Question

Q4.Why is it that, in the short-run, after a certain number of workers has been hired, output increases by less and less with each additional worker hired? Illustrate your answer with an example. Would there be any circumstances under which this phenomenon would not occur?

Answer 1

In the short run production function behaves in the law of variable proportions. Paul samulson has defined the short run law of variable proportion as : “An increase in some inputs relative to other fixed inputs will, in a given state of technology, cause output to increase; but after a point the extra output resulting from the same addition of extra inputs will become less.” . So here we observe that as no.of variable factor (say Labour , L ) increases the output first increases at an increasing rate (upto T1) after which it increases at a decreasing rate (T1 to T2 range) and lastly output falls (beyond T2)

lets first list the assumptions behind this law. the 5 main assumptions for the law to hold in the short run is:

1. state of technology is assumed to be given and constant.

2.there must be some inputs the quantity of which is kept fixed.

3.there must be a possibility of producing output by changing the factor proportions.

4.Homogenous units of labour are considered here.

5.This is operative in short run.

The reason for output to behave in such a way is the follows:

stage of increasing returns : at this stage every additional variable factor adds more and more to the total output. MP_L   (change in quantity per unit change in labour ) increases up to L1 labour units and its curve is higher than the average product, so that total product is increasing at increasing rate.

Reasons for operation of this stage:

1. fixed factors are better utilised in this stage: Initially fixed factors have too little variable factors to work with,as more and more labour is hired the optimum combination between fixd and variable factors improves and moves towards best combination.
2. variable factors have an increased efficiency: efficiency of variable factor improves hence there is a greater cooperation and coordination between variable factors.
3. indivisibility of fixed factors: fixed factors cannot be usually broken down to smaller parts.so as more labour is hired they have a decent size of fixed factors to work with.

all this causes the producer to experience an increasing stage of production. however he wont stay in this stage for long. unless he reaches the maximum average product of labour he will go on increasing production.

stage of diminishing returns:In the second phase, every additional variable factor adds lesser and lesser amount of output.At this stage, MP_L decreases up to L2 labour units where MP_L curve intersects the X-axis. at this level MP_L = AP_L after this, MP_L curve is lower than the AP_L. TP_L increases at decreasing rate. This is the stage where a rational producer will always aim to produce in this phase because TP is maximum and MP of each variable factor is positive.

reasons for behaviour of ouutput in this stage

1. optimum combination of factors has been acchieved
2. factors are imperfect substitutes,there is a limit to how much one factor can be substituted for the other. after a point labour cannot do capital's work and vice versa. this leads to diminishing returns.

stage of negative returns: after L2 units of labour the MP_L becomes negative, the AP_L continues falling but remains positive.After this unit of labour, TP_L declines with the employment of more units of variable factor (L). So, no firm would deliberately choose to operate in this phase.no employer would like to operate in this stage.

reasons for this stage:

1. limitation of fixed factors: beyond a point fixed factors cannot be increased even if variable factors are being increased therefore production declines and cost increases to hire the variable factor.
2. poor coordination between variable and fixed factors: overcrowding of variable factor happens because they have far exceeded the optimum combination of fixed factors.
3. decrease in the efficiency of variable factor: this happens because efficiencies of variable factor is exhausted , the labour cannot extract advantages of division of labour and specialisation.

let us explain with a real world example: say Rhonda has started a new business of photocopying documents so she has 2 photocopy machines and 1 labour working on it. as more demand comes up more work needs to be done in lesser times so she increases the variable factor labour. initially work happens faster and more photocopies are being done per labour. but after a point work happens slower, and finally production is even slower as labourers start wasting time talking to each other and getting into each other's way during the production. obviously we know that for 2 photocopy machine 4 labourers are enough. anything beyond this will be over crowding.

yes this LAW OF VARIABLE PROPORTION will not work if assumptions are changed.

1. If a better technology comes then even in stage 3 we will see high production, then output/labour wont fall infact will rise.
2. if variable inputs of labour are not homogenous then say after L2 whichever labour is hired he has a higher efficiency than previous labourers . in that case MPL will increase and not decrease.
3. this works only in short run. in long run the fixed units also change so instead of 2 photocopy machines ,Rhonda will keep 10 photocopy machines and get a higher increased MPL.
4. If factors work in fixed proportions only , say 2:3 then as labour in increased fixed factor will also be increased so in that case output will also increase per unit of labour.