[3] Production and Costs

PRODUCTION AND COSTS 45

PRODUCER BEHAVIOURAND SUPPLY

INTRODUCTORY MICROECONOMICS46

In Chapter 2 we studied the consumersbehaviour. In Chapters 3 and 4 we will beconcerned with the producers behaviour. Inthis chapter in particular, we study importantconcepts associated with production andcosts.

A producer or a firm is in business tomaximise profit.1 By definition, profit earnedby a firm is equal to its total revenues minusthe total costs. As an example, suppose thatyou are in the business of making hammers,and, during a month, you produce and sell500 hammers. They are selling at the price ofRs. 20 each. Then the total revenuesgenerated are equal to price quantity, thatis, Rs. 20 500 = Rs. 10,000.

Producing hammers requires inputs suchas labour, building, equipment and rawmaterials. This is a technological relationship.In turn, inputs have to be paid. The sum totalof payments to all inputs is the total cost ofproduction. Let the total cost of making 500hammers over the month be Rs. 6,500.

Then your profit is equal to Rs. 10,000 Rs. 6,500 = Rs. 3,500.

1 In this chapter and others, we will use the term profitor profits. Both are correct uses.

CHAPTER 3

3.1 Production

3.2 Costs


The above example is illustrative ofsome important linkages. On one hand,the amount produced, or, what is calledoutput, is linked to total revenues inthe product market. On the other hand,output is linked to inputs viatechnology, which is called productionfunction (to be defined in a moment),and, the employment of inputs leads totheir payments. This chain links outputto costs.

output. In section 3.2, we will analysethat between output and payments toinputs. The link between output andrevenues will be examined in Chapter4 (and in Chapter 6 also).

3.1 PRODUCTION3.1.1 Production Function

The most basic concept here is whatis called the production function,defined as a technological relationshipthat tells the maximum outputproducible from various combinationsof inputs.

For instance, a firm employs onlytwo factors or inputs, say, labour(measured in hours) and land (inacres), and, Table 3.1 lists some factorcombinations and the correspondingoutput levels. 1 hour of labour and2 acres of land produce at the most5 units output, 2 hours of labour and4 acres of land produce at the most

Table 3.1 Production Function

Labour Land Output(in hours) (in acres) (in units)

A 0 0 0

B 1 2 5

C 2 4 11

D 3 6 18

E 4 8 24

F 5 10 30

G 6 12 35

H 7 14 40

Fig. 3.1 Linkages

These linkages are depicted infig. 3.1. In Section 3.1, we will studythe relationship between inputs and


11 units of output, and so on. It isnormally assumed that inputs work tothe best of their efficiency. Hence,instead of maximum output, we justsay output, e.g., 2 hours of labourcombined with 4 acres of land produce11 units of output.2

Note that the notion of productionfunction is not just confined to twoinputs. There can be other inputs likecapital, raw material etc.3

3.1.2 Returns to an Input

A production function given in thetabular form such as in Table 3.1 doesnot reveal much about the contributionof a single factor towards production.A reasonable way to assess this will beto vary the employment of one inputwhile keeping the employment of otherinputs fixed. Three concepts arise in thisexperiment.

One is total product or totalphysical product, denoted by TPP. Itsimply defines the total output at aparticular level of employment of aninput when the employment of allother inputs is unchanged. The nextone is marginal product or marginalphysical product (MPP). This isdefined as the increase in the totalphysical product per unit increase inthe employment of an input when theemployment of other inputs is given.4

When the employment of an inputchanges, we call it a variable input.

Finally, we define Average Productor Average Physical Product (APP) asthe TPP per unit employment of thevariable input, i.e., APP = TPP/L, whereL is the level of employment of thevariable input.

These are also respectively calledtotal, marginal and average returnsto an input.

A numerical example showing aTPP schedule is given in Table 3.2,where the variable input, L, is calledlabour. If we graph a TPP schedule, weget a total physical product curve.

Table 3.2 A Total PhysicalProduct Schedule

Labour Hours Total Physicalemployed (L) Product (TPP)

0 0

1 10

2 22

3 33

4 43

5 51

6 56

7 56

8 48

9 36

2 Table 3.1 gives only some, not all, possible combinations of inputs and output.3 Also, we can differentiate between unskilled labour and skilled labour.4 These are respectively similar to the concepts of total utility and marginal utility discussed in Chapter 2.


Fig. 3.2 shows the TPP curve for the TPPschedule given in Table 3.2.

Fig. 3.2 The Total Physical Product CurveCorresponding to Table 3.2

the MPP at L = 2, which is 12, is equalto the difference between TPP at L = 2,which is 22, and TPP at L = 1, which is10. The MPP schedule correspondingto the TPP schedule in Table 3.2 is givenin column (2) of Table 3.3. Likewise, theAPP schedule, given in column (3) ofTable 3.3, is obtained through dividingTPP by L in Table 3.2. The graphs of anMPP schedule and an APP schedule arerespectively called the marginalphysical product curve and theaverage physical product curve. Thesegraphs corresponding to Table 3.3 aregiven respectively in figs. 3.3 and 3.4.

Note the following :

1. It is not true that the concepts ofTPP, MPP and APP are applicable to

Table 3.3 Marginal Physical and Average Physical Product Schedules

Labour Marginal AverageHours Physical Physical

employed (L) Product (MPP) Product (APP)

0

1 10 10

2 12 11

3 11 11

4 10 10.75

5 8 10.20

6 5 9.33

7 0 8

8 -8 6

9 -12 4

The marginal physical product,MPP, is derived from the total physicalproduct, TPP, just as marginal utility isobtained from total utility. For instance,


one particular input (e.g. labour)and not to others (e.g. land or

variable input increases. Thisrelationship is verified from TPPand MPP schedules. In Table 3.2,TPP increases up to L = 6; fromTable 3.3, we see that MPP ispositive in this range. In Table 3.2,TPP decreases from L = 8 onwards;in Table 3.3, MPP is negative in thisrange.

4. Although we have derived MPP andAPP from TPP above, in general,given any one of these, we canderive the other two. SupposeMPPs are given to us. Then we canget TPP by adding MPPs (as TPP isthe sum of MPPs). Once we get TPP,we can readily obtain APP byapplying its definition. Similarly, ifthe APPs are known, we get TPPby multiplying APP with the levelof employment. Then MPPs areobtained by applying its definition.

Law of Variable Proportions and Lawof Diminishing Returns

As we will see later in this chapter andin the next, the most importantschedule (curve) from our viewpoint isthe marginal physical product schedule(curve). We notice from fig. 3.3 that theMPP initially increases with an increasein the employment of the input inquestion, then it diminishes and finallyit becomes negative. This pattern of MPPis called the Law of VariableProportions. Put differently, this lawoutlines three stages of production. Instage I, when the level of an inputsemployment is sufficiently low, its MPPincreases. In stage II, it decreases butremains positive, and, finally, in stage

Fig. 3.3 The Marginal Physical ProductCurve Corresponding to Table 3.3

Fig. 3.4 The Average Physical ProductCurve Corresponding to Table 3.3

equipment). It is applicable to allinputs, but one at a time.

2. Since MPPs are additions to the TPP,TPP is the sum of MPPs ( just as totalutility is the sum of marginalutilities). For example, in Table 3.2,the TPP at L = 3 is equal to 33. InTable 3.3, the MPPs at L = 1, 2 and3 add up to 33.

3. The MPPs being additions to theTPP also implies that if MPP ispositive, TPP must be increasingand if MPP is negative, TPP mustbe decreasing as the level of the


III, it becomes negative. In our example,stage I holds till L = 2, stage II isoperative between L = 3 and L = 7, and,stage III sets in at L = 8.

Note that in stages I and II, TPPincreases with the employment of thevariable input as MPP in this range ispositive. But in stage III, it decreasessince MPP is negative.

Closely associated with this law isanother important law, called the lawof diminishing marginal product orthe law of diminishing marginalreturns (which is similar to the law ofdiminishing marginal utility). Morebriefly, it goes by the name of the lawof diminishing returns. This saysthat, the employment of other inputsremaining the same, as more of aparticular input is used in production,after a certain level, its marginalphysical product decreases withfurther employment of it.

Fig. 3.5 illustrates these laws moreclearly. Suppose that the input can bemeasured continuously like points ona line, not just in integer units like 1,2, 3 etc. Then the resulting TPP, MPPand APP curves will look smooth. Asmooth MPP curve is drawn in fig. 3.5.We observe that the MPP increasesbetween 0 to A. This region marks stageI. The MPP diminishes but remainspositive between A to B, which marksstage II. From the point B onwards, itis the stage III, wherein the MPP isnegative. Diminishing returns holds instages II and III.

The reason behind the law ofvariable proportions or the law ofdiminishing returns is fundamentally

the same. As the employment of aparticular input gradually increaseswhile all other inputs are keptunchanged, the factor proportionsbecome initially more suitable forproduction, but, after a certain level,the variable factor can work with othergiven inputs only less efficiently, thatis, factor proportions becomeincreasingly unsuitable forproduction.

The significance of these stages ofproduction is that a profit-maximisingfirm will never operate in stage III. It isbecause, by entering stage III, a firmwill have to incur higher costs on onehand (as it is hiring more of the input),and, at the same time, since output isfalling, in the output market, it will getless revenues. This implies that profitswill be less.

It is not obvious at this point, butwe will learn in Chapter 7 that a profit-

Fig. 3.5 Three Stages of Production andDiminishing Returns

maximising firm will not operate instage I either. That leaves out only stageII, in which the marginal returns to an


constant: the output always increaseswhen all inputs are increased.5

The production function outlinedin Table 3.1 contains stages showingall three types of returns to scale. Forexample, from B to D there areincreasing returns to scale. Why? Incombination B, 1 unit of labour and 2units of land produce 5 units ofoutput. Compared to B, thecombination C has double the amountof each input, but output (equal to 11)is more than double of the output atcombination B. Similarly, from C to D,inputs increase by 50% but outputincreases by more than 50% (as 18 ismore than 50% higher than 11).

Likewise, you can calculate that,in the range from D to F, there areconstant returns, and, finally from Fonwards there are decreasing returnsto scale.

3.2 COSTS

We now move on to discuss some costconcepts. As fig. 3.1 suggests, costconcepts are very much related toconcepts associated with the productionfunction. This point will be clearer aswe go along.

3.2.1 Short Run

Fixed and Variable Costs

At a given point of time, a firm facestwo types of costs: fixed costs andvariable costs. Fixed costs are thosethat do not vary with the level ofoutput. (These are also called overhead

input is positive but diminishing. Fromthe viewpoint of the operation of the firm,this is the most relevant stage.

Finally, note that the law ofdiminishing returns implies that theMPP curve is inverse U-shaped. Inturn, this implies that the APP curveis inverse U-shaped also.

3.1.3 Returns to Scale

Suppose that, instead of increasingone input at a time, you increase theemployment of all inputs by the sameproportion (e.g. by 20%). The effectof this change on output is capturedby the notion of returns to scale. Ofcourse, the output is going toincrease. But by how much? Will itincrease (a) by more than 20%,(b) by less than 20% or (c) exactly by20%? The possibilities (a), (b) and (c)respectively illustrate increasingreturns to scale, decreasing ordiminishing returns to scale andconstant returns to scale.

In other words, suppose all inputsare increased by a given proportion.Increasing (respectively decreasing)returns to scale hold when outputincreases more (respectively less) thanproportionately. Constant returns toscale hold when output increasesexactly by the proportion in whichinputs are increased.

You should not make the mistakethat the terms decreasing,diminishing or constant mean thatthe output decreases or remains

5 This holds as long as the MPP of each factor is positive, i.e., the firm is not operating in stage III.


costs.) For example, you operate agarment factory. You pay a fixed rentfor the factory building, fixed insurancepayments for your machinery againstfire etc. These are independent of howmany garments per month youproduce.

There is a time element ininterpreting these costs as fixed. Thatis, even if these costs are fixed at anygiven point of time or within a shorttime period, in a long run horizon, youcan think of renting more or less space,having more or less number ofmachinery depending on yourbusiness outlook for the future. Hencethe rent and insurance costs etc. thatare fixed in the short run can vary inthe long run. In other words, fixed costsare present only in the short run, notin the long run.

Note that these notions of short runand long run do not refer to anyparticular calendar time. They referonly to different periods of planninghorizon by producers in an industry.Hence, they can vary from one industryto another.

Having noted this difference, wereturn to the short run situation.Besides fixed cost, there are variablecosts those that change with the levelof output, e.g., labour costs and costsof raw materials. If you want toproduce more garments, you have tobuy more cotton and other rawmaterials, hire more workers and soon. Variable costs increase withoutput.

Instead of being termed simply fixedand variable cost, these are formally

called Total Fixed Cost (TFC) andTotal Variable Cost (TVC). Total cost(TC) is then, by definition, total fixedcosts + total variable costs. Table 3.4presents a numerical example. Noticethat TFC, given in column (2), do notchange with output. But TVC, given incolumn (3), does. The columns (2) and(3) against column (1) are respectivelytotal fixed cost and total variable costschedules.

Graphs of these schedules are thetotal fixed cost curve and the totalvariable cost curve respectively.Figure 3.6 depicts these, togetherwith the total cost curve that graphs theTC schedule, given in the last columnof Table 3.4. The TFC curve is horizontalbecause fixed costs do not change withthe output. However, since TVC and TCincrease with the output, these curvesare upward sloping. By definition, thetotal cost curve is the verticalsummation of the total fixed and totalvariable cost curves. Notice that, at thezero level of output, TC = TFC, becauseTVC is zero when output is zero.

Average Costs

If we divide total fixed cost and totalvariable cost by output, we respectivelyget the Average Fixed Cost (AFC) andthe Average Variable Cost (AVC). Thatis, AFC = TFC/Output and AVC = TVC/Output. Similarly, by dividing total costby output, we obtain the Average TotalCost (ATC), i.e., ATC = TC/Output. Notethat, by definition, ATC = AFC + AVC.Average total cost is sometimes looselycalled average cost only. The AFCs, theAVCs and the ATCs corresponding to

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Table 3.4 Total Fixed Costs and Total Variable Costs

Output Total Fixed Costs Total Variable Costs Total Costs(Rs.) (Rs.) (Rs.)

0 10 0 10

1 10 8 18

2 10 13 23

3 10 16 26

4 10 20 30

5 10 26 36

6 10 35 45

7 10 47 57

8 10 63 73

9 10 83 93

Fig. 3.6 TFC, TVC and TC Curvescorresponding to Table 3.4

Table 3.4 are given in Table 3.5, andfig. 3.7 graphs them. The AFC curvecontinuously decreases as outputincreases, because the numerator of theratio TFC/Output is constant while thedenominator increases. The AVC and

ATC curves slope downwards initiallyand then upwards, i.e, they areU-shaped. The reason behind thisshape will be discussed later.

Marginal Costs

There is another important costconcept, the marginal cost (MC). Similarto marginal utility or marginal product,this is defined as the increase in totalcost when one extra unit is produced.Thus, it is the (additional) cost ofproducing an extra unit. In the examplegiven in Table 3.4, suppose that thecurrent level of output is 7. The MC ofthis output level is Rs. 12. It is becausethe 7th unit of output costs Rs. 57 Rs. 45 = Rs. 12. The MC schedulecorresponding to Table 3.4 is given inTable 3.6.


Table 3.5 AFC, AVC and ATC Schedules (Based on Table 3.4)Output AFC (Rs.) AVC (Rs.) ATC (Rs.)

0 - - -

1 10 8 18

2 5 6.50 11.50

3 3.33 5.33 8.66

4 2.50 5 7.50

5 2 5.20 7.20

6 1.66 5.84 7.50

7 1.43 6.71 8.14

8 1.25 7.875 9.125

9 1.11 9.22 10.33

MCs (just as total utility is the sum ofmarginal utilities). For example, theTVC of producing 2 units is Rs. 13,and, this is the sum of the MC ofproducing one unit (= Rs. 8) and thatof producing two units (= Rs. 5).

Fig. 3.8 graphs the MC schedulegiven in Table 3.6. It is the marginal costcurve.

Assuming that the output isperfectly divisible, a smooth(hypothetical) marginal cost curve isdrawn in fig. 3.9. Recall that the TVCis sum of the marginal costs. Thisimplies a property associated with asmooth marginal cost. That is, the TVCis equal to the area under the marginalcost curve. For example, at output q0,the TVC is equal to the area 0ABq0.This result will be used in Chapter 4.

Fig. 3.7 AFC, AVC and ATC CurvesCorresponding to Table 3.5

Note that, since total costs andtotal variable costs differ only by aconstant term (equal to the total fixedcost), MC can be equivalently definedas the increase in the total variablecost when one extra unit is produced.Moreover, TVC is equal to the sum of


As you see from fig. 3.8 or fig. 3.9,the MC curve is initially decreasing inoutput and then it is increasing, i.e, itis U-shaped. The reason behind the U-shape of the MC curve is the law ofdiminishing returns. As you recall, thislaw says that, as other inputs are kept

Output

Costsin Rs

.

MC

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10

Fig. 3.8 The MC Curve corresponding toTable 3.6

Table 3.6 Marginal Costs (based on Table 3.4)

Output Marginal Cost (Rs.)

0 -

1 8

2 5

3 3

4 4

5 6

6 9

7 12

8 16

9 20

unchanged, an increase in any giveninput leads first to an increase in itsmarginal physical product, and, then,after certain point, leads to a decreasein its marginal physical product. Let ussuppose that this particular input isthe only variable input, so that the totalpayment to it is equal to the totalvariable cost. Similarly, interpret theother inputs, which are keptunchanged, as the fixed factors, thetotal payment to which is the total fixedcost.

Fig. 3.9 A Smooth Marginal Cost

Let us now turn around thestatement of the law of diminishingreturns and say equivalently that, asmore and more output is produced,initially, the rate of increase in therequirement of the variable input willbe less and less, and, after a certainpoint, it will be more and more. Thisimplies that, initially, the rate of increasein the variable cost which is same asthe marginal cost will be less and lessas output increases, and then, it willbe more and more when output


increases further. This explains the U-shape of the MC curve.6

Once we know that the MC curveis U-shaped, it follows that the AVCand the ATC curves are U-shaped also.

There is indeed another relationshipthat holds between AVC, ATC and MCcurves. Consider fig. 3.10, whichdepicts smooth AVC, ATC and MCcurves. Observe that the MC curve cutsthe AVC and ATC curves at theirminimum points. The reason behindthis is mathematical, not economic,and, it can be understood through thefollowing example.7

Consider the game of cricket.Suppose that you are interested incalculating the average score ofbatsmen out as wickets continue to fall.Begin to calculate this after, say, 3wickets are down. The runs scored bythose already out are say 40, 105and 2. The average is (40 + 105 + 2)/3= 49. The game goes on and the fourthwicket falls. You calculate the averageagain and find that it has increasedfrom 49 runs. Has then the fourthbatsman, who got out, scored more orless than 49? The answer is more.Why, because otherwise the averagewouldnt have increased. Similarly, if theaverage had fallen from 49, the fourthbatsman must have scored less than49. This simple deduction means thefollowing.

Think of the runs scored by thefourth batsman out as marginal (i.e.

additional runs scored by the nextunit or batsman, when 3 are alreadyout). We are then saying that if theaverage increases (respectivelydecreases), the marginal should beabove (respectively below) the average.Now go back to fig. 3.10. The AVCcurve is decreasing in the range ofoutput from 0 to q0. Then it must betrue that, (a) at any output level in thisrange, MC AVC.Now, statements (a) and (b) togetherimply that the MC curve must cut theAVC curve at the AVCs minimum point.

By definition, MC is the addition toboth the TVC and the TC. Hence theabove logic applies to the relationship

6 Indeed, the MC curve is a mirror reflection of the MPP curve.7 This is contained in Richard Manning and Kenneth Henry, The Logic of Markets, The Dunmore Press

Limited, New Zealand, 1983, Chapter 7.

Fig. 3.10 AVC, ATC and MC Curves

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between MC curve and ATC curve also.The former cuts the latter at itsminimum point too.

3.2.2 Long Run

Recall that, in the long run, all inputsare variable, because costs that arefixed in the short run can be changedif the planning horizon of theproducer is long enough.Accordingly, there are no TFC or AFCcurves in the long run. There is nodistinction between total costs andtotal variable costs; we simply usethe term total costs. Similarly, thereis no distinction between averagetotal costs and average variable costsand we will use the term long-runaverage cost, denoted by LAC, whereL stands for long run. The concept ofmarginal cost remains exactly thesame however; we will abbreviate itto LMC.

In what follows, we discuss theshapes of the LAC and LMC curves, thereasons behind their shapes and therelationship between them.

Like the short run average andmarginal cost curves, the LAC and LMCcurves, in general, are U-shaped, and,the LMC curve cuts the LAC at itsminimum point. However, the reasonbehind the U-shape is not the law ofdiminishing returns. Instead, since allinputs are variable, it is the pattern ofthe returns to scale, which determinesthe U-shape of these curves. 8

In particular, increasing returns toscale mean that if output is increasedat a given rate (say 10%), inputs needto be increased only by less thanproportionately (say by 7%). Thisimplies that the average cost must fallas output expands. Similarly,decreasing returns to scale imply thatthe average cost must rise with output.Finally, if returns to scale are constant,the average cost is constant independent of output. We cansummarise all this as follows:

Increasing returns to scale LACdecreases with output

Constant returns to scale LACdoes not change with output

Decreasing returns to scale LACincreases with output.

Now look at fig. 3.11. It shows aU-shaped LAC curve. This means that,as output is gradually increased

8 The short-run and long-run average or marginal cost curves are not unrelated however. As you willlearn in a higher course in microeconomics, the LAC curve is flatter than short-run average variablecost curves.

Fig. 3.11 The Long-Run Average andMarginal Cost Curves

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starting from a small level, there areincreasing returns to scale (in theoutput range 0 to q0) such that LACfalls, then there are constant returns toscale (at q0), and finally decreasingreturns to scale prevail at output levelshigher than q0, such that LAC increaseswith output. In fig. 3.11, increasing,constant and decreasing returns toscale are written in short forms asIRS, CRS and DRS respectively.

Now the question is why do IRSoccur first, followed by CRS andDRS? Starting from a relatively small-scale operation (output), as the scaleof operation increases, a firm wouldbe able to reap the advantages of (a)division of labour and (b) volumediscounts. To cite an example in caseof former, suppose that a firmhas only one manager, whosespeciality is in marketing but who islooking into both marketing andmanufacturing. Now, as the firmincreases its production and hiresanother manager who expertise is inmanufacturing, then each managercan specialise in their expertise and be more efficient. This iscalled division of labour, meaningallocation of tasks according to thespecialisation of workers.9 In case ofvolume discounts, for instance, agarment factory buys 100 tons ofyarn at a certain price. If, instead, it

plans to buy 200 tons of yarn it cannegotiate a better price.

However, as the output level goesbeyond a certain limit, difficulties inmanaging an enterprise crop up.Crowding and congestion occurtypically, which lead to decreasingreturns to scale.

In between IRS and DRS, a firmexperiences constant returns to scale.It is shown at point q0 in fig. 3.11. Moregenerally, CRS may prevail over a rangeof output, rather than at a single levelof output. In this case, the LAC will havea flat portion in the middle.

A couple of remarks are in order:

First, given that initially increasingreturns, then constant returns andfinally decreasing returns to scale occuras output increases, the long runaverage cost is minimised whereconstant returns to scale prevail, suchas at point q0. In some sense, this is thelevel at which production is mostefficient.

Second, the U-shape of the LACcurve implies the U-shape of the LMCcurve. This is different in nature fromthe short run, where the U-shape of themarginal cost curve implies the U-shapeof the average cost curve.

The concepts developed in thischapter will be used very much in thefollowing chapters.

9 The same applies to other kinds of workers and to machinery and land. For instance, at a small scale ofoperation, the firm may have only one room, which is used as a storage as well as office space for itsemployees. Storing merchandise and taking them out generate traffic, which would adversely affect theproductivity of other employees. If, instead, the firm acquires an additional room, one of them can beused as storage only and as a result the productivity of employees will improve.

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SUMMARY

TPP is equal to the sum of MPPs. There are generally three stages of production. In the initial stage, the

MPP increases with input employment, then it diminishes but remainspositive and finally it becomes negative.

A profit-maximising firm will never employ an input at such a level thatits MPP is negative.

The MPP and APP curves are generally inverse U-shaped. The law of diminishing returns explains why the MPP curve is inverse U-

shaped. In turn, the inverse U-shape of the MPP curve implies a similarshape of the APP curve.

In the short run, there are fixed costs and variable costs. In the long run, there are only variable costs.

The AFC curve is downward sloping.

The MC, AVC and ATC curves are generally U-shaped.

The sum of MCs equals the TVC.

The area under the MC curve is equal to the TVC.

The law of diminishing returns explains why the MC curve is U-shaped.In turn, the shape of the MC curve implies the similar shape of the AVCand ATC curves.

The MC curve cuts the AVC curve and the ATC curve at their minimumpoints.

The long run marginal cost (LMC) curve and the long run average cost(LAC) curve are generally U-shaped.

The LMC curve cuts the LAC curve at the latters minimum point.

The U-shape of the LAC curve follows from a firm experiencing increasingreturns to scale initially, followed by constant returns to scale and thenby decreasing returns to scale.

The U-shape of the LAC curve implies the U-shape of the LMC curve.

In the long run, the sources of increasing returns to scale lie in the divisionof labour and volume discounts.

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EXERCISES

Section I3.1 What is a production function?3.2 List any three inputs used in production.3.3 What is meant by total physical product?3.4 What is meant by average physical product?3.5 What is meant by marginal physical product?3.6 How is total physical product derived from the marginal physical

product schedule?3.7 What will you say about the marginal physical product of a

factor when total physical product is falling?3.8 What is the general shape of the MPP curve?3.9 What is the general shape of the APP curve?

3.10 What do returns to scale refer to?3.11 Give the meaning of increasing returns to scale.3.12 Give the meaning of constant returns to scale.3.13 Give the meaning of decreasing returns to scale.3.14 Classify the following into fixed cost and variable cost.

(a) Rent for a shed.(b) Minimum telephone bill.(c) Cost of raw materials.(d) Wages to permanent staff.(e) Interest on capital.(f) Payment for transportation of goods.(g) Telephone charges beyond the minimum.(h) Daily wages.

3.15 How does total fixed cost change when output changes?3.16 How is total variable cost derived from a marginal cost schedule?3.17 How can one obtain total variable cost from a marginal cost

curve?3.18 What is the general shape of the AFC curve?3.19 What is the general shape of the MC curve?3.20 What is the general shape of the AC curve?3.21 What will happen to ATC when MC > ATC?3.22 What does division of labour mean?3.23 What are volume discounts?3.24 Name two factors behind increasing returns to scale in the long

run.


Section II3.25 What is meant by the law of variable proportions?

3.26 Calculate the APPs and the MPPs of a factor from the followingtable on its TPP schedule.

3.27 The following table gives the MPP of a factor. It is also knownthat the TPP at zero level of employment is zero. Determine itsTPP and APP schedules.

Level of Factor Employment TPP

0 0

1 5

2 12

3 20

4 28

5 35

6 40

7 42

Level of Factor Employment MPP

1 20

2 22

3 18

4 16

5 14

6 6

3.28 The following table gives the APP of a factor. It is also knownthat the TPP at zero level of employment is zero. Determine itsTPP and MPP schedules.


3.29 Explain the law of diminishing marginal returns. In other words,why does the marginal product of an input decline with furtheremployment of it?

3.30 How does the total physical product change with the change inthe marginal physical product of an input?

3.31 What is meant by the law of diminishing returns?3.32 Distinguish between fixed and variable costs.3.33 With the help of a suitable diagram, explain the relationship

between TC, TFC and TVC.3.34 Do ATC and AVC curves intersect? Give reasons.3.35 Why is the MC curve in the short run U-shaped?3.36 A firm is producing 20 units. At this level of output, the ATC

and AVC are respectively equal to Rs. 40 and Rs. 37. Find outthe total fixed cost of this firm.

Section III3.37 A firms total cost schedule is given in the following table.

Level of Factor Employment APP

1 50

2 48

3 45

4 42

5 39

6 35

Output (in units) Total Cost In (Rs.)

0 40

1 120

2 170

3 180

4 210

5 260

6 340

7 440

8 550


(a) What is the total fixed cost of this firm?(b) Derive the AFC, AVC, ATC and MC schedules.

3.38 Complete the following table if the AFC at 1 unit of productionis Rs. 60.

3.39 A firms fixed cost is Rs. 2,000. Compute the TVC, AVC, TC and ATCfrom the following table.

Output TC TVC TFC AVC AFC ATC MC

1 90

2 105

3 115

4 120

5 135

6 160

7 200

8 260

Output (in units) Marginal Cost (in Rs.)

1 2,000

2 1,500

3 1,200

4 1,500

5 2,000

6 2,700

7 3,500


3.40 Suppose that a firms total fixed cost is Rs. 100, and the marginalcost schedule of a firm is the following.

Output (in units) Marginal Cost (in Rs.)

1 10

2 20

3 30

4 40

5 50

6 60

7 70

(a) Is the MC curve U-shaped?(b) Derive the AVC schedule. Will the AVC curve be U-shaped?

Discuss why or why not.

3.41 Explain the relationship between ATC, AVC and MC with asuitable illustration.

3.42 Tables A and B below outline two production technologies orproduction functions. There are two factors: unskilled labourand skilled labour. Show that the production function given inTable A satisfies increasing returns to scale and that in Table Bsatisfies decreasing returns to scale.

Table A

Unskilled Labour Skilled Labour Output(in hours) (in hours) (in units)

8 4 2

10 5 3

12 6 4

14 7 5


Table B

Unskilled Labour Skilled Labour Output(in hours) (in hours) (in units)

8 4 6

10 5 7

12 6 8

14 7 9

3.43 Increasing and decreasing returns to scale respectively implydownward and upward sloping portion of the long run averagecost curve. Defend or refute.

Documents

[3] Production and Costs