 Total Product (TPx) = total amount of outputTotal Product (TPx) = total amount of output
produced at different levels of inputsproduced at different levels of inputs
 Marginal Product (MPx) = rate of change in output asMarginal Product (MPx) = rate of change in output as
input X is increased by one unit,input X is increased by one unit, ceteris paribusceteris paribus..
X
X
TP
MP
X
∆
=
∆

8. Production Function of a Rice FarmerProduction Function of a Rice Farmer
Table 1.Table 1.
Units of LUnits of L Total ProductTotal Product
(Q(QLL or TPor TPLL))
Marginal ProductMarginal Product
(MP(MPL)L)
00 00 --
11 22 22
22 66 44
33 1212 66
44 2020 88
55 2626 66
66 3030 44
77 3232 22
88 3232 00
99 3030 -2-2
1010 2626 -4-4

9. FIGURE 1. Total product curve. The total product curve shows the behavior of
total product with an input (e.g., labor) used in production assuming a certain
technological level.
L
QL
QL
2
6
12
20
26
30
32
Labor
Totalproduct
0 2 4 6 8 1097531

10. Marginal ProductMarginal Product
 TheThe marginal productmarginal product refers to the rate of change in outputrefers to the rate of change in output
as an input is changed by one unit, holding all other inputsas an input is changed by one unit, holding all other inputs
constant.constant.
 Observe that the marginal productObserve that the marginal product initially increases, reaches ainitially increases, reaches a
maximum level, and beyond this point, the marginal product declines,maximum level, and beyond this point, the marginal product declines,
reaches zero, and subsequently becomes negative.reaches zero, and subsequently becomes negative.
 TheThe law of diminishing returnslaw of diminishing returns states that "as the use ofstates that "as the use of
an input increases (with other inputs fixed), a point willan input increases (with other inputs fixed), a point will
eventually be reached at which the resulting additions toeventually be reached at which the resulting additions to
output decrease"output decrease"

11. Total and Marginal ProductTotal and Marginal Product
-10
-5
0
5
10
15
20
25
30
35
0 1 2 3 4 5 6 7 8 9
TPL
MPL
FIGURE 2.

12. Law of Diminishing MarginalLaw of Diminishing Marginal
ReturnsReturns
 As more and more of an input is addedAs more and more of an input is added
(given a fixed amount of other inputs)(given a fixed amount of other inputs), total, total
output may increase; however, as theoutput may increase; however, as the
additions to total output will tend toadditions to total output will tend to
diminish.diminish.
 Counter-intuitive proof: if the law ofCounter-intuitive proof: if the law of
diminishing returns does not hold, thediminishing returns does not hold, the
world’s supply of food can be produced inworld’s supply of food can be produced in
a hectare of land.a hectare of land.

13. Average Product (AP)Average Product (AP)
 Average product is a concept commonlyAverage product is a concept commonly
associated with efficiency.associated with efficiency.
 TheThe average productaverage product measures the total output permeasures the total output per
unit of input used.unit of input used.
 The "productivity" of an input is usuallyThe "productivity" of an input is usually
expressed in terms of its average product.expressed in terms of its average product.
 The greater the value of average product, theThe greater the value of average product, the
higher the efficiency in physical terms.higher the efficiency in physical terms.
 Formula:Formula: L
L
TP
AP
L
=

14. TABLE 2. Average product of labor.
Labor (L)
Total product of
labor (TPL)
Average product of
labor (APL)
0 0 0
1 2 2
2 6 3
3 12 4
4 20 5
5 26 5.2
6 30 5
7 32 4.5
8 32 4
9 30 3.3
10 26 2.6

15. Rise = Y
Run = L0
L
Y
The slope of the line from the origin
is a measure of the AVERAGE
Y
L1 L2
a b
rise
Slope =
run
Y
L
=
FIGURE 3.

16. Labor
Q
QL
0
Total
Product
a
b
c
d
The average product at b is highest.
AP at c is less than at a.
AP at d is less than at c.
FIGURE 4.
L

17. L
Q
TPL
Highest Slope of Line
from Origin
Max APL
Inflection point
Max MPL
0 L1 L2 L3
FIGURE 5.

18. Relationship between Average andRelationship between Average and
Marginal CurvesMarginal Curves
 When the marginal is less than the average, theWhen the marginal is less than the average, the
average decreases.average decreases.
 When the marginal is equal to the average, theWhen the marginal is equal to the average, the
average does not change (it is either at maximumaverage does not change (it is either at maximum
or minimum)or minimum)
 When the marginal is greater than the average,When the marginal is greater than the average,
the average increasesthe average increases

19. Relationship between Average and MarginalRelationship between Average and Marginal
Curves: Example of Econ 11 ScoresCurves: Example of Econ 11 Scores
 When the marginal score (new exam) is lessWhen the marginal score (new exam) is less
than your average score, the averagethan your average score, the average
decreases.decreases.
 When the marginal score (new exam) is equalWhen the marginal score (new exam) is equal
to the average score, the average does notto the average score, the average does not
change.change.
 When the marginal score (new exam) isWhen the marginal score (new exam) is
greater than your average score, the averagegreater than your average score, the average
increases.increases.

20. L
Q
Max APL
Max MPL
0 L1
L2 L3
MPL
APL
At Max AP,
MP=AP
FIGURE 5.
AP, MP

21. L
AP,MP
0 L1
L2 L3
MPL
APL
Stage I
MP>AP
AP increasing
Stage II
MP<AP
AP decreasing
MP still positive
Stage III
MP<0
AP decreasing
L
TP
0 L1 L2 L3
TPL
FIGURE 6.

22. Three Stages of ProductionThree Stages of Production
 In Stage IIn Stage I
 APAPLL is increasing so MP>AP.is increasing so MP>AP.
 All the product curves are increasingAll the product curves are increasing
 Stage I stops whereStage I stops where APAPLL reaches its maximum atreaches its maximum at
pointpoint A.A.
 MP peaks and then declines at pointMP peaks and then declines at point CC and beyond,and beyond,
so the law of diminishing returns begins to manifestso the law of diminishing returns begins to manifest
at this stageat this stage

23. Three Stages of ProductionThree Stages of Production
 Stage IIStage II
 starts where thestarts where the APAPLL of the input begins to decline.of the input begins to decline.
 QQLL still continues to increase, although at astill continues to increase, although at a
decreasing rate, and in fact reaches a maximumdecreasing rate, and in fact reaches a maximum
 Marginal product is continuously declining andMarginal product is continuously declining and
reaches zero at pointreaches zero at point D,D, as additional labor inputsas additional labor inputs
are employed.are employed.

24. Three Stages of ProductionThree Stages of Production
 Stage III starts where theStage III starts where the MPLMPL has turnedhas turned
negative.negative.
 all product curves are decreasing.all product curves are decreasing.
 total output starts falling even as the input istotal output starts falling even as the input is
increasedincreased

25. Cost of ProductionCost of Production
 Opportunity Cost Principle -Opportunity Cost Principle - the economic cost of an inputthe economic cost of an input
used in a production process is the value of outputused in a production process is the value of output
sacrificed elsewhere. The opportunity cost of an inputsacrificed elsewhere. The opportunity cost of an input
is the value of foregone income in best alternativeis the value of foregone income in best alternative
employment.employment.
 Implicit vs. Explicit CostsImplicit vs. Explicit Costs
 Explicit costsExplicit costs – costs paid in cash– costs paid in cash
 Implicit costImplicit cost – imputed cost of self-owned or self employed– imputed cost of self-owned or self employed
resources based on their opportunity costs.resources based on their opportunity costs.

26. Costs on Short-RunCosts on Short-Run
1.1. Total Fixed CostTotal Fixed Cost (TFC)(TFC)
2.2. Total Variable CostTotal Variable Cost (TVC)(TVC)
3.3. Total CostTotal Cost (TC=TVC+TFC)(TC=TVC+TFC)
4.4. Average Fixed CostAverage Fixed Cost (AFC=TFC/Q)(AFC=TFC/Q)
5.5. Average Variable CostAverage Variable Cost (AVC=TVC/Q)(AVC=TVC/Q)
6.6. Average Total CostAverage Total Cost (AC=AFC+AVC)(AC=AFC+AVC)
7.7. Marginal CostMarginal Cost (MC= ∆AVC/∆Q(MC= ∆AVC/∆Q

27. Short Run AnalysisShort Run Analysis
 Total fixed cost (TFC)Total fixed cost (TFC) is more commonly referredis more commonly referred
to as "sunk cost" or "overhead cost."to as "sunk cost" or "overhead cost."
 Examples: include the payment or rent for land,Examples: include the payment or rent for land,
buildings and machinery.buildings and machinery.
 The fixed cost is independent of the level ofThe fixed cost is independent of the level of
output produced.output produced.
 Graphically, depicted as a horizontal lineGraphically, depicted as a horizontal line

28. Short Run AnalysisShort Run Analysis
 Total variable cost (TVC)Total variable cost (TVC) refers to the cost thatrefers to the cost that
changes as the amount of output produced ischanges as the amount of output produced is
changed.changed.
 Examples - purchases of raw materials, payments toExamples - purchases of raw materials, payments to
workers, electricity bills, fuel and power costs.workers, electricity bills, fuel and power costs.
 Total variable cost increases as the amount of outputTotal variable cost increases as the amount of output
increases.increases.
 If no output is produced, then total variable costIf no output is produced, then total variable cost
is zero;is zero;
 the larger the output, the greater the total variablethe larger the output, the greater the total variable
cost.cost.

29. Short Run AnalysisShort Run Analysis
 Total costTotal cost (TC)(TC) is the sum of total fixed costis the sum of total fixed cost
and total variable costand total variable cost
 TC=TFC+TVCTC=TFC+TVC
 As the level of output increases, total cost of theAs the level of output increases, total cost of the
firm also increases.firm also increases.

30. Table 3Table 3-Costs-Costs
Units of
Labor
Total
Product
Total
Fixed
Cost
Total
Variable
Cost
Total
Cost
Marginal
Cost
Average
Cost
L TPL TFC TVC TC MC AC
0 0 100 0 100 - -
1 6 100 30 130 30 130
2 10 100 50 150 20 75
3 12 100 60 160 10 53.3
4 13 100 65 165 5 41.25
5 15 100 75 175 10 35
6 19 100 95 195 20 32.5
7 25 100 125 225 30 32.14
8 33 100 165 265 40 33.12
9 43 100 215 315 50 35
10 55 100 275 375 60 37.5

31. Q0
TFC
(Total Fixed Cost)
Costs
TVC
(Total Variable Cost)
TC
(Total Cost)
“TOTAL” COST CURVES
FIGURE 7.

32. Q0
AFC
(Average Fixed Cost)
Costs
AFC=TFC/Q.
As more output is produced, the
Average Fixed Cost decreases.
FIGURE 8.

33. Q0
Costs
TVC
(Total Variable Cost)
q1
The Average Variable
Cost at a point on the
TVC curve is measured by
the slope of the line from
the origin to that point.
AVC=TVC/Q
Minimum AVC
FIGURE 9.

34. Q0
Costs
MC
q1
Inflection
point
TVC
(Total Variable Cost)
q1
AVC
FIGURE 10.

35. Q0
Costs
AVC
(Average Variable Cost)
q1
The Average Variable Cost is U
shaped. First it decreases, reaches a
minimum and then increases.
Minimum AVC
FIGURE 11.

36. Q0
Costs
AVC
(Average Variable Cost)
q1
The Marginal Cost curve passes through
the minimum point of the AVC curve.
It is also U-shaped. First it decreases,
reaches a minimum and then increases.
Minimum AVC
MC (Marginal Cost)
FIGURE 12.

37. Q0
Costs
AVC
q1
MC
AFC
AC
The “PER UNIT” COST CURVES
FIGURE 13.

38. Table 4-Average CostsTable 4-Average Costs
(Q) (TC) (AC)
0 100 -
1 130 130.00
2 150 75.00
3 160 53.33
4 165 41.25
5 175 35.00
6 195 32.50
7 225 32.14
8 265 33.13
9 315 35.00
10 375 37.50

39. Total Product
(Q)
Total Variable Cost
(AVC)
Average Variable Cost
(AVC)
0 0 0
1 30 30.0
2 50 25.0
3 60 20.0
4 65 16.3
5 75 15.0
6 95 15.8
7 125 17.9
8 165 20.6
9 215 23.9
10 275 27.5
Table 5-Average Variable Costs

40. LongRunTotalCostLTC LTC
Q
Total Product
All inputs are variable in the long
run. There are no fixed costs.
LONG-RUN TOTAL COST CURVE
FIGURE 14.

41. Long Run ACLong Run AC
 The LAC curve is an envelop curve of allThe LAC curve is an envelop curve of all
possible plant sizes. Also known as “planningpossible plant sizes. Also known as “planning
curve”curve”
 It traces the lowest average cost of producingIt traces the lowest average cost of producing
each level of output.each level of output.
 It is U-shaped because ofIt is U-shaped because of
 Economies of ScaleEconomies of Scale
 Diseconomies of ScaleDiseconomies of Scale

42. LAC
SAC1
Q0
COSTS
SAC3
LONG-RUN AVERAGE COST CURVE
SAC4
SAC5
SAC6
SAC7
SAC8
SAC9
SAC2
FIGURE 15.

43. LAC
Q0
COST
SAC1
q0
FIGURE 16.

44. LAC
Q0
COST
SAC1
q0
SAC2
Building a larger sized plant (size 2)
will result in a lower average cost of
producing q0
FIGURE 17.

45. LAC
Q0
COST
SAC1
q0
SAC2
Likewise, a larger sized plant (size
3) will result to a lower average
cost of producing q1
q1
SAC3
FIGURE 18.

46. Economies and Diseconomies of ScaleEconomies and Diseconomies of Scale
 Economies of ScaleEconomies of Scale- long run average cost- long run average cost
decreases as output increases.decreases as output increases.
 Technological factorsTechnological factors
 SpecializationSpecialization
 Diseconomies of ScaleDiseconomies of Scale: - long run average cost: - long run average cost
increases as output increases.increases as output increases.
 Problems with management – becomes costly,Problems with management – becomes costly,
unwieldyunwieldy

47. LAC
SAC1
Q0
COST
SAC2
LONG-RUN AVERAGE COST CURVE
Q1
Economies of Scale Diseconomies of Scale
FIGURE 19.

48. LAC
SAC1
Q0
COST
LONG-RUN AVERAGE and MARGINAL COST CURVES
Q1
LMC
SMC1
SMC2
SAC2
FIGURE 20.

49. LAC and LMCLAC and LMC
 Long-run Average Cost (LAC) curveLong-run Average Cost (LAC) curve
 is U-shaped.is U-shaped.
 the envelope of all the short-run average costthe envelope of all the short-run average cost
curves; driven by economies and diseconomiescurves; driven by economies and diseconomies
of size.of size.
 Long-run Marginal Cost (LMC) curveLong-run Marginal Cost (LMC) curve
 Also U-shaped;Also U-shaped;
 intersects LAC at LAC’s minimum point.intersects LAC at LAC’s minimum point.