The Law of Variable Proportions

Imag­ine that a farmer is cul­ti­vat­ing wheat only by using more and more labour in a cir­cum­stance where land is a fixed fac­tor and labour is a vari­able fac­tor. Here’s a cru­cial query: Will the amount of wheat pro­duced by each addi­tional unit of labour used in the given area be equal? Will the MP of the labour remain the same for each and every new unit of labour used, in other words? Never say “maybe.” It is not pos­si­ble.

A coun­try like India would have pro­duced more and more wheat by employ­ing more and more labour on the same piece of land, if the MP of labour remained con­stant (regard­less of how much labour is used). There would never have had a food short­age. The real­ity shows that MP must even­tu­ally decrease. The rea­son is sim­ple: There is always some per­fect ratio of the fac­tors of pro­duc­tion. The opti­mum ratio can only be main­tained by adjust­ing L if L(Labour) and K(Cap­i­tal) are both present and K is a con­stant. MPL should be at its high­est value to cor­re­spond to the opti­mal K:L ratio. But when the ideal ratio is reached, any increase in L would indi­cate overuse of the vari­able com­po­nent. Alter­nately, it would imply decreas­ing fixed fac­tor avail­abil­ity for every unit of the vari­able com­po­nent. It could also refer to overus­ing the fixed fac­tor. There­fore, MPL must begin to decrease. It might even­tu­ally get to the point where adding a new labour unit (on the same land) does not affect over­all out­put. This implies that MPL becomes zero. As pre­vi­ously stated, MP might even become neg­a­tive in excep­tional cir­cum­stances. This is how the Law of Returns or the Law of Vary­ing Pro­por­tions works.

Returns to Fac­tor: Law of Vari­able Pro­por­tions

Returns to a fac­tor refer to the rise in the total prod­uct that results from increas­ing just one fac­tor while hold­ing the other fac­tors con­stant. The pro­duc­tion of the firm dis­plays the Law of Vari­able Pro­por­tions in the short term when one input is vari­able, and the other inputs are fixed.

State­ment of Law of Vari­able Pro­por­tions

The Law of Vari­able Pro­por­tions states that as we increase the quan­tity of only one input while keep­ing other inputs fixed, the total prod­uct(TP) increases ini­tially at an increas­ing rate, then at a decreas­ing rate, and finally at a neg­a­tive rate.

As per the law of vari­able pro­por­tions, the changes in TP and Mar­ginal Prod­uct (MP) can be cat­e­gorised into three phases:

Phase 1: TP rises at an increas­ing rate, and MP increases.

Phase 2: TP rises at decreas­ing rate, MP decreases and is pos­i­tive.

Phase 3: TP falls, and MP becomes neg­a­tive.

Assump­tions of the Law of Vari­able Pro­por­tions

1. It oper­ates in the short run because the fac­tors are cat­e­go­rized as vari­able and fixed.
2. The law applies to all fixed fac­tors, includ­ing land.
3. The law of vari­able pro­por­tions allows for the com­bi­na­tion of sev­eral vari­able units with fixed fac­tors.
4. This law pri­mar­ily applies to the pro­duc­tion sec­tor.
5. It is sim­ple to cal­cu­late the impact of a change in out­put caused by a change in vari­able fac­tors.
6. It is con­sid­ered that after a cer­tain point, fac­tors of pro­duc­tion become imper­fect sub­sti­tutes for one another.
7. For this law to func­tion, it is assumed that the state of tech­nol­ogy would remain con­stant.
8. All vari­able fac­tors are thought to be equally effec­tive.

For exam­ple, Let’s say a farmer has 1 acre of land (i.e., fixed fac­tor) and wants to use labour (i.e., vari­able fac­tor) to improve the pro­duc­tion of rice there. The out­put increased ini­tially at an increas­ing rate, then at a decreas­ing rate, and finally at a neg­a­tive rate as he employed more and more units of labour. The below table dis­plays the out­put behav­iour in this case.

Phase I: Increas­ing Returns to a Fac­tor (TP increases at an increas­ing rate)

In the ini­tial stage, each addi­tional vari­able com­po­nent raises the total pro­duc­tion by an increas­ing amount. This indi­cates that each vari­able’s MP rises and that TP rises at an increas­ing rate.

• It occurs as a result of the ini­tial vari­able input quan­tity being too small in com­par­i­son to the fixed input. Due to the divi­sion of labour, effi­cient use of the fixed input dur­ing man­u­fac­tur­ing increases the pro­duc­tiv­ity of the vari­able input.
• One labour gen­er­ates 5 units, as shown in the sched­ule and dia­gram, whereas two labours pro­duce 20 units. It means that MP rises until it reaches its max­i­mum point at point P, which sig­ni­fies the end of the first phase, while TP rises at an increas­ing rate (up to point Q).

Point of Inflex­ion A point from where the slope of TP curve changes is known as point of inflex­ion. Till the point of inflex­ion, TP increases at an increas­ing rate, and from this point down­wards, it increases at a dimin­ish­ing rate.

Phase II: Decreas­ing Returns to a Fac­tor (TP increases at a decreas­ing rate)

Every extra vari­able in the sec­ond phase increases the out­put by a less and smaller amount. This indi­cates that when the vari­able fac­tor increases, MP decreases, and TP rises at a decreas­ing rate. This stage is known as the dimin­ish­ing returns to a fac­tor.

• This occurs as a result of pres­sure on fixed inputs that results in a decline in vari­able input pro­duc­tiv­ity after a cer­tain level of out­put.
• When MP is zero (point S), and TP is at its max­i­mum (point M) at 40 units, the sec­ond phase comes to an end.
• The sec­ond phase is highly impor­tant because a ratio­nal pro­ducer will always try to pro­duce dur­ing this time because MP and TP are both pos­i­tive for each vari­able fac­tor.

Phase III: Neg­a­tive Returns to a Fac­tor (TP falls)

The third phase shows a decline in TP due to the use of more vari­able fac­tors. MP has now become neg­a­tive. As a result, this stage is referred to as neg­a­tive returns to a fac­tor.

• It occurs when the amount of vari­able input exceeds the fixed input by a great dif­fer­ence, which causes TP to decrease.
• The third phase in the above graph begins after points S on the MP curve and M on the TP curve.
• In the third phase, MP for each vari­able fac­tor is neg­a­tive. There­fore, no com­pany would delib­er­ately decide to oper­ate at this phase.

Phase of Oper­a­tion

A log­i­cal or ratio­nal pro­ducer will always attempt to oper­ate in Phase II of the Law of Vari­able Pro­por­tion at all times.

• Every addi­tional unit of a vari­able fac­tor used in Phase I results in an increase in pro­duc­tion or mar­ginal prod­uct. There­fore, if pro­duc­tion is increased with more units of the vari­able fac­tor, there is scope for greater prof­its.
• In Phase III, each vari­able’s mar­ginal prod­uct is neg­a­tive. There­fore, this phase is elim­i­nated due to tech­ni­cal inef­fi­ciency, and a ratio­nal man­u­fac­turer would never engage in the third phase of pro­duc­tion.

This leads us to the con­clu­sion that a pro­ducer will seek to oper­ate in Phase II since the MP of each vari­able fac­tor is pos­i­tive and TP is at its high­est level.

Rea­sons for Vari­able Pro­por­tions

The rea­sons for the three phases of the law of vari­able pro­por­tions are:

Rea­sons for Increas­ing Returns to a Fac­tor (Phase I)

The oper­a­tion of increas­ing returns to a fac­tor is car­ried out for three key rea­sons:

1. More Effec­tive Use of Fixed Fac­tor: In the ini­tial stage, a num­ber of fixed fac­tors are avail­able, while there aren’t enough vari­able fac­tors. The fixed fac­tor is there­fore not com­pletely utilised. The fixed fac­tor is bet­ter used, and out­put increases at an increas­ing rate when the vari­able fac­tors are increased and com­bined with fixed fac­tors.

2. Increased Effi­ciency of Vari­able Fac­tor: The vari­able fac­tors must be increased and com­bined with the fixed fac­tor, in order to use the for­mer more effi­ciently. Besides, there is a high degree of spe­cial­i­sa­tion and increased coop­er­a­tion among the dif­fer­ent units of the vari­able fac­tors.

3. Fixed Fac­tor Indi­vis­i­bil­ity: In gen­eral, fixed fac­tors that are inte­grated with vari­able fac­tors are not divis­i­ble. It means that these ele­ments can­not be divided into smaller parts. As more units of the vari­able com­po­nents are given, the util­i­sa­tion of the fixed fac­tor improves after an invest­ment has been made in an indi­vis­i­ble fixed fac­tor. As long as the ideal level of vari­able and fixed fac­tor com­bi­na­tion is attained, increas­ing returns is applic­a­ble.

Rea­sons for Decreas­ing Returns to a Fac­tor (Phase II)

The occur­rence of dimin­ish­ing returns to a fac­tor is due to these three key rea­sons:

1. Opti­mum Com­bi­na­tion of Fac­tors: There is only one opti­mal com­bi­na­tion between a vari­able and a fixed fac­tor where the over­all prod­uct is max­i­mum. The mar­ginal return of the vari­able fac­tor begins to decrease after the fixed fac­tor has been utilised to its fullest poten­tial. For instance, if a machine (fixed fac­tor) is being used to its full poten­tial with 4 work­ers, adding a fifth worker will only slightly improve TP, and MP will begin to decline

2. Over-uti­liza­tion of Resources: The fixed com­po­nent finally reaches its lim­its and begins to pro­duce dimin­ish­ing returns as one con­tin­ues increas­ing the vari­able fac­tor.

3. Imper­fect Sub­sti­tutes: Fixed and vari­able fac­tors are imper­fect sub­sti­tutes for one another, which results in dimin­ish­ing returns to a fac­tor. There is an extent to which one fac­tor of pro­duc­tion can be sub­sti­tuted for another. For instance, until a cer­tain point, cap­i­tal may be used in place of labour or labour may be used in place of cap­i­tal.  Beyond a cer­tain point, they start to lag behind each other and pro­duce declin­ing returns.

Rea­sons for Neg­a­tive Returns to a Fac­tor (Phase III)

The occur­rence of neg­a­tive returns to a fac­tor is due to these three major rea­sons:

1. Lim­i­ta­tion of Fixed Fac­tor: The rea­son why some pro­duc­tion fac­tors have neg­a­tive returns is that they are fixed in nature and can­not be raised in the short run together with an increase in the vari­able fac­tor.

2. Lack of Coor­di­na­tion: When the vari­able fac­tor dom­i­nates the fixed fac­tor, they inter­fere with one another. It causes a lack of coor­di­na­tion between the fixed and the vari­able fac­tor. As a result, total out­put falls rather than rises, and the mar­ginal prod­uct becomes neg­a­tive.

3. Decrease in Effi­ciency of Vari­able Fac­tor: The ben­e­fits of spe­cial­i­sa­tion and the divi­sion of labour begin to dimin­ish as vari­able fac­tors con­tinue to increase. It causes inef­fi­cien­cies of vari­able fac­tors, which is another ele­ment that finally leads to neg­a­tive returns.

Key terms

Mar­ginal Prod­uct (MP)

Mar­ginal prod­uct is an addi­tional quan­tity of the com­mod­ity pro­duced by using an addi­tional unit of a vari­able fac­tor.