Forms. of Cornpetitio,a i, cl11s­ si!ted Heither perlcct or~ feet. F11rmcr1, ;and r11nchet, ocwnc Ill dose n 11rry sector in. the economy of utidying !he cor,c:1;. tiotls lot pct{ect compctitio,i.

Businesses ttnploy 2 widt nriety of resources durfog Lht prooess of producing a p2r1icubr good or service. A "'heat fum. fo1 e1ample. uses 3 different cosnbina­ don of resources ch:tn dots a oouon gin or a n\C::u-pacldng firm. Some busines.s,es wt b.bcu on a mere seaso~ basis rhan cehers do. And some businesses requlre mere land when produci.1tg their produet rhan ochers do.

Desphe the nujor dilferenoet i.n resources used by cenain rypet of busi­ nesses Involved it1 the U.S. food and Obu indU$tty. tbctt are :1 numbo of ftuurti asscclared wi1:h tbe use of resources by these businesses W1 cau be gener.Jit~. Fin.1. inpuu can be greeped huo several sptclfi,c cittgorid 1tut f:icniwe their dC$.Cription and atUly.sis. AJI these 0N'IU also shut sp«iOc p,oduc,ion and cost rd:nionsbips: t!'l2t prevlde cbe foundation for ihe ecoecmlc dtt:Wons nude by a business. induding the level of output to produot 1M th.e level of v:u-bbk inputs to employ as it uri:liw hs CUl"l'tm peedcedve ClpilCiry.

ln thi$ cb:i.pter, we will assume rhe t::dsctnttof ptt{«t tompditfo,n. 1'ht f:um .staorcomt."S ~ th.an aoy 0th.er secrcr of the «onocny ro sartdfing rhe rondiLloru of paf('('t cxunpet.ition. We wiU -also focu,; Initially on undnst:i.nding the tlfc.a that VM)'iog the use of :1.singk input has uport the producr:ion of :1 Wlgk ,n,Jwt. Both of thdt :wumprioru will be revewed in l:u:trdupctn: ~·hen Wt exan1int rnuhipk input choiou. inuhipk product chelcea. :md rh.e enurc of decisions under Imperfect romprtidon. whkh exiru in ~I sectors of L~ food and Gbt:r indusuy.

MSESS,NG SHORT·RUN BUSINESS COSTS 11S TotalCostsandtheTI'PC- us AV'eQ9e Costs !Ind the APP Curve 11? M~ICostsandthcMPPCurvc 117

ECONOMICS OF SHORT ·RUN OEos.tONS 118 Maiginlll and Average RC"Yenuc 118 Le,,cl of Output MC • MR 1 t8

leYetof ReSOUKe Use: MVP• w.lC 121 WHAT UES AHEAD? 122 SUMMAltY 123

KEY TERMS 123 TESTING VOUR ECONOMIC

oeonesr 124

Chapter Outline CONDITtONS FOR PERf'ECT

COMPETITION 108 Cl.ASSIFICATION OF lNPUTS 108

land IOB Labo, 108 Capital 109 M11N19emcnt 109

IMPORTANT PROOUCTtON RElATK>NSHIPS 110 The Ptoduction Function 110 Tot,I Physical Product Cur.,c 111 Mllqr111I Phy,;ica.1 Product Cunie 112 ~era,gc Physical Product Cun,e 113 Stegcs of Production 114

Introduction to Production and Resource Use

Labor uhor in.dudes :JI J;i.bor servioes mtd in ptodueti.on wilh th~ a:cepti.on of n):uugeri.:il activities. ln crop produc1J.on. l:ibor :a('tivltl('S include setJ bed f>1epi:.indon. pbtuing. inig,uion. dl001ica..l :ipplbticu,s. :i.nd h2tvdt.ing. Ubor :aicrlvhks i.n ;i. ca.nnlng pl:i.,u

Land l.:i.nd Inckrdes m>1 only rbe bnd fom'IS usod:ueJ wid1 the earrb's crust bu1 also resources- such as ntiner2ls. fo,esu. groundwa1er. and orht'r resources given by nanee. Sud!. resources are d;uSiOed as dt.ber rmrw11/J/, (e.g .. fortsu). 01 ntJnrmr­ •lm resources (e.g .• n1iner.1.ls). An ex:1.mpk of :i. key bnd input In &tmi"g acdvitks is psedccroe eepsetl, which h:as many of rhe :ittiibuttl of a no1m .. -new.ible rt.S()uroe i.dentiOed in Ch:apta 2.

h is helpful 10 have sorne bread d:usUieui-oru in 1nhld when discuWng proch.N.~ti.on rtlaiion.shipd. These cbssitlatio,,s nor only p101no1e effiden, 001nmuni,c,.uion bu1 also help to condua ecoaomlc :i.n;Jyst.t. AJd)OUgb not uniformly sceepeed, dw:ilic:i­ don ofinpu1s into bnd. bbor. capii2l. :i.nd m2n:igttnen1 has p1ovtn useful.

CLASSIFICATION OF INPUTS

Wh:u docs it t'21::t 10 h2~ a pcrfttdy co1npcthiVl" «onomic situa1.io1)? Bdott v.-t dk­ ,u.ss bow eccecmlc dtt:idons are made, ler us look :u the tt:0noink environmau in which thq> are eede. An input or product mukd Structure an be cbss:if.ed ;as ptr­ fealy oompttiUtt If the following conditions hold:

11\e peedcers sold by businesses in a uctor are homogeneous. In crher words. the ptoduct sold by one bcsieess is :i. peifect .substhuu~ for 2 produtt sold by the 01htt busleesses. 1·Ms enables buyers In the n'lvktt to choos.t from a number of sellers, Any buslneu can enter or leave the sector without tnrountcdng serious bru­ rkrt for entry. Rtsoutcd must be frtt to move Imo the secrcr without en­ eoceredng barriers 10 entty (e.g .. p:utntt. lken.sing). The same ccndhlcn holds for resources le:t.ving the secccr. l'hert ,nu.st be :t. br~ number of stUe.rs of the product. No slngk .seller hu a disp..oponi.oiute inOunttt oc, prier. each one Is .i prlce talrer. Perfee1 inform2tion mus1 edse for all p:u1Lcipants ttgarding prkts. quanti­ ties. qua.lilies. sources o( supply. eed so on.

When all four conditions hold. we can S:I)' ~ m:i.tker't snucrere is pttfoctly ooinpec:ititt. Businessts 1h2r satkfy these ccndhlcns 2rt WO. by definition. perfectly ctun~tid'\~. A pt:rftttly oompnhive b~inffl k 2 pntt t':lkn. or h 2ocq,tt rhe pntt of the produc1 h receives in the product tn:u-4.et cu pays in rhe input:!$ givee. A com f:mnn h ;i. geed eumple of :i. pt:rfeet oomprtiror. There are d\Ouunds etf ccm pecdoe­ at who pecdcee a boenogeoeoue product (e.g .. no. 2 yellow oorn). each Ylirh eqU2l access to oo,m 11u.rkn tnfonu:1110111. and tads wi1h M :lbi1iry re control the price of oom he or she m::tivts OC' the prloe be or she P,}'i for fuel.

CONDITIONS FOR PERFECT COMPETITION

&qpltt uugori~J consist of laM. bbOI". eapi:al. aM m•......,..._

108 CHAf>TEll stx I U\"TROOUCTIOS TO rllODUCTIOS AND k.E.SOUllCf. USE

Tbe fOCUi of this ch:.iprtr is on introducing some impomuu physical a!\d eco­ nomk rtbdot15htps. which will be broadened in l:utl' eh:i.preo.. A thorough ueder­ sanding of rhe concepts preseneed in this clupter is essmdal bdott proettding with the rein:ainlng di:apl'ers in this book.

1J2.rgon ofttn comes under enack by rhcse ouu.ide .t discipline of srudy. f.or oc.tm.pk:. Edwin Newmae in StNJ:tiJ Sp,rAking. New York. 1980. \'('irner Boob. has s:adriud rhe excessive use of such L;\.f\gu::i~. Ecoocrmcs seems to be no bener or worse tlutt 01htt disdplincs. Indeed. in most introductory classes. leuning the jugoo ls au imporunt pon:ion of rhe course.

Management The final input category is management. Its functions arc varied and arc easier ro conceptualize than to measure. Like the leader of an orchestra, farmers and agribusi­ ncsscs must make decisions as to how, when, and what to produce when organizing their inputs, when and how to market the business's output, how large to gro\\', and how to finance business expansion.

In rhis chapter, we abstract from most of management's differences and instead highlight some concepts common to all inputs, with particular emphasis on tech­ nical relationships. Input and product prices will be meshed with these technical

Capital The term capital takes on different meanings in different contexts. When using the term capital, a banker is referring to stockholders' equity appearing on a bank's bal­ ance sheet. In a discussion of input use in the context of production, however, capital refers to manufactured goods such a, fuel, chemicals, tractors, trucks, and buildings that provide: productive services to their users. 1

A key aspect of capital goods is chat they do not provide consumer satisfaction directly but rather aid in the production of other goods and services. Nondurable capital inputs such as fuel and chemicals arc entirely used up during the current pro· duction period. Durable capital inputs such as machinery and buildings, on the other hand, arc utilized over a period of years.

include receiving and grading of fruit and vegetables arriving from the field, blanch­ ing, inspection, canning, and warehousing.

Several combines pickfr,g aOO shelling com demonst,ate the combination of land, capital, and labot to produce a raw agricultural product Credit: mak.aule/Fotol~.

109 CHAPTER SIX INTRODUCTION TO PRODUCTION AND RESOURCE USE

2A.no1hcr wiy of ch2r1c1tri2ing 1 production function Is 10 think of it as a cooking redpt. for esample, it uW" sptci6c combinar.On of inputs 10 bake a C31ct:. 8aki.ng a cake requirei flout. eggs. w.uer. and other ingredients. h 2lso rtquires labor to blend the ingredients and apiul (i.n ihe form of an oven and enttgy) to b:IU 1he Ingredieers. "11u terms 1>u1pu1 and uw,./ pl,y,it11.J pl'OdMl't an 2nd will be used lmercheegeably thmughou1 this and subsequtnt chaprces.

The Production Function A production function characterizes the physical relationship between the use of inputs and the level of output. Suppose you arc a salesperson for a fertilizer com· pany and a fumcr asks you to recommend the amount of fcnilizcr to apply per acre to maximize profit. Before you can recommend the quantity of fertilizer the farmer should apply, you must have some knowledge of the physical relationship between yields and the level of fcrrilizer use. If the applicarion of more fertilizer has no effect on crop yields, the answer is simple: a profit-maximizing farmer obviously should nor apply any additional fertilizer.

In the general case, where there arc II number of identifiable inputs, a produc­ tion function may be expressed as

output = /(quantity of input 1, quantity of input 2, ... , quantity of input 11) (6.1)

which, in words, simply stares rhar the level of output is a function of (i.c., depends on) how much of input 1, input 2, ... , and input 11 you use. For example, in an early 1880s agricultural setting, crop output was a function of the services provided by labor, land, seed, a workhorse, a fC'W' basic implements, and management.

A production function is a rule associating an output to given levels of the inputs used. Output is measured in physical units such as bushels of wheat, gallons of milk, and cases of canned pcas.2 If one input in a production is varied and all the other inputs arc held fixcd at their cxisting level, we can rewrite Equation 6.1 as

output = /(labor I capital, land, and management) (6.2)

in which the bar separating the first input from all other inputs indicates rhat only the first input is being varied and the other inputs arc held fixed at existing lcvels.3 This enables us to examine the relationship between labor and output as opposed to the other inputs employed in the firm's production process.

Column 2 in Table 6-J reports the potential output levels rhc hypothetical firm TOP-AG can achieve per day with specific levels of labor use. One input (labor) is varied here, and all other inputs (capital, land, and management) arc held fixed at their current levels. Column I in Table 6-1 indicates the level of daily labor use associated with the levels of output in column 2. For example, if the daily use oflabor is 10 hours a day, column 2 in Table 6-1 indicates that the level of output would be one unit.

Several key relationships between the level of output and the level of input use must be understood before we consider the prices of these inputs and outputs. These rela­ tionships include the concept of a produccion function that reflects this input-output relationship and the concepts of marginal and average product.

IMPORTANT PRODUCTION RELATIONSHIPS

relationships in this chapter when we discuss those input-output combinations that achieve a specific economic goal, such as profit maximization.

Production functjon The relationship between out­ puts and inputs is captured in a production function.

CHAM'ER Stx I INTRODUCFION TO PRODUCTION AND RESOURCE USE 110

Th• total physical product (TPP) curve shows the relanonship between output a.nd one input, holding othe< inputs in the production function constant.

Figure 6-1 The marg;nal physical product curve for TOP-AG crosses the horizontal a.,6s (i.e., negative) when the total physical product curve has reached its peak and begins to decline.

14

12

10

8

i 6 0

4

2

10 16 20 22 26 32 40 so 62 76 Labor use

Total Physical Product Curve

Total Physical Product Curve If \VC were to connect this and other combinations of ourput and labor use reported in columns I and 2 in Table 6-1, we would obtain the input-output relationship known as the total physical product (TPP) curve presented in Figure 6-l. By read· ing along the X, or horizontal axis to a particular input level, reading up to the TPP curve, and then reading over to rhc Y, or vertical, axis, you can determine the level of output associated with this input use.

The TPP curve typically will initially increase at an increasing rate, then increase at a decreasing rate, and finally decrease over a full range of potential input use levels.

Table 6-1 PRODUCTION RELATIONSHIP FOR TOP-AG, INC.

(1) (2) (3) (4) Point Daily Daily Marginal Physical Average Physical

on Labor Output Product, Product, Figure 6-1 Use Level .1(2) + !1.(1) (2) + (1)

A 10.0 1.0 0.10 8 16.0 3.0 0.33 0.19 c 20.0 4.8 0.45 0.24 D 22.0 6.5 0.85 0.30 E 26.0 8.1 0.40 0.31 F 32.0 9.6 0.25 0.30 G 40.0 10.8 0.15 0.27 H 50.0 11.6 0.08 0.23 I 62.0 12.0 0.02 0.19 J 76.0 11.7 -0.02 0.15

INTRODUCTION TO PRODUCTION AND RESOURCE USE I CHAPTER SIX 111

4Somc tder to iu:trgin~ physi.c:a.l product as .s.imply .. m:trgin:t.l product." We will follow t.hc rime-honored tradition of using ehe word phJskal in out diKussi.on. which maffl it clear th:u the units or messutemcnt are in physical units rather th:a.n doll:it$. ry'he narure of the linear scgrncnu comprising rbe roul physi,c:ll product (fPP). m:i:tgi":ll physical product (MPJ>). and avenge physial product (APP) curves precludes the MltP curve from intcrs«ring rhe APP curve a, its exace muimum aod rhe 1\,t'PP curve frorn being pttcisdy sere :u tilt: pesk of rhe 1·pp curve in figure ~I. A smooc-hing o(

these rebcioru.bips 01 small linear scg~ms would more closely :tpprOJC.imuc these conditions.

in which the d sign stands for marginal or "change in." To illustrate the calculation and interpretation of the marginal physical prod­

uct, consider the data for TOP-AG in Table 6-1. There may be some confusion regarding which level of output to associate with a marginal physical product as you read this table. Why arc the values in column 3 on a different line than the other columns in this table' While the other columns represent levels of activity, column 3 reflects changes in levels of activity.

For example, when the daily labor use at TOP-AG is increased from 10 hours to J 6 hours, the marginal physical product would be 0.33 units of output (i.c., 0.33 = [3.0 - 1.0) + [16.0 - 10.01). Thus, if labor use is increased by 1 hour, the business can complete assembling one-third of another spare pan. This value is listed between the rows associated with 10 hours and 16 hours of labor and one and three units of output. If 20 hours of labor were used, the marginal physical product would be 0.45 units of outpur (i.e., 0.45 = [4.8 - 3.0] + [20.0 - 16.0]) and so on. The marginal physical product curves for TOP-AG arc plotted in Figure 6-2.

An important relationship exists between the total and marginal physical prod­ ucts. The slope of the total physical product curve (with respect to the use of labor) is approximately equal to the marginal physical product. If the change in labor use is very small, the marginal physical product is exactly equal to the slope of the total physical product curve. In other words, the marginal physical product curve measures the rare of change in output in response to a change in the use oflabor.

The marginal physical product curve takes certain twists and turns as we move along the total physical product curve. For example, the marginal physical product curve cuts the average physical product from the top at approximately 30 hours of labor, where the total physical product curve in Figure 6-1 began to increase at a decreasing rate.; A particularly important twist is that when the total physical prod­ uct curve is decreasing. the marginal physical product curve will be negative. This can be seen in Table 6-1 at the point at which TOP-AG increases its use of labor from 62 hours a day to 76 hours. Column 3 shows that the marginal physical product

(6.3)

Marginal Physical Product Curve If a furmcr adds another pound offcrriliz.cr per acre, will corn yields increase? If so, by how much? Or would more fertilizer burn out the crop and cause yields to decline? Docs the addition of another employee at a grain elevator expand its output? These questions give rise to the important concept of marginal physical producr.4

The marginal physical product (MPP) for an input is the change in the level of output associated with a change in the use of a particular input, where all other inputs used in the production process remain fixed at their existing levels. Stated in equation form, the marginal physical product is equal to

d output marginal physical product = • .

.u. input

These and other properties of the total physical product curve can be better under­ stood by calculating two additional product curves.

Th• MPP c.urve shows the change in output from the use of another unit of one input, nolding other inputs in the product.ion function constant,

112 CHAPTER srx I INTRODUCTION TO rRODUCTtoN AND RESOURCE use

The APP curv• shows the level of output from a level of use of a specific input, holding other inputs in the production function constant.

62

'Yoo an find ehe point :u which ehe TftP curve changes from incrt":1.Sing :it :itt iocrC2S:ing rate to incrcuing :u :a. de­ ctt:tSing r:ue by dr.iwing ~ uy emanadng from the origin :u,d S('cing where thl$ r.ty is t.tngem to 1ht Tl>P curve. AJ. this point of taogency. TOP-AG's nurgin:tl physia.l product is equal to its a~ physical product.

Average Physical Product Curve A final input-output relationship is rhe average physical product. The average physical product (APP) is related to the level of output relative co the level of input use: instead of their incremental change. Stated in equation form

output average physical producr = -. -- (6.4)

input

In the context of our example, the average physical product represents the output per hour of labor with all other input levels held constant.

Column 4 in Table 6-J presents the value of the average physical product for labor use for TOP-AG. The average physical product is shown to rise as output rises, but then falls as output expands at a decreasing rate. The average physical product curve for TOP-AG in Figure 6-2 is intercepted from above by the marginal physical product curve as output begins to increase at a decreasing rare.

becomes negative at about 70 hours. The point at which the marginal physical prod­ uct becomes negative corresponds ro the point where the total physical product curve begins to dcclinc.6 Remember the marginal physical product approximates the slope of the total physical product curve. This characteristic will help us identify the rational range of production over the total physical product curve. This issue will be addressed shortly when we discuss the stages of production.

Figu:r• 6-2 The marginal physical ptoduct curve illusttates the char>ge in output associated with a change i.n labor input use by TOP-AG. The marginal physical product curve for labor falls below zero at app,-oximately 70 hours of labor use.

labor use so 40 32 26 22 20 16

1-------Stage 1-------~----Stage ll----+::Stage Ill

76

Marginal physical product

D

Marginal and Average Product Curves

INTRODUCTION TO PRODUCTION AND RESOURCE USE I CHAPTER SIX 113

0.8

& 0.6 ~~ ! -g " - 0.4 ~~ ~~ ·a~ j (> 0.2

0

-0.2 10

Ill

Yes Yes No

Usage of Labor

Between O and 30 Between 30 and 70 Greater than 70

Operate?

Table 6-2 STAGES OF PRODUCTION

Stage

Stages of Production To understand the production relationships illustrarcd in Table 6-J, you may divide rhcm into stages of production. Stage I is the point at which rhe marginal physical product lies above the average physical product curve. Stage II of production is rhc poinr at which input use begins at the end of stage I and continues until the value of the marginal physical product becomes zero. Stage Ill of production begins at the poinr where input use lies ro the right of stage II, or at which the marginal physical product is negative.

Returning to the example in Figure 6-2, rhc stages of production associated with the use of labor by TOP·AG arc outlined in Table 6-2. The irrational nature of stage Ill under normal economic conditions can be easily explained. If input is increased beyond 70 units of labor, output will full. It is irrational to increase the use of an input if it only leads to less output. Would you recommend that TOP·AG increase its daily use of labor to 76 hours daily knowing that output would full'

Electing to stop in stage I is also irrational, although it may be more difficult to sec why. A good grade on your last examination (marginal physical product) that raises your semester average (average physical product) is an example of an outcome occurring during stage I. If you were permitted to take a make-up test for the last examination and substitute this grade for your original test score, you would likely rake this make-up test only if you felt you could increase your semester average grade.

In the conrcxr of Table 6-1, look at the values in columns 3 and 4. A marginal physical product of 0.85 units per hour increases the average physical product from 0.24 units to 0.30 units. And a marginal physical product of 0.40 units increases the average physical product from 0.30 units to 0.31 units. But a lower marginal physical product of0.25 units brings the average physical product down to 0.30 units. The first rwo observations arc in stage I, and the: third observation would occur in stage ll.

Why should you stop producing if rhc output of your business is increasing at an increasing rate? As long as the average physical product is rising, you should expand input use. We will leave the presentation of the economic rationale for sup-­ port of this argument for later in this chapter. At this point, we recognize that stage II appears to hold primary interest for a firm that wishes to maximize irs profits.

We now have the three input-output relationships for which we need to cvalu­ arc: ranges of rational and irrational regions of production.

A review ofT able 6-J and Figure 6-2 suggests the following conclusions:

If the marginal physical product curve is above the average physical product curve, the average physical product curve must be rising. If the marginal physical product curve is below the average physical product curve, the average physical product curve must be falling. The marginal physical product curve therefore cuts the average physical product curve from above at thar point where the average physical product curve reaches its maximum.

Stage II of production represents the range of interest to economists. Why stop in stage I, and why produce in stage Ill?

114 CHAl'TER SIX I INTRODUCTION TO PRODUCTION AND RESOURCE USE

Table 6-3 SHORT·RUN COST SCHEDULE FOR TOP-AG, INC., AND SELECTED COST CONCEPTS

(1) (21 (31 (4) (S) (6) (7) (81 Average Average Average

Point Variable Total Variable Total Marginal Total on Total Total Fi><ed Cost, Variable Cost, Cost, Cost, Cost,

Figure 6-1 Output Cost (21 + (1) Cost (4) + (1) (2) + (4) a(6J + a(1J (31 + (S)

A 1.0 100.00 100.00 50.00 50.00 150.00 150.00 B 3.0 100.00 33.33 80.00 26.67 180.00 15.00 60.00 c 4.8 100.00 20.83 100.00 20.83 200.00 11.11 41.67 D 6.S 100.00 15.38 110.00 16.92 210.00 5.88 32.31 E 8.1 100.00 12.35 130.00 16.05 230.00 12.50 28.40 F 9.6 100.00 10.42 160.00 16.67 260.00 20.00 27.78 G 10.8 100.00 9.26 200.00 18.52 300.00 33.33 27.78 H 11.6 100.00 8.62 250.00 21.55 350.00 62.50 30.17

12.0 100.00 8.33 310.00 25.83 410.00 150.00 34.17 J 11.7 100.00 8.55 380.00 32.48 480.00 n/a 41.03

Total Costs and the TPP Curve Figure 6-J shows that the TPP curve typically first increases at an increasing rate, then increases at a decreasing rate, and finally decreases. In light of this curve, what do the total variable cost curve and total fi.xed cost curve look like?

A complete cost schedule for our hypothetical business TOP-AG is presented in Table 6-3. We have assumed that TOP-AG pays $5 per hour for labor and has fixed

Vart.lbt• and ttX•d co..sts Variable costs vary with the level of production. Fixed costs do not.

The total cost of production is chc costs associated with the use of all inputs to production. A l:iusincss s tiiial costs in me ~rt run can · vi&a into fixal costs~ v.inable costs.: \Ylc learned that fixed costs arc chose costs chat do not vary with the level of input use and chat variable costs arc chose costs chat do vary with the lcvd of input use. It is important to understand the measurement of these and ocher concepts of cost and their relationship to the lcvd of production activity when making short-run economic decisions.

Two additional cos, concepts related to the level of production that arc extremely important to economic decision making arc marg1na costs ana average; costs. Each of these cost concepts, and how they arc related to the total, average, and marginal product curves. is addressed in this section.

ASSESSING SHORT-RUN BUSINESS COSTS

Figure 6-2 shows that the marginal physical product of labor use is fulling throughout stage 11. This phenomenon is so frequently observed that it is called a law-the law of diminishing marginal returns. This law states that

as successive units of a variable input are added to a production process with the other inputs held consranr, the marginal physical product eventually decreases.

Therefore, in the region of grcarcsc economic interest, we would expect to observe diminishing marginal physical product for variable inputs.

A farmer obviously would not knowingly apply lime to rhe point where stage Ill occurs. If a furmcr asked you to identify the application rate in stage ll chat makes rhe most economic sense, what would you advise chis farmer? Do you have all the information you need to provide: the farmer an answer? The answer is 11-0. Although knowledge of the production relationships discussed thus fur is extremely important, we must also know the costs of production.

INTRODUCTION TO PRODUCTION AND RESOURCE USE I CHAPTER SIX 115

0Ulp01

11.6 9.6 10.8 Oso Dee

8.1 6.5 4.8 3

--'i~"""t----:------ Average fixed cost

_____ Average variable cos,

H

Margjnal and average cost

Output 9.6 10.8 11.6 12.0 8.1 6.5 4.8 3

Total cost

I

Total cost

Cost Re&ationsh~s A

500

400

300 f!1 .. ;g

200

100

0

8

70

60

50

I!? 40

i 30

20

10

0

costs of S 100 per hour. This includes $75 of explicit costs and $25 of implicir costs. No matter whar happens to output in column l , fixed costs in column 2 remain rhe same. The current propcriy rax assessment owed by a business will be the same whether ir produces ar its capacity or produces nothing ar all.

Total variable costs per hour for our hypothetical business TOP-AG arc shown in column 4 of Table 6-3. Looking at columns I and 4, we sec char when the level of output rises, the level of rota! variable costs rises. A fucroiy will need more labor and will incur more labor costs if managcmcnr decides to expand production.

Figure 6-3A, graphically illustrates the nature of the total cosr, total variable cost, and total fixed cost series reported in Table 6-3. The total flxcd cost curve is parallel to the horizonral axis, thus illustrating its fixed nature when output rises. The roral variable cosr curve, on the other hand, rises when the level of output rises. Finally, the

Figure ~3 The cost relatiooships calculated for TOP-AG in Table 6-3 are plotted. Output levels Os, and Oso illustrate that the marginal cost curve intersects the average variable and average total cost cul\les at rheir minimum.

CHAPTER SIX I INTRODUCTION TO PRODUCTION AND RESOURCE USE 116

7Subscripts BE and SO r('fer to ehe bre11k-n-m and 1hutd(lwn levels or ourpu1. These levels of ou1put will take on sptci:tl sig,,ifla,a l:uer in this CNpc:er wbei, wt: t'X:t.mi.~ how dunging m:uht price kvtli :affect the level of ourpur desteed by profit-ni:a.rimiring businesses.

in which t. represents the change in a particular item (e.g., costs, ourput). Marginal cost also rcprcscms the slope of the roral cost and total variable cost curves.

The level of marginal costs for TOP-AG is calculated in column 7 of Table 6-3. The marginal cost curve for this business is plotted in Figure 6-3B. Like average vari­ able cost, marginal cost first fulls and then rises. It curs the average total cost and aver­ age variable cost curves at their minimums (sec outputs OaE and OsD in Figure 6-3B).7

(6.8)

Marginal Costs and the MPP Curve Marginal cost is perhaps the most important concept. Marginal cost is the change in the business's total costs per unit of change in output. Marginal cost is measured as

t. rotal cost marginal cost = •

u output

(6.7)

(6.6)

(6.5) total costs average total cost = ---­

output

total fixed costs average flxed costs = -----­

output

total variable costs average variable costs = ------­

output

Average fixed costs for TOP-AG arc calculated in column 3 of Table 6-3. Average variable costs for this business arc calculated in column S. Average total costs, which arc equal ro average fixed costs plus average variable costs, arc calculated in column 8 in Table 6-3. Figure 6-3B, illustrates the general nature of these three short-run average cost curves. Average fixed costs decline over rhe entire range of production because they do not vary with output. Average variable costs, on the other hand, normally decrease up to a certain output level and then increase when output expands further.

If you compare the average variable cost curve in Figure 6-3 with the APP curve in Figure 6-2, you will sec that these two curves arc mirror image-s of each other. Although the APP curve for TOP-AG is convex, its average variable cost curve is concave. The maximum of the APP curve of 0.31 units in column 4 of Table 6-J is attained at 26 hours of daily labor use and 8. I units of ourput. The minimum of the average variable cost curve of$J6.0S in column S of Table 6-3 was also attained at 8.1 units of output. The reason for this inverse relationship is that when output per unit of labor rises, average variable costs must necessarily decline. (Review Equa­ tion 6.7 if this is unclear.)

Average Costs and the APP Curve The concept of average cost involves measuring costs per unit of output, or the level of cost associated with the level of output. The concepts of total costs, fixed costs, and variable costs discussed may be expressed in terms of average costs as

total cost curve, which reflects both fixed and variable costs, rises when output rises. The constant gap between the total cost curve and total variable cost curve when out· put rises is equal to $100, or the level of fixed costs for our hypothetical business.

These total cosr measures serve as the basis for average variable> average fixed, and average total costs, and for margi naJ costs.

INTRODUCTION TO PRODUCTION AND RESOURCE USE I CHAPTER SIX 117

Profrt maximization To determine where in stage II we should ptoduce to maximize profits, we need to study average and marginal costs associated with production.

•u..d<, im,..,...,.. -~I ,.,..,,.,_ -V--1 ~II<' •ii d&, h'OM -~I ptice, whid, - wiU .liot-. ... a,,,-,.

level of Output; MC = MR Ex~nS:ion oft.he bush.eil't variable input use in the currtrtt period ts pro612ble 21 the m:ugin or as long as ehe m.:aigln:al revenue exceeds die m:ugin:al eosr. A business s:houkl not Increase the use of 2n input if marginaJ cosr exceeds nutghul revenue. er if the chaogc hr <'OSI of pu.rchuing :aJdir.On:1.I lupuu is greater th.a.n the revenue

which is iJendc:al to rhc m:arkec price this business receives whtrt II sells hs product i.n the markt1pl:ace and 10 d,e m:argin.al revenue calculated in Equ:ation 6.10. The tl.Uf'8h,:i.l revenue and :avenig('. revenue c:urves under ccndldous of perfect competi­ tion assumed in ,his ch2p1er will be perfectly flat. wh.k:h we will iJluur:art sh.ordy. This 1ef1ecu rhe not lo,, th:ar~ l>lU.itlt'jS ls a pdce uktr. nmhing it does wiJI eh:i.ngt the prke received for !cs output. Jn the o::ampk presented earlier. the inttr«pt of rhese two curves on the ,·crrk:J. or Y. n:is wouJd be S45.

(6.12)

Marginal and Averag• Revenue ln the last secrioe. 'A'e discussed ,ht calccladcn of n.utginal and :average cosrs of prcdcedee. They have rhei.t coun1erp:at1 on the revenue side. TM ch:ange in total eeseece is called marginal eeeeece. :1.11d it 1eprdtncs ehe C!h:u,ge in revenue from pcoducing mere ourpur. or

ma.iginal reseaue = ~ 101:J ,evei,ue + d ourpur (6.9)

which. wKltr pufta comptt:hion. will :Ji0 be ~u:al 10 tht peer unit sales priot of the product (pi!« pa bushel. per ton. per pcued, ere.I for rht bu.s.i1~'s product. 8

If TOP-AC looeased lrs prodcctlco from 11.6 unil$ per how to 12 uni1Sptr hour. i1S 1oral reveeue would Increase from $522 an hour (Le., I I .6 unhs of outpu1 muhipliai by:, pcoduct priot of S45 pn unil) to S)10.

If TOP-AC expands hs ou1put from 11.6 unhs to 12 uniu prr hour. iu

m:ughul revence = ($540 - $522) + (12.0 - 11.6) = $18 + OAO unh:sofou1ptu = $4; (6.10)

which is idauial to the S45 rn2rktt pdee assumied fo1 ·roP-AG•i product. The oonttp1 of a~eragt: reveeee rtllecu rhe revenue ptt unit of oui-put tht

business receives fo, its product. or

:rrtr..gt revenue = tot:i.l revenue + ou1pot (6.11)

which simply nopre:senu anocbcr w1y of looking at the price of the product. lfTOP­ AC prcdcced 12 uni cs of output :in hour and received $45 for e-..ch unit it p,odlffi. its tout revenue wouJd be S540 per hour. TOP-AC's :average revenue under thcst circu.m.u:anees would be

:avcr..gerertnue = S.540 + 12uniuofoutpu1 = S45

Now that wt have galeed an underS1:1.ndi.ng of the pbys:lcaJ 2..(p«U and CMI :tSp«ts of peodcedce. tht nut logi~ issue is ro determine the k,fl of output :and lnput use that will rna.dmltt rbt busieess's cerrene economic profit. lkfo,t we an do ,his. however. we n1ust dlsccss ,wo addhion:J revenue ooncepu: m:..rgin-al revenue a,,d :wtngt revenue.

M•gin.llte¥-IM ~ m.argin;ill'C'Ycn~ ~r conditiorls of pmed competiliofl is the- prioe thc­ pc,c:fucer IKll'iv,n from the m.arbt.

ECONOMICS OF SHORT-RUN DECISIONS

118 ClUPT"Ell Sl:X I n,'TRODUCTION TO f>RODUCTIOS' ASO ll.E.SOUllCJ: USE

119

Measuring prortt The level of profit is equal to the level of output multiplied by average profit, or the difference between price and average total cost.

MC = MR criteria Profit from p<oduction is maximized when the fotm operates wher'e matginal cost is equal to marginal rErVeoue.

or to the point at which the marginal revenue from the sale of another unit of output equals the marginal cost of producing this unit.

Let us expand our discussion of TOP-AG developed in Tables 6-1 and 6-3 to determine its profit-maximizing level of output. Rows F and G of Table 6-4 suggest that when TOP-AG expands its production from 9.6 units of outpur to 10.8 units of ourpur, the business will achieve an economic profit of $186 pct hour. TOP-AG's total revenue would be $486 per hour, while its total costs would be $300 per hour. The cnrry in column 5 of row G of $186 is the largest entry in this column, which suggests that profit is maximized at 10.8 units of output. Is it>

le is very important that you understand the economic rationale underlying the profit-maximizing level of output. If TOP-AG expanded its output to 11.6 units of output, the business's economic profit would fall from $186 to $172 an hour (sec row Hin Table 6-4). Obviously, TOP-AG's management would not wish to expand its operations in rhc current period if its goal is to maximize profits.

As TOP-AG expanded its output from 9.6 units of output to 10.8 units, its marginal cost was $33.33 as shown in column 6, and its marginal revenue was $45 as shown in column 7. The net benefits from chis expansion arc positive. But ifTOP-AG further expands its operations from 10.8 units per hour ro 11.6 units, the marginal cost of doing so would be $62.50 as compared with a marginal revenue of only $45. The level of output that maximizes profit, or the point at which the marginal revenue associated with the expansion just equals rhc marginal cos, associated with the expan· sion, occurs when marginal cost equals $45. This will occur somewhere between rows G and Hor between I 0.8 and 11.6 units of output as shown in Figure 6-4.

Reviewing Figure 6-4. we sec that the marginal revenue curve is perfectly flat, reflecting the fuct that this business is a price taker. The business thinks that rhc level of its production is small enough not to have a perceptible impact on the market price. Because we have assumed the presence of perfect competition in this chapter.

(6.13) marginal revenue = marginal cost

the business would receive from their use. Furthermore, as long as a higher profit is preferred over a smaller profit, a business should not stop expanding production if marginal revenue exceeds marginal cost.

This logic leads to the following economic strategy, under conditions of perfect competition in rhc short run, in which you produce at the point at which

Table 6-4 DETERMINATION OF TOP·AG's PROFIT·MAXIMIZING LEVEL OF OUTPUT

(1) (2) (3) (4) (5) (6) (7) Point Market Total Economics Marginal Marginal

on Total Product Revenue, Total Profit, Cost. Revenue, Figure 6-1 Output Price S (1)X(2)S Costs$ (3) - (4) $ d(4) + d(1) $ d(3) + d(1) $

A 1.0 45.00 45.00 150.00 -105.00 B 3.0 45.00 135.00 180.00 -45.00 15.00 45.00 c 4.8 45.00 216.00 200.00 16.00 11.11 45.00 D 6.5 45.00 292.50 210.00 82.50 5.88 45.00 E 8.1 45.00 364.50 230.00 134.50 12.50 45.00 F 9.6 45.00 432.00 260.00 172.00 20.00 45.00 G 10.8 45.00 486.00 300.00 186.00 33.33 45.00 H 11.6 45.00 522.00 350.00 172.00 62.50 45.00

12.0 45.00 540.00 410.00 130.00 150.00 45.00 J 11.7 45.00 526.50 480.00 46.50 n/a n/a

INTRODUCTION TO PRODUCTION AND RESOURCE USE I CHAPTER SIX

the marginal revenue curve also reflects the average revenue. The intersection of this marginal revenue curve and the marginal cost curve indicates that output Or..tAX, or slightly more than 11 units of output, would maximize TOP-AG's profit.

Two additional output levels deserve special mention here-s-rhe break-even level of production and the shutdown level of production. If the marginal revenue curve falls in a parallel fashion to the point where it is just tangent with the minimum point on the average total cost curve, the business's average total costs will be, exactly equal to its aver­ age revenue. The business would just be able to meet both its fued and variable costs of production with the revenue it received during the current period or brea.kcven.

If the marginal revenue curve were to fall further (again in a parallel fashion) to the point at which it is just tangent to the minimum point on TOP-AG's average variable cost curve, TOP-AG would be just able to cover its variable costs bur none of its fued costs. Further declines in marginal revenue would cause the business to cease operations in rhc current period. TOP-AG could no longer pay its fuel bill, meet its hired labor payroll, or pay other expenses that vary with the level of production. Either the fuel supplier will stop making deliveries, hired workers will leave, or other factors critical to production will be curtailed. Thus, ourput level 050 represents the shutdown level of production, and the minimum point on TOP-AG's effective mar­ ginal cost curve, or its supply curve.

Finally, the level of economic profits in Figure 6-4 is equal to the shaded rccr­ angle formed by the difference between TOP-AG's average revenue and average total cost per unit at output O~wc, or $45 minus approximately $28, multiplied by the quantity of output at O~wc, or approximately 11.1 units. The level of economic profit here would be, approximately $189 (i.c., [$45 - $28] X 11.1 ).

Figure6-4 We can detetmine graphically what Table 6-4 could only hint at given the levels of produc- tiot't studied in that table. Given the MC = MR ctitetion expressed in Equation 6.13 for p(Ofit maximizatk>n, we see that ptofits would be maximized at OMAX, or slightly more than 1 J units of ourput per hour.

Oulput

Oso 10.8 9.6 8.1 6.5 4.8 11.6 3

70

60

50

40 1!! "' 8

30 Pee

20 Pso····

10

0

CHAPTER srx I rxraooucnox TO rRooucTtON AND RESOURCE use

Profi1 Maximization

120

Table 6-5 DETERMINATION OF TOP-AG's PROFIT-MAXIMIZING LEVEL OF LABOR Use

(1) (2) (3) (4) (5) (6) Marginal Marginal

Point Marginal value Net Cumulative on Use of Physical Product. Benefit, Net

Figure 6-1 Labor Product' (2) x $45 Wage Rate (3) - (4) Benefit

A 10 B 16 0.33 14.85 5.00 $9.85 9.85 c 20 0.45 20.25 5.00 15.25 25.10 D 22 0.85 38.25 5.00 33.25 58.35 E 26 0.40 18.00 5.00 13.00 71.35 F 32 0.25 11.25 5.00 6.25 77.60 G 40 0.15 6.75 5.00 1.75 79.35 H so 0.08 3.60 5.00 -1.40 77.95

62 0.03 1.35 5.00 -3.65 74.30 J 76 -0.02 -0.90

"Column 3 in Table 6-1.

If additional labor were employed beyond this point, the marginal input cost (i.c., the wage rate) would exceed the marginal benefits (i.e., the marginal value product for labor).

Ler us illustrate the determination of the proflt-maximizing level of input use by applying Equation 6.15 to the information presented in Table 6-5. This table illustrates that the price ofTOP-AG's product is $45 per unit and the cost of labor is equal to $5 per hour. Multiplying the marginal physical product in column 2 by $45 gives us the marginal value product reported in column 3, or the marginal benefit from adding another hour of labor.

Column 4 in Table 6-5 indicates that TOP-AG is a price taker in the labor market because its increased use oflabor had no effect on hourly wage rates. The contribution to profit (marginal net benefh) is reported in column 5. This value is found by subtracting the marginal cost in column 4 from the marginal benefit reported in column 3.

(6.15) MVP1,1xx = wage rate

The optimum, or profit-maximizing, level of input use occurs when the marginal value produce equals the marginal input cost. For the case of labor, the optimal level of labor use LS given by

(6.14)

Level of Resource Use: MVP = MIC Now that we have determined the level of output at which a business should operate if its management wishes to maximize its profit, we must next determine what this means for the level of resource use. In the single-variable input case, such as in our labor exam­ ple for TOP-AG in Table 6-J, this is a relatively simple process. If you have determined the profit-maximizing level of output, you simply go to column 2 and read over to col­ umn I and observe the level of input me associated with this ourput.

An alternative approach to determining profir .. maximizing input demands involves comparing rhe marginal benefit for a given level of input use with the marginal input cost or cost of an additional input. Because revenue is equal to the product price times output, it is clear that the marginal benefit from input use is equal to the change in total revenue per unit change in the input. This marginal benefit is called the marginal value product• and for labor is equal to

marginal value product for = MVP111,o, = M PP1,1xx X product price

labor

INTRODUCTION TO PRODUCTION AND RESOURCE USE I CHAPTER SIX 121

Marginal value product (MVP) rep<esents the additional revenue earned frotn employing another unit of input. Marginal input cost (MIC) is the cost of using that additional unit of input.

The focus of this chapter was on the economic decisions fuccd by a business in the shore-run or current period. We looked at the effects that varying the use of one input (hired labor) would have on output and the business's costs of producrion. This chapter determined the profir-maximizing level of output in the shore run and the profit-maximizing use of a variable input.

Chapter 7 will broaden the focus of the business's decisions by examining the determination of the least ... cost combination of variable inputs in the short run and the optimal expansion path for labor and capital over rhe long run. This chapter will also address the profit-maximizing combination of products to produce.

WHAT LIES AHEAD?

The information in Table 6-5 illustrates that TOP-AG should use slightly more than 40 hours of labor. The wage rate in column 4 would equal the marginal value product of using additional labor in column 3. If labor were expanded to 50 hours, the cumulative net benefit in column 6 would be declining.

The marginal value product and marginal input cost relationships calculated in Table 6-5 arc plotted in Figure 6-5. Because the marginal value product curve is noth­ ing more than the marginal physical product curve multiplied by a fixed producr price, the marginal value product curve looks very much like a marginal physical product curve. As Table 6-5 suggcsrs, the labor use rhat maximizes profits is about 41 hours, the point at which the marginal value product curve intersects the marginal input cost curve.

The analysis presented in Table 6-5 and Figure 6-5 can be extended ro other inputs. It represents a general way of characterizing the profit-maximizing level of input use. Profit maximization requires that the marginal value product (marginal benefit) of each variable input equal its marginal input cost simulrancously.

Figur• 6-'5 Equation 6. l S indicates that the profit-maximizing level of inpur use in the shol't run OCCUl'S at the point at wh;ch the marginal value product of labor equafs the margit>al input cost. In the case of TOP-AG, we see that this occurs at approximately 41 hours of labor per day if the wage rate is $5 an hour, or at quantity LMAX.

labor use

Profit~Ma.ximizing Level of labor Use

D

122 CHAPTER SIX I INTRODUCTION TO PRODUCTION AND RESOURCE USE

76 62 -10 ~~~~~~~~~~~~~~~~~~~~~~~~~~~

10 16 20 22 26 32 49 50

c:

Profit Shutdown Stage II of production Total costs Total fixed cost Total physical product curve Total revenue Total variable cost Variable costs

Input categories Law of diminishing marginal returns Marginal cost Marginal input cost Marginal physical product Marginal revenue Marginal value product Perfect competition Production function

Average cost Average fixed costs Average physical produce Average revenue Average total costs Average variable costs Breakeven Fixed costs Imperfect competition

8. The profit·maximizing level of input use occurs in the short run at rhe input level at which MVP = MIC. The competitive business takes the per unit price of the variable input (MIC) as given by the marketplace and makes its purchasing deci­ sions by equating MVP = MIC.

9. The business will break even (TR = TC) in the short run at the outpur level where the price the business receives for its produce fulls to rhc poinr a, which AR = ATC or where average profit per unit of output is zero. The business may continue to operate in the short run if AR < ATC, because it can minimize its losses (i.c., cover ar least some of its fixed costs).

10. The business will cease operations, or shut down, in rhe short run if the price rhe business receives for its product falls to the point at which AR < AVC. When this occurs, the business will no longer be able to cover its variable costs of pro· duction (e.g., pay its fuel bill) and will be unable to acquire additional inputs.

KEY TERMS

The purpose of this chapter is to illustrate the various physical relationships rhar exist between inputs and outputs with which agricultural economists must be familiar. The major points of this chapter arc sum ma· rized as follows:

1. Farm inputs can be classified into land, labor, capi­ tal, and management.

2. A production function captures the causal physical relationship between input USC and me level of output.

3. The total physical product reflects the level of out· put of a given level of input use. Marginal physi­ cal product represents the change in the level of output associated with a change in the use of a particular input. Finally, average physical product reflects the level of output per unit of input use. In each case, all other inputs arc held fixed. The value of the marginal physical product represents the slope of the total physical product curve. No rational farmer would want co produce beyond the point at which the marginal physical product equals zero, because further input use would cause the level of output ro full.

4. There arc three stages of production: • Stage I is the point ar which me marginal physical

product curve for a particular input is rising but still lies above the average physical product curve.

• Stage fl is the point at which the marginal physi­ cal product equals the average physical product and continues until the marginal physical prod· ucr for the: input in question reaches zero.

• Stage III is the point at which stage II left off or where the total physical product curve begins to decline and the marginal physical product curve becomes negative.

SUMMARY

INTRODUCTION TO PRODUCTION AND RESOURCE USE I CHAPTER SIX 123

5. The law of diminishing marginal rcrurns states that as the: use of an input increases, its marginal physical product will eventually fall.

6. Marginal cost is the change in total cost with respect to a change in output. Average cost is total cost divided by total output. Fixed costs arc those costs that do not vary with output.

7. The profir-rnaximizing level of output occurs in the shorr run at the output level at which MC = MR. The competitive business takes the market price (MR) as given by the marketplace and makes its production decisions by equating MC= MR.