49688217

7/27/2019 49688217

1/46

Producers Behaviour

7/27/2019 49688217

2/46

ProductionThe theory of the firm describes how a firm makes cost-

minimizing production decisions and how the firmsresulting cost varies with its output.

The production decisions of firms are analogous to the

purchasing decisions of consumers, and can likewise beunderstood in three steps:

1. Production Technology

2. Cost Constraints

3. Input Choices

The Production Decisions of a Firm

7/27/2019 49688217

3/46

THE TECHNOLOGY OF PRODUCTION

The ProductionFunction

factors of production Inputs into the productionprocess (e.g., labor, capital, and materials).

Remember the following:

( , )q F K L

Inputs and outputs are flows .

This Equation applies to a given technology.

Production functions describe what is technically feasible when the firm operates efficiently .

production function Function showing the highestoutput that a firm can produce for every specifiedcombination of inputs.

7/27/2019 49688217

4/46

THE TECHNOLOGY OF PRODUCTION

The Short Run versus theLong Run short run Period of time in which quantities of one or

more production factors cannot be changed.

fixed input Production factor that cannot be varied.

long run Amount of time needed to make allproduction inputs variable.

7/27/2019 49688217

5/46

7/27/2019 49688217

6/46

Production with One Variable Input

0 10 0

1 10 10 10 10

2 10 30 15 20

3 10 60 20 30

4 10 80 20 20

5 10 95 19 15

6 10 108 18 13

7 10 112 16 4

8 10 112 14 0

9 10 108 12 4

10 10 100 10 8

PRODUCTION WITH ONE VARIABLE INPUT(LABOR)

TotalOutput ( q )

Amountof Labor ( L )

Amountof Capital ( K )

MarginalProduct ( q / L )

AverageProduct ( q /L )

7/27/2019 49688217

7/46

PRODUCTION WITH ONE VARIABLE INPUT(LABOR) Average and Marginal Products

average product Output per unit of a particular input.

marginal product Additional output produced as an input isincreased by one unit.

Average product of labor = Output/labor input = q/LMarginal product of labor = Change in output/change in labor input

= q/L

Elasticity of production: A measure of proportionality between

changes in inputs and resulting changes in output

Q L

LQ

E L

7/27/2019 49688217

8/46

PRODUCTION WITH ONE VARIABLE INPUT (LABOR)

The Slopes of the Product Curve

The total product curve in (a) showsthe output produced for differentamounts of labor input.

The average and marginal productsin (b) can be obtained (using thedata in Table 6.1) from the totalproduct curve.

At point A in (a) , the marginalproduct is 20 because the tangentto the total product curve has aslope of 20.

At point B in (a) the average productof labor is 20, which is the slope of the line from the origin to B.

The average product of labor atpoint C in (a) is given by the slopeof the line 0 C .

Production with One Variable Input

7/27/2019 49688217

9/46

PRODUCTION WITH ONE VARIABLE INPUT (LABOR)

The Slopes of the Product Curve

To the left of point E in (b) , themarginal product is above theaverage product and the average isincreasing; to the right of E , the

marginal product is below theaverage product and the average isdecreasing.

As a result, E represents the pointat which the average and marginalproducts are equal, when theaverage product reaches its

maximum. At D, when total output ismaximized, the slope of the tangentto the total product curve is 0, as isthe marginal product.

Production with One Variable Input(continued)

7/27/2019 49688217

10/46

LABOR INPUT

PRODUCTION WITH TWO VARIABLE INPUTS

Production with Two Variable Inputs

Capital Input 1 2 3 4 5

1 20 40 55 65 75

2 40 60 75 85 90

3 55 75 90 100 105

4 65 85 100 110 1155 75 90 105 115 120

Isoquants

isoquant Curve showing

all possible combinationsof inputs that yield thesame output.(isoquants.pdf )
http://localhost/var/www/apps/conversion/tmp/scratch_5/isoquants.pdfhttp://localhost/var/www/apps/conversion/tmp/scratch_5/isoquants.pdf

7/27/2019 49688217

11/46


Isoquants

isoquant map Graph combining a number of isoquants, used to describe a production function.

A set of isoquants, or isoquant map, describes the firmsproduction function.Output increases as we movefrom isoquant q1 (at which 55units per year are produced atpoints such as A and D),

to isoquant q2 (75 units per year atpoints such as B) and

to isoquant q3 (90 units per year atpoints such as C and E ).

Production with Two Variable Inputs

7/27/2019 49688217

12/46


Diminishing Marginal Returns

Holding the amount of capitalfixed at a particular level say3, we can see that eachadditional unit of labor generates less and lessadditional output.

7/27/2019 49688217

13/46

PRODUCTION WITH TWO VARIABLE INPUTSSubstitution Among Inputs

Like indifference curves,isoquants are downward slopingand convex. The slope of theisoquant at any point measuresthe marginal rate of technicalsubstitution the ability of thefirm to replace capital with labor while maintaining the same level

of output.On isoquant q2, the MRTS fallsfrom 2 to 1 to 2/3 to 1/3.

Marginal Rate of TechnicalSubstitution

marginal rate of technical substitution (MRTS) Amount by which the

quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant.

MRTS = Change in capital input/change in labor input = K /L (for a fixed level of q)

(MP ) / (MP ) ( / ) MRTS K L L K

7/27/2019 49688217

14/46


Production Functions Two SpecialCases

When the isoquants arestraight lines, the MRTS isconstant. Thus the rate atwhich capital and labor canbe substituted for eachother is the same no matter what level of inputs is beingused.

Points A , B, and C represent three differentcapital-labor combinationsthat generate the sameoutput q3. (ex-musicalinstruments)

Isoquants When Inputs ArePerfect Substitutes

7/27/2019 49688217

15/46


Production Functions Two Special Cases

When the isoquants are L-shaped, only onecombination of labor andcapital can be used toproduce a given output (as at

point A on isoquant q1, pointB on isoquant q2, and point C on isoquant q3). Adding morelabor alone does not increaseoutput, nor does adding morecapital alone. (e.g. one labor + one jackhammer)

Fixed-ProportionsProduction Function

fixed-proportions production function Production function

with L-shaped isoquants, so that only one combination of labor and capital can be used to produce each level of output.

The fixed-proportions production function describessituations in which methods of production are limited.(Leontief production function)

7/27/2019 49688217

16/46

Ridge Lines

Revisiting Cobb-Douglas Production function

Elasticity of output (are the values of exponents in the Cobb-Douglas function)

7/27/2019 49688217

17/46

Cobb-Douglas Production Function

21 K LQ

Homogeneous of degree 1+ 2

7/27/2019 49688217

18/46

RETURNS TO SCALE

returns to scale Rate at which output increases asinputs are increased proportionately.

increasing returns to scale Situation in which outputmore than doubles when all inputs are doubled.

constant returns to scale Situation in which outputdoubles when all inputs are doubled.

decreasing returns to scale Situation in which output

less than doubles when all inputs are doubled.

7/27/2019 49688217

19/46

RETURNS TO SCALE

When a firms production process exhibitsconstant returns to scale as shown by amovement along line 0 A in part (a) , theisoquants are equally spaced as outputincreases proportionally.

Returns to Scale

However, when there are increasingreturns to scale as shown in (b) , theisoquants move closer together asinputs are increased along the line.

Describing Returns to Scale

7/27/2019 49688217

20/46

COST OF PRODUCTION

7/27/2019 49688217

21/46

MEASURING COST: WHICH COSTS MATTER?

Economic Cost versus Accounting Cost

accounting cost Actual expensesplus depreciation charges for capitalequipment.

economic cost Cost to a firm of utilizing economic resources inproduction, including opportunity cost.

Opportunity Cost

opportunity cost Cost associated with

opportunities that are forgone when afirms resources are not put to their bestalternative use.

7/27/2019 49688217

22/46


Sunk Costs sunk cost Expenditure that has

been made and cannot berecovered.

Because a sunk cost cannot be recovered, it should notinfluence the firms decisions.

For example, consider the purchase of specializedequipment for a plant. Suppose the equipment can be usedto do only what it was originally designed for and cannot beconverted for alternative use. The expenditure on thisequipment is a sunk cost. Because it has no alternative use,its opportunity cost is zero . Thus it should not be included aspart of the firms economic costs.

7/27/2019 49688217

23/46


Fixed Costs and Variable Costs

total cost (TC or C) Total economiccost of production, consisting of fixedand variable costs.

fixed cost (FC) Cost that does notvary with the level of output and thatcan be eliminated only by shuttingdown.

variable cost (VC) Cost that variesas output varies.

The only way that a firm can eliminate its fixed costs is by shutting down.

7/27/2019 49688217

24/46


Fixed Costs and Variable Costs Shutting Down

Shutting down doesnt necessarily mean going out of business.

By reducing the output of a factory to zero, the company could eliminate thecosts of raw materials and much of the labor. The only way to eliminate fixedcosts would be to close the doors, turn off the electricity, and perhaps even selloff or scrap the machinery.

Fixed or Variable?How do we know which costs are fixed and which are variable?

Over a very short time horizon say, a few months most costs are fixed.Over such a short period, a firm is usually obligated to pay for contracted

shipments of materials.Over a very long time horizon say, ten years nearly all costs are variable.Workers and managers can be laid off (or employment can be reduced byattrition), and much of the machinery can be sold off or not replaced as itbecomes obsolete and is scrapped.

7/27/2019 49688217

25/46


Marginal and Average Cost

A Firms Costs Rate of Fixed Variable Total Marginal Average Average Average Output Cost Cost Cost Cost Fixed Cost Variable Cost Total Cost (Units (Dollars (Dollars (Dollars (Dollars (Dollars (Dollars (Dollars per Year) per Year) per Year) per Year) per Unit) per Unit) per Unit) per Unit)

(FC) (VC) (TC) (MC) (AFC) (AVC) (ATC) (1) (2) (3) (4) (5) (6) (7)

0 50 0 50 -- -- -- -- 1 50 50 100 50 50 50 100 2 50 78 128 28 25 39 64 3 50 98 148 20 16.7 32.7 49.3 4 50 112 162 14 12.5 28 40.5

5 50 130 180 18 10 26 36 6 50 150 200 20 8.3 25 33.3 7 50 175 225 25 7.1 25 32.1 8 50 204 254 29 6.3 25.5 31.8 9 50 242 292 38 5.6 26.9 32.4 10 50 300 350 58 5 30 35 11 50 385 435 85 4.5 35 39.5

Marginal Cost (MC)

7/27/2019 49688217

26/46


Marginal and Average Cost Average Total Cost (ATC)

average total cost (ATC)Firms total cost divided by itslevel of output.

average fixed cost (AFC)Fixed cost divided by the level of output.

average variable cost (AVC)Variable cost divided by the level of output.

7/27/2019 49688217

27/46

COST IN THE SHORT RUN

The Determinants of Short-Run CostThe change in variable cost is the per-unit cost of the extra labor w timesthe amount of extra labor needed to produce the extra output L. Because

VC = w L, it follows that

The extra labor needed to obtain an extra unit of output is L/q = 1/MP L. As a result,

Diminishing Marginal Returns and Marginal Cost

Diminishing marginal returns means that the marginal product of labor declines as the quantity of labor employed increases.

As a result, when there are diminishing marginal returns, marginal costwill increase as output increases.

7/27/2019 49688217

28/46

7/27/2019 49688217

29/46


The Shapes of the Cost Curves

Cost Curves for aFirm

In (a) total cost TC is thevertical sum of fixed costFC and variable cost VC.In (b) average total cost

ATC is the sum of average variable cost

AVC and average fixedcost AFC.Marginal cost MCcrosses the averagevariable cost and average

total cost curves at their minimum points.

7/27/2019 49688217

30/46


The Shapes of the Cost Curves

The Average-MarginalRelationship

Consider the line drawn fromorigin to point A in (a). Theslope of the line measuresaverage variable cost (a total

cost of $175 divided by anoutput of 7, or a cost per unitof $25).Because the slope of the VCcurve is the marginal cost ,the tangent to the VC curveat A is the marginal cost of production when output is 7.

At A, this marginal cost of $25 is equal to the averagevariable cost of $25 becauseaverage variable cost isminimized at this output.

7/27/2019 49688217

31/46

COST IN THE LONG RUN

The Isocost Line

Producing a Given Output atMinimum Cost

Isocost curves describe thecombination of inputs to

production that cost thesame amount to the firm.Isocost curve C 1 is tangentto isoquant q1 at A andshows that output q1 can beproduced at minimum costwith labor input L1 andcapital input K 1.Other input combinations L2, K 2 and L3, K 3 yield thesame output but at higher cost.

7/27/2019 49688217

32/46


Choosing Inputs

Recall that in our analysis of production technology, weshowed that the marginal rate of technical substitution of labor for capital (MRTS) is the negative of the slope of the isoquantand is equal to the ratio of the marginal products of labor andcapital:

It follows that when a firm minimizes the cost of producing a particular output, the following condition holds:

We can rewrite this condition slightly as follows:

7/27/2019 49688217

33/46


Cost Minimization with Varying Output Levels

expansion path Curvepassing through points of tangency between a firmsisocost lines and its isoquants.

The Expansion Path and Long-Run Costs

To move from the expansion path to the cost curve, we follow threesteps:

1. Choose an output level represented by an isoquant. Then findthe point of tangency of that isoquant with an isocost line.

2. From the chosen isocost line determine the minimum cost of producing the output level that has been selected.

3. Graph the output-cost combination.

7/27/2019 49688217

34/46

LONG-RUN VERSUS SHORT-RUN COST CURVES

The Inflexibility of Short-Run Production

The Inflexibility of Short-RunProduction

When a firm operates in theshort run, its cost of productionmay not be minimized

because of inflexibility in theuse of capital inputs.Output is initially at level q1.In the short run, output q2 canbe produced only byincreasing labor from L1 to L3 because capital is fixed at K 1.

In the long run, the sameoutput can be produced morecheaply by increasing labor from L1 to L2 and capital fromK 1 to K 2.

7/27/2019 49688217

35/46


Long-Run Average Cost

Long-Run Average andMarginal Cost

When a firm is producing atan output at which the long-run average cost LAC isfalling, the long-run marginalcost LMC is less than LAC.Conversely, when LAC isincreasing, LMC is greater than LAC.The two curves intersect at

A , where the LAC curveachieves its minimum.

7/27/2019 49688217

36/46


Long-Run Average Cost

long-run average cost curve (LAC)Curve relating average cost of production tooutput when all inputs, including capital, arevariable.

short-run average cost curve (SAC)Curve relating average cost of production tooutput when level of capital is fixed.

long-run marginal cost curve (LMC)Curve showing the change in long-run total costas output is increased incrementally by 1 unit.

7/27/2019 49688217

37/46


Economies and Diseconomies of Scale

As output increases, the firms average cost of producing that outputis likely to decline, at least to a point.

This can happen for the following reasons:

1. If the firm operates on a larger scale, workers can specializein the activities at which they are most productive.

2. Scale can provide flexibility. By varying the combination of inputs utilized to produce the firms output, managers can organize the production process more effectively.

3. The firm may be able to acquire some production inputs atlower cost because it is buying them in large quantities andcan therefore negotiate better prices. The mix of inputsmight change with the scale of the firms operation if managers take advantage of lower-cost inputs.

7/27/2019 49688217

38/46



At some point, however, it is likely that the average cost of production will begin to increase with output.

There are three reasons for this shift:

1. At least in the short run, factory space and machinery maymake it more difficult for workers to do their jobs effectively.

2. Managing a larger firm may become more complex andinefficient as the number of tasks increases.

3. The advantages of buying in bulk may have disappearedonce certain quantities are reached. At some point,available supplies of key inputs may be limited, pushingtheir costs up.

7/27/2019 49688217

39/46



economies of scaleSituation in which output can bedoubled for less than a doublingof cost.

diseconomies of scale

Situation in which a doubling of output requires more than adoubling of cost.

Increasing Returns to Scale: Output more than doubles whenthe quantities of all inputs are

doubled.Economies of Scale: A doubling of output requires less

than a doubling of cost.

7/27/2019 49688217

40/46



Economies of scale are often measured in terms of a cost-outputelasticity, E C. E C is the percentage change in the cost of productionresulting from a 1-percent increase in output:

To see how EC relates to our traditional measures of cost, rewritethe equation as follows:

7/27/2019 49688217

41/46


The Relationship Between Short-Run and Long-Run Cost

Long-Run Cost withEconomies and Diseconomiesof Scale

The long-run average costcurve LAC is the envelope of

the short-run average costcurves SAC 1, SAC 2, andSAC3.With economies anddiseconomies of scale, theminimum points of the short-run average cost curves donot lie on the long-runaverage cost curve.

7/27/2019 49688217

42/46

PRODUCTION WITH TWO OUTPUTS ECONOMIES OF SCOPE

Economies and Diseconomies of Scope economies of scope

Situation in which joint output of asingle firm is greater than output thatcould be achieved by two different

firms when each produces a singleproduct.

diseconomies of scopeSituation in which joint output of asingle firm is less than could be

achieved by separate firms wheneach produces a single product.

7/27/2019 49688217

43/46

PRODUCTION WITH TWO OUTPUTS ECONOMIES OF SCOPE

The Degree of Economies of Scope

degree of economies of

scope (SC) Percentage of costsavings resulting when two or moreproducts are produced jointly rather than Individually.

To measure the degree to which there are economies of scope, weshould ask what percentage of the cost of production is saved whentwo (or more) products are produced jointly rather than individually.

DYNAMIC CHANGES IN COSTS

7/27/2019 49688217

44/46

DYNAMIC CHANGES IN COSTS THE LEARNING CURVE

The Learning Curve

A firms production cost mayfall over time as managers andworkers become moreexperienced and more effectiveat using the available plant and

equipment.The learning curve shows theextent to which hours of labor needed per unit of output fall asthe cumulative outputincreases.

learning curve Graph relating amount of inputs needed by a firm to produce each unit of output to its cumulative output.

7/27/2019 49688217

45/46

ESTIMATING AND PREDICTING COST

Average Cost of Production in the Electric Power Industry

The average cost of electric power in 1955 achieved a minimumat approximately 20 billion kilowatt-hours.By 1970 the average cost of production had fallen sharply andachieved a minimum at an output of more than 33 billion kilowatt-hours.

7/27/2019 49688217

46/46

Documents

49688217