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joan robinson the production function and the theory of capital 1 joan robinson the production function and the theory of capital the review of economic studies vol 21 no 2 ...

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          Joan Robinson
          The Production Function and the Theory of Capital
          1
          Joan Robinson
          “The Production Function and the Theory of Capital”
          The Review of Economic Studies, Vol. 21, No. 2 (1953 - 1954), pp. 81-106
          2
          D. G. Champernowne
          “The Production Function and the Theory of Capital: A Comment”
          The Review of Economic Studies, Vol. 21, No. 2 (1953 - 1954), pp. 112-135
          3
          Robert M. Solow
          “The Production Function and the Theory of Capital”
          The Review of Economic Studies, Vol. 23, No. 2 (1955 - 1956), pp. 101-108
          4
          Joan Robinson
          “The Production Function and the Theory of Capital--A Reply”
          The Review of Economic Studies, Vol. 23, No. 3 (1955 - 1956), p. 247
           The         Production                    Function                and        the       Theory 
                                                  of       Capital 
                                                    INTRODUCTION 
                The dominance in neo-classical economic teaching of the concept of a production 
          function, in which the relative prices of the factors of production are exhibited as a 
                                                                                                             know- 
          function of the ratio in which they are employed in a given state of technical 
          ledge, has had an enervating effect upon the development of the subject, for by con- 
                                                                                                         attention 
                                                                       of factors it has distracted 
          centrating upon the question of the proportions                                                       the 
                                        but more rewarding questions of the influences governing 
          from the more difficult 
          supplies of the  factors and of the  causes and consequences of changes in technical 
          knowledge.          the                  function  has  been  a  powerful instrument  of  mis- 
                Moreover,          production                                          0     f         where L is 
          education. The student of economic theory is taught to write                       f  (L, C) 
          a             of           C a quantity of capital and 0 a rate of output of commodities.' 
             quantity       labour,                                                    in              of 
              is              to                                                          man-hours 
          He  instructed          assume all             alike,       to measure L 
                                               workers           and                                      labour; 
                                                                                                         a unit of 
                                                                               involved in choosing 
          he is told                 about the index-number problem 
                       something                                                                    he will forget 
                      and then                                                  in the hope that 
          output ;                he is hurried on to the next question,                              a 
          to      in                                                    does        he has become  professor, 
                                      is measured. Before ever he 
             ask     what units C                                             ask,              to the next. 
                so          habits of                             on         one generation 
          and      sloppy               thought are handed            from         The            in existence at 
                The              is             not an                  answer.          capital 
                      question      certainly            easy one to 
                                                              "       of the  environment in which labour 
          any moment may be treated simply as  part                                                    This is the 
                                          a                                                   alone. 
          works."2 We then have             production function in terms of labour                           goods 
                                  the                                   the supply of concrete capital 
          right procedure for          short period within which                                     for it 
                not                                                                   line to               means 
          does               but            the                       a very weak             take, 
                      alter,      outside       short period it is      of capital (which can be made over 
                                            a change in the stock 
          that we cannot distinguish                                  the weather (an act of God). 
          the                                    from a change in 
               long run by accumulation)                                                              in 
                                                                                          the            existence 
                           look         a        of                                of all 
                We                        stock              as the specific list             goods 
                     may         upon               capital                               of                   But 
          at        moment                    work-in-progress in  the  pipe lines            production). 
              any               (including                                                         any change in 
                                                                      of the short period, for 
          this again is of no use outside the strict bounds                                   of                and 
                                                                                of methods       production 
          the ratio of capital to labour involves a re-organisation                                all  the 
                     a            in  the            sizes                         of  many or               goods 
          requires      change             shapes,          and specifications 
                       in the                 3 
                                         list. 
          appearing            original                                                                     Should 
                As soon as       leave                                     host of 
                                                                         a          difficulties appear. 
                             we         the short period, however,                          costs ? 
                   be                        to                               or its 
                                                                      power          past 
          capital      valued according         its future earning                                with  a  certain 
                When we know the  future expected rate of output associated                            of 
                                                                              if               a rate     interest, 
                                                                       then,  we are given 
                          and              future prices and costs, 
          capital good,        expected                                                             which       will 
          we can value the capital good as a discounted stream of future profit                              it 
          earn.  But to do so, we have to begin by taking the rate of interest as given, whereas 
          the main purpose of the production function is to show how wages and the rate of 
                                                                                                                and 
                                                                                                  conditions 
                                 as the                                           by technical 
          interest (regarded             wages of capital) are determined 
          the factor ratio. 
               i  Throughout  this  essay  we  shall  be  abstracting  from  land  as  a  factor  of  production,  so  we  will  not 
          bother  the  student  with  it. 
               2                               . 
                         General Theory, p.  2  4 
                Keynes,                     I               tenth  man  joins  nine  who  are  digging  a hole,  nine  more 
               8  In  Professor  Robertson's  example,  when  a  and  a  bucket  to  fetch  beer.  (Economic Fragments, 
          expensive  spades  are turned  into  nine  cheaper  spades 
          P.  47-) 
                                                              8I 
                                                OF                  STUDIES 
                             THE  REVIEW             ECONOMIC 
         82 
                                                                                            money 
              Are we then to value capital goods by their cost of production ?  Clearly power 
                                                                             the purchasing 
                                                             we can specify 
                                            nor       unless 
                            is         here     there 
         cost of production  neither                                                             to 
                                                                                          effect, 
                                                                               that is, in 
                                                                         units, 
                                                                of wage 
                                                          terms 
                                cost                   in 
                                                 goods 
                        we           the capital 
                    but    may 
         of money,                    of a      of          labour. 
                  their cost in terms      unit   standard 
         measure                                                                                 to 
                                                                        in the past is congenial 
                               as                       time expended 
              To treat capital    a quantity of labour                                   nature of 
                                                   for                 to  the  essential 
                                   point of            it  corresponds 
         the production-function             view,                                        employ- 
                                                                                        in 
                                                                            in essence, 
                                      of              Investment consists, 
                          as a factor    production. 
                 regarded 
         capital                                                                         is making 
                                                                                 saving 
                                                                           while 
                                   which will       its fruits in the future 
                         in a                 yield 
                    now       way 
             labour 
         ing     products available for the workers to  consume in the meantime;  and the 
         current                                                               that was expended 
                                             in the fact that a unit of labour 
                         of capital consists 
         productiveness     in the       is more valuable to-day than a unit expended to-day, 
         at a certain time         past 
                           are 
                  its fruits   already ripe. 
         because                                                                      of     whole 
                                                                      lies at the root   the 
                                      a                        which 
                       we encounter  fundamental 
              But here                                difficulty                                 is 
                                                                     in a       form.  All work 
                                                 is                       pure 
                  of capital.  A unit of labour     never expended 
         problem                    of goods of some kind or another.  When Adam delved and 
         done with the assistance                                          in existence.  The cost 
                         were evidently a spade and a spindle already 
                   there 
         Eve span                                                                           before 
                                                                             be constructed 
                                                       and       they must 
                            the cost of         goods,      since 
         of        includes             capital 
            capital                                                                       between 
                                                                       the        of time 
                                                                  over     period 
                                                       is interest 
                                 of the cost of capital 
                  be used, part 
         they can            work was done in                  capital goods and the time when 
         the moment when                          constructing       a               of capitalism, 
              are             a stream of output.  This is not just    consequence 
         they     producing                                                            will yield a 
                                                                        to-day, which 
                                                  of         expended 
                        a          society a unit    labour, 
         for         in   socialist 
             equally                         the same        as a unit which will yield a product 
                  in            time, is not           thing 
         product     five years' 
         to-morrow.  even if it  were possible to  measure capital simply in terms of labour 
              Finally,                                             of       units is              ? 
                                                                      what             composed 
                                                   the                               C 
                               not have answered 
         time, we still should                         question:         of        as            in 
                                                    is         to 
                we are                            it   natural    think    capital    measured 
                                   accumulation, 
         When          discussing                                   in            from consuming 
                                          of               consists    refraining 
                of           The process     accumulation 
         terms    product.                                                 we consider what 
                                        to the       of          But when                     addi- 
                                 to            stock    wealth. 
                           order 
                         in         add 
                 output 
         current                       a                                         we must measure 
                                                        of               makes, 
              to            resources  given amount       accumulation 
         tion    productive                          the stock of                         made 
                                                  to                                            by 
                                     the addition 
                 in labour       for                                          equipment 
         capital           units,                                 productive       in 
                                                         how much          is done    constructing 
                 an            of                                    work 
                    increment                      upon 
         adding                   capital depends          of an        labour.        as we move 
                                         of                     hour's 
            not       the       in terms    final                               Thus, 
         it,    upon      cost,                  product,                              in terms of 
               one        on a              function to  another, measuring capital 
         from       point       production                             to see the effect 
                   we have to know the                   rate in order                   upon pro- 
         product,                         product-wage                             in labour 
         duction of            the ratio of capital to labour.  Or if we measure             units, 
                     changing                                                            would be 
                                                        to see how much accumulation 
             have to know the                  in order 
         we                     product-wage                                              with the 
                               a                   of          But the        rate alters 
                   to produce  given increment        capital.          wage 
         required                                             both for a           of          and 
                                one                     stand             quantity    product 
                 the factors :                  cannot 
               of                   symbol, C, 
         ratio       of labour time. 
         a quantity          the           which the               function            to  analyse, 
              All the same,       problem              production            professes 
         although it  has been too much puffed up by the attention paid to it,  is a genuine 
                                                                        is       cleared     a few 
         problem.  To-day, in country Alpha, a length of roadway          being      is  by  made 
                                 in Beta a road                   the same             being 
              with bulldozers                       near-enough             quality) 
         men                   ;                 (of                                   of men 
                             of men with         and ox-carts.  In Gamma thousands              are 
                   hundreds 
         by some                           picks                       the             all 
                                shovels and little baskets to remove       soil.  When     possible 
                  with wooden 
         working                made for              in national character and            and for 
                     have been             differences                            climate, 
         allowances                                                                             for 
                     in the state of              it  seems pretty clear that the main reason 
         differences                 knowledge,                                  in        than in 
                              is that         in some sense is more plentiful       Alpha 
         this state of affairs        capital  of        of                           it 
         Gamma. Looked at from the point           view     an individual capitalist,   would not 
                                                                            were             at 
                                                                    finance                    the 
                                     in                if unlimited               available) 
              to use        methods     Gamma 
         pay         Alpha                       (even  at       the        of view of           it 
         rate of interest which is ruling, and looked       from      point             society, 
                       PRODUCTION FUNCTION AND  THE  THEORY  OF  CAPITAL  83 
               THE 
                                                                       to  raise all the  labour available in 
                                          effort of accumulation 
          would need a prodigious                                                  is a real one.  We cannot 
                     even to the Beta level of technique.  The problem 
          Gamma                                                                      the element of common- 
                                                                         to rescue 
                                                   without an effort 
                                        function 
                     the production 
          abandon                              in it. 
                            been entangled 
          sense that has 
                                         THE  QUANTITY OF CAPITAL 
                                                                                         is called.  The capital 
                                                      is         it is what its name 
                "Capital"  is not what capital          called,                 in existence at that moment. 
                                                               all the goods 
                                                 of time are 
                  in existence at a moment 
          goods                                                                                            Blanc. 
                                                                                                    Mont 
                                                                                               nor 
                                                                                        heap 
                                                                            a rubbish 
                                                                   neither 
                                     in existence.  It includes 
          It is not all the things            "         " are              is that  they  have value, that is 
          The characteristic by which  goods                   specified                             tin is not a 
                                                                                 an empty petrol 
                                                                         Alpha 
                                                            in country 
                                            other. Thus, 
                                over each 
                        power 
          purchasing 
          "                                    where old tins are a source of valuable industrial raw 
            good," whereas in Gamma 
                      it is. 
          material,                                       It  is so         actual               objects, called 
                The list of goods is quite specific.                many            particular               from 
                                                                                  the same name differ 
                                                                          under 
                                                               grouped 
          blast furnaces,                 etc., etc.  Goods 
                             overcoats,                                        and these must not be over- 
          each other in the details of their physical specifications                              twenty years 
                                   in their ages are also important.  A blast furnace 
          looked.  Differences                                                               in other respects, 
          old is not equivalent to a brand new one of the same specification 
                                                                                            is          relevant 
                                                                              one.  There  another 
                                                                        new 
                                                           to a brand 
                                         old equivalent 
               is         twenty days 
                     egg 
          nor  an                                                                 to                 an       one 
                                                                                      wear      and      egg 
                                                                      one                   it, 
                                            An              requires       body 
          characteristic of the goods.           overcoat                                                       or 
                                                          one                  are           and two bodies 
                      eat                 one          or      mouth, they         useless, 
          mouth to         it.  Without        body,                    in        them.  But a blast furnace 
                                                                share      using 
                                             of time) cannot 
          mouths (at a given moment                                                            iron. 
                                                                                iron      into         Therefore 
                                                                       to            ore 
                                                            of            turn 
                            a                 of numbers  bodies 
               be used                 range 
          can           by  certain                                                                   a 
                                                                           of its rate of          as  function 
                                                             an account                   output 
                             of  blast furnace includes 
          the description       a                                        not discuss 
                                                                   shall                              problems, 
                                                               we                      short-period 
                                                   it.  (Since 
             the number of bodies operating 
          of                                                                            in                   with 
                                                         each          of equipment,       the situations 
                                               working          piece 
                                    actually 
                         of bodies 
          the number                                                                  most                 to it.) 
                                                                      is                     appropriate 
                  we                         is the number which  technically 
          which       shall be 
                               concerned,        the         which is quite different. Of two overcoats, 
                       is            aspect of        goods 
               There      another                                     is on the         of Mrs.           who is 
                                                                 one             body             Jones, 
          completely similar in all the above respects,                               is on the           of Mrs. 
                                    delight at her fine appearance. Another                       body 
                    with inward 
          purring                                                   income           what it      she is obliged 
                    who is                        her husband's              being            is, 
                                        because, 
          Snooks,            grizzling            In what follows we shall not  discuss this aspect of 
                                       clothes. 
          to  buy  mass-produced                                             is an overcoat             IV), and 
                                          that  an overcoat             IV)                     (Mark 
          goods at all.  We take it                             (Mark 
          no nonsense.                           who of individual              is not a thing what we can 
                       this              who's                          goods 
               Now,          enormous                                                    to            the items 
                                                       a           of         we have       evaluate 
                      all          To            it as   quaantity  goods 
          handle at       easily.      express                 the         in terms of the real cost of pro- 
          of         it is composed. We can evaluate               goods 
             which                                       the                                            to  make 
                                      the  work and                      existing goods required 
          ducing them-that  is,                               formerly                                or 
                                                             in some unit of                  power,      we can 
                                of their                                        purchasing 
          them, or in terms              value expressed                   is, what the stock of goods will 
                                         to their productivity-that 
          evaluate them according            is        in                      it. 
                       the future if work       done                     with 
                    in                                    conjunction 
          become                                      three evaluations            equivalent results ;  there 
               In a             of                all                       yield 
                     position      equilibrium                                  to another                    the 
          is a quantity which can be translated from one number                               by changing 
                          the               of                 It entails that there have been no events 
          unit.  This is       definition      equilibrium.                                        between the 
                                                                                    the relation 
          over the relevant             of past time which have disturbed 
                                period                              that the human              in the situation 
                                   a         stock of          and                     beings 
                                of                     goods, 
                   valuations        given 
          various          the future to be just like the past-entirely  devoid of such disturbing 
          are expecting the rate of                       to-day is the rate which was expected to rule 
                                                 ruling 
          events.  Then                   profit                                                              the 
                                                                             now extant was              and 
                          the decision to invest in                   good                       made, 
          to-day when                                   any capital              of          are          to  the 
          expected future receipts, capitalised at the  current rate                 profit,       equal 
                                                are             to            them. 
          cost of the                   which        expected      produce 
                       capital goods 
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...Joan robinson the production function and theory of capital review economic studies vol no pp d g champernowne a comment robert m solow reply p introduction dominance in neo classical teaching concept which relative prices factors are exhibited as know ratio they employed given state technical ledge has had an enervating effect upon development subject for by con attention it distracted centrating question proportions but more rewarding questions influences governing from difficult supplies causes consequences changes knowledge been powerful instrument mis moreover f where l is education student taught to write c quantity rate output commodities labour man hours he instructed assume all alike measure workers unit involved choosing told about index number problem something will forget then hope that hurried on next does become professor measured before ever ask what units so habits one generation sloppy thought handed existence at not answer certainly easy environment any moment may be ...

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