In this video we will learn about the firm’s demand for labour.
Specifically, we’ll calculate the marginal revenue product for a firm and work towards
understanding why exactly it is the firm’s demand curve for labour.
Once we’ve covered that we will next look at how changes in MRP, or marginal revenue
product, affect the demand for labour.
Before we begin, we should establish our assumptions.
When we discuss the marginal product of labour we are discussing the short run.
In the short-run, at least one of the factors of production is fixed.
Assume that all factors are fixed except labour.
Remember what the law of diminishing marginal returns states that marginal output will start
to decline if more and more units of one variable factor of production are combined with a given
quantity of fixed factors.
In the long run, the demand curve for labour is downward sloping because capital can be
substituted for labour.
Furthermore, in the short run, a firm’s capital is fixed.
Therefore, the higher the price of labour, the less labour firms will hire.
In the short run, the wage rate would have to fall to encourage the employer to take
on an extra worker.
In the long run, firms will substitute capital for labour if it is economical.
Now that we’ve set our assumptions we are ready to move towards calculating marginal
revenue product.
We have to move there step by step to ensure you get it.
It can be quite confusing, but the explanation that follows should make it easier for you
to understand.
So let’s start by calculating marginal physical product.
I’ve put together some made up numbers to help us calculate marginal physical product.
The first column is for our variable input, labour.
The second column is a tally of their total product.
That is the total amount produced with the given amount of labour.
Third is marginal physical product.
This is the difference between the current level of output and the previous level of
output divided by the change in the number of workers.
I’ve only increased the number of workers by one in each instance, this is to keep the
calculations simple.
With no workers, we can safely assume that output is zero.
Once the first worker is hired, they create an additional 6 units of output.
This is also their marginal physical product.
As we hire the second worker, total output increases to 18.
This is an increase of 12 units from our previous level of total production.
Again, we’ve only hired one worker so we divide that increase of 12 by 1 to give us
a marginal physical product of 1.
We continue this calculation all the way through to the end and you’ll notice that the marginal
physical product is decreasing.
This is exactly what we would expect given the law of diminishing marginal returns.
The final column contains the price of the product.
This is constant at $20, indicating that this firm is operating in a perfectly competitive
product market.
This won’t always be true in all problems, so bear that in mind.
Now that we’ve completed step 1, we can now move on to calculating marginal revenue
product and contribution.
Let’s use the information we just calculated to determine MRP and contribution.
Columns 1-4 are identical to what we’ve just seen.
Now I’ve added columns 5, 6 and 7.
Column 6 contains the wage rate per worker, which is constant at $120.
This wage rate is set in the perfectly competitive labour market.
Later on in this unit, you’ll see how wages are determined in perfectly competitive markets.
For now, let’s work with the constant wage rate of $120 and later we’ll look at why
it remains the same.
In column 5 we have marginal revenue product.
Marginal revenue product is the additional amount of revenue earned by a firm after employing
an additional unit of labour.
We can calculate that by taking the marginal physical product and multiplying it by the
product price.
In this case, we already have that information so now we will just calculate each one.
For the first worker, we multiply 6 times $20 for a marginal revenue product of $120.
Once the second worker has been employed, our marginal revenue product is equal to 12
times $20, which is $240.
We continue this through the sixth worker whose MRP is equal to $100.
In the final column we have our contribution.
That is essentially the amount over the wage rate the worker is contributing to the firm’s
profit.
We’ll calculate that as we seek out the firm’s optimal level of employment.
The optimal level of employment for a profit maximizing firm is relatively simple to deduce
logically and according to economic theory.
The firm will employ workers as long as the worker’s marginal revenue product exceeds
their wage rate.
Once MRP is equal to the wage rate, the employer will stop hiring more workers.
If the wage rate is above the MRP of the worker, then the firm will not employ them.
Let’s check each instance one by one.
In this case the MRP is equal to the wage rate, but we look for MRP to equal the wage
rate when MRP is falling, not rising.
MRP rises to $240 here and the wage rate is $120.
This gives the second worker a contribution of $120.
The third worker generates an additional $160 in revenue and costs $120.
Thus, their contribution is $40.
The fourth worker adds an additional $140 and costs $120, bringing their total contribution
to $20.
As MRP is falling, we know we are approaching our equilibrium level of employment.
The fifth worker generates MRP of $120 and has a wage rate of $120.
With a contribution of $0, we have reached our equilibrium level of employment for this
firm.
You can probably anticipate what will happen next as the marginal revenue product of the
sixth worker is lower than the wage rate.
If the firm hires one more worker, they will lose $20 by employing them.
Since the wage rate is greater than the additional revenue gained by employing this worker, the
firm will not hire the sixth unit of labour.
This topic is a little challenging so I’m providing an example for you to try.
Stop the video here and try to complete this table.
Calculate total revenue product and marginal revenue product.
Pause the video now and I’ll share the answers shortly.
Your answers should match the table here.
Check your work against the answers given.
If you’ve made a mistake or yours doesn’t quite match up, leave a comment and let’s
see if we can solve the problem together.
Using this information, we’re now going to try and determine the amount of workers
the firm would hire at different wage rates.
Consider how many workers the firm would hire if the weekly wage for worker is $50, $30
and $25?
Pause the video here to answer the questions by yourself before continuing.
You should have selected the following answers.
If you weren’t able to correctly answer these questions, explain why below and we
can work on the answer together.
All of this work brings us here.
The MRP represents the firm’s demand curve for labour.
Essentially, the maximum amount a firm is willing to pay an employee is equal to the
additional revenue that worker generates.
It is fairly logical for the profit maximizing firm.
As the wage rate falls from W1 to W2, there is an increase in the quantity demanded of
labour by the firm, from QL1 to QL2.
Remember, in the short-run, the firm faces diminishing marginal returns of labour and
thus will only employ more labour at lower wage rates.
Just like the demand curve for a product, the marginal revenue product curve, or the
demand for labour, shows us the maximum price a firm is willing to pay to employ an additional
unit of labour.
You may also see the marginal revenue product for labour drawn like this.
There’s no need to be confused, they are the same thing.
The firm’s demand curve for labour can also shift.
There are two main reasons why marginal revenue product may change given that marginal revenue
product equals marginal physical product x the price of the
product.
The only way to change MRP is to change either the level of worker productivity or the price
of the product.
Suppose the productivity of each worker rises.
What do you think will happen to the demand for labour?
Remember we stated this before.
Let’s see what happens when we increase worker productivity by double.
After productivity doubles, each worker is producing twice as much in the same amount
of time.
Assuming the firm can sell all that it produces, the TRP also doubles, as does MRP.
If you’d like to see why, pause the video and attempt the calculations on your own.
Similarly, if we double the price and leave productivity at its original level we will
see that TRP and MRP also double.
The end result is the same.
Thus an increase in the physical productivity of labour or the price of the product will
cause the MRP, or the firm’s demand for labour to increase and shift rightwards.
Conversely, decreasing the physical productivity of labour or the price of the product will
cause the MRP, or demand for labour to decrease and shift to the left.
By this point, you should have a better understanding of how to calculate marginal revenue product
and its implications for the quantity of labour employed by a firm.
Additionally, you should be able to analyse changes in MRP and understand how they affect
the demand for labour.
If you have any questions or comments, leave them below and let’s try to work through
them together.