How to Calculate the Marginal Product of Labor and Total Profit

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“This video. We re going to look at a typical example on a short run run production function. Here. We have one column with the number of workers on the total product or output per day.

So for example with no workers. There s no output with one worker that worker produces 26 units of output. Two workers together produces. A combined output of 54 units etc.

So we re going to look at a couple of examples that would come with a table like this and the first one we look at is to calculate the marginal product per worker for this company. So the key thing here is to understand what the words marginal product. Means and also to know the formula so marginal just refers to extra product as we saw on the table refers to output. So what s the extra output per worker.

So once we have an additional worker employed by this company what would does that work or contribute in terms of the extra output that s produced by that company so for example. When no workers are employed. There s no output. When one worker is employed there s 26 units.

So the marginal product or the extra product is 26 units. When two workers are employed in other words. An additional worker that extra worker gives us the difference here between the 54 and a 26. So we re going to use excel in order to calculate this table.

So i m going to copy this table into the excel file. And we re going to calculate the marginal product per worker. So this is the formula you need to use mpl marginal product of labor equals. The change in quantity or output over the change in labor or the number of workers let me call it mp and we cannot type.

It the first figure in the first first cell here so we have to move on because there wasn t any preceding number of units or labor before this so our starting point will be second cell. So i m just going to put in the formula that s represented by a change in quantity over the change in labor. So it s your new output or quantity or product your previous one cause the change in lasts. And we will divide that by the change in labor.

Which is 1 0..

And there we have our 26 units. Something i just already refer to earlier so we do the same so it s the change in output or product. So 54 26 divide that by our change and labor. So again there s only one additional worker or one.

The marginal worker here is 1 2. The one and there we have a change or sorry. There we have marginal product equal to 28. So that additional one worker produced 28 units.

I m going to do the formula calculation again and then i ll scroll down. So we have to change now. Put. 84 your 54 divided up by your change and labor 3 2.

And again that additional worker gives us 30 units. So that s the extra product or extra output or the marginal product. And you just do the same all the way through and you ll notice here that for the fourth worker or wanted that extra worker here all 4 produce 112 units. But i extra worker produces 28.

The extra worker renders 5. Employed you produce it 25 then we have 21 and the seventh worker. Gives an additional 3 units of output. So that s how you calculate the marginal product of labor.

The next question if each worker employed by the company is paid 100 euro per day. So that s your wage. The company s fixed costs are 500 euro per day fixed costs are those costs that do not change irrespective of the number of units that are being produced. So if no unit is being produced your fixed cost is 500 euro and if 1000.

Units are being produced your fixed cost is still 500 euro per day. So you re asked here to calculate the total cost again. You need to know formula for the total cost is your fixed cost plus your variable cost and again variable. Cost is a cost that changes.

When output changes..

So i m just going to put a heading here a fixed cost. It s going to be 500 irrespective of the number of units being produced our variable costs. However change we re told it s 10 you 100 euro. So that s your wage for the labor.

So there s no workers and we multiply that by 100 euro. So there s zero euro. We get to 100 euro here. You re being your variable cost coming from one worker being paid 100 euro.

Your wage for your second. One will be two workers for 100 of each. Which is 200 euro and you probably guess that 300 euro. All the way down to 700 euros.

So. 7. Workers. Each being paid 100 euro each.

So our total cost as a result is your fixed. Cost. Plus. Your variable cost.

So your next. Total cost is. 600 700. Etc.

Okay. So that s our total cost. At each level of output. Your next question assume these products are being sold for 10 euro.

Each you re asked to calculate the total revenue and profit and loss or profit or loss at each output level..

So here. What you need to do or what you need to know is know that formula for total revenue. So total revenue is price by quantity p by q. So now we have a price being 10 euro.

We multiply that by the quantity or the output or the product that we already have so you see in the second column here total product or output per day. So what s your revenue generated. If you re producing these at this level of output. So total revenue is your price times your quantity.

So we have your 10 by your output or quantity and obviously. Ten by zero is going to give you zero your next one. If you multiply this by 10 euro for each of the units of twenty six you get 260 unlike wise multiplying each of these by ten euro. We have your respective total revenues.

We were also asked to calculate profit and profit is your total revenue minus your total cost so. The company here is making a loss because it has fixed costs with no unit of labor being able to produce any output giving no revenue. So you remember fixed costs remain the same irrespective of the amount of output being produced again for your next scenario. Where you have one worker in 26 units.

Being employed your profit is your total new your total cost again. The company is making a loss. But a lower lower loss. So we continue on thus subtracting each total revenue by their respective total costs.

And we have now what s known as a profit for each of the scenarios. Where we have zero to seven workers being employed. So you see the companies making a lot loss initially and then it s making its profit. So we ve just answered that other question okay part d.

How many employees should a firm hire. And what total daily output should they produce in order to maximize profits so i suppose we have to identify where the company is maximizing its profits and then we shall be able to find the daily output and the number employees they should hire so we re just looking for the maximum profit and we just scroll down draw our profit figures and identify your maximum profit here so i m just going to highlight all of this this being our maximum profit. This is the number of units. They should produce and this being the number of workers.

They should hire..

So six workers should be hired to produce 158 units of output per day. Giving a profit of 480 euro for the firm. So even though. 161 units could give you mistakenly you might believe could give you a higher profit.

It s not the case. I m finally one more question to look at when those diminishing returns set in for the firm and explain why it occurs and just a brief note on diminishing returns. When explaining the diminishing returns. We must use marginal product per worker and let s look at the calculation.

We saw earlier so here we have marginal product per worker and if you notice. The first worker. Adds. 26 units for the firm.

The second worker will add 28 units. The third worker will give 34th worker will give 28 and you ll notice that as you employee more workers from 0 to 3 you see returns to labor increasing so each of these workers are producing two units better than the previous worker. However. The fourth worker.

Their returns are lower the fourth worker is only producing 28 units. Compared to the previous worker. The 5th is producing an even lower amount of output at 25. The 6th at 21 and the seventh is producing a dismal three units of output.

So diminishing returns is where marginal product of labor. Is falling as each additional worker is hired. So we re last when does a set in it sets in at the third worker. Because after the third worker returns diminishes.

I hope this really helps and check out other videos that i will be posting on economic theory. And some calculations. ” ..


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