# The Product Or Value Added Method

In product method we calculate the aggregate annual value of goods and services produced (if a year is the unit of time). How to go about doing this? Do we add up the value of all goods and services produced by all the firms in an economy? The following Farmer-Baker example will help us to understand.

Let us suppose that there are only two kinds of producers in the economy. They are the wheat producers (or the farmers) and the bread makers (the bakers). The wheat producers grow wheat and they do not need any input other than human labour. They sell a part of the wheat to the bakers. The bakers do not need any other raw materials besides wheat to produce bread. Let us suppose that in a year the total value of wheat that the farmers have produced is ₹ 100. Out of this they have sold ₹ 50 worth of wheat to the bakers. The bakers have used this amount of wheat completely during the year and have produced ₹ 200 worth of bread. What is the value of total production in the economy? If we follow the simple way of aggregating the values of production of the sectors, we would add ₹ 200 (value of production of the bakers) to ₹ 100 (value of production of farmers). The result will be ₹ 300.

A little reflection will tell us that the value of aggregate production is not ₹ 300. The farmers had produced ₹ 100 worth of wheat for which it did not need assistance of any inputs. Therefore the entire ₹ 100 is rightfully the contribution of the farmers. But the same is not true for the bakers. The bakers had to buy ₹ 50 worth of wheat to produce their bread. The ₹ 200 worth of bread that they have produced is not entirely their own contribution. To calculate the net contribution of the bakers, we need to subtract the value of the wheat that they have bought from the farmers. If we do not do this we shall commit the mistake of ‘double counting’. This is because ₹ 50 worth of wheat will be counted twice. First it will be counted as part of the output produced by the farmers. Second time, it will be counted as the imputed value of wheat in the bread produced by the bakers.

Therefore, the net contribution made by the bakers is, ₹ 200 – ₹ 50 = ₹ 150. Hence, aggregate value of goods produced by this simple economy is ₹ 100 (net contribution by the farmers) + ₹ 150 (net contribution by the bakers) = ₹ 250.

The term that is used to denote the net contribution made by a firm is called its value added. We have seen that the raw materials that a firm buys from another firm which are completely used up in the process of production are called ‘intermediate goods’. Therefore the value added of a firm is, value of production of the firm – value of intermediate goods used by the firm.

The value added of a firm is distributed among its four factors of production, namely, labour, capital, entrepreneurship and land. Therefore wages, interest, profits and rents paid out by the firm must add up to the value added of the firm. Value added is a flow variable.

In the above example, we can think of the market prices of the goods being used to evaluate the different variables, and we can introduce more players in the chain of production in the example and make it more realistic and complicated. For example, the farmer may be using fertilisers or pesticides to produce wheat. The value of these inputs will have to be deducted from the value of output of wheat. Or the bakers may be selling the bread to a restaurant whose value added will have to be calculated by subtracting the value of intermediate goods (bread in this case).

The concept of depreciation, is also known as consumption of fixed capital. Since the capital which is used to carry out production undergoes wear and tear, the producer has to undertake replacement investments to keep the value of capital constant. The replacement investment is same as depreciation of capital.

• If we include depreciation in value added then the measure of value added that we obtain is called Gross Value Added.
• If we deduct the value of depreciation from gross value added we obtain Net Value Added.

Unlike gross value added, net value added does not include wear and tear that capital has undergone. For example, let us say a firm produces ₹ 100 worth of goods per year, ₹ 20 is the value of intermediate goods used by it during the year and ₹ 10 is the value of capital consumption. The gross value added of the firm will be, ₹ 100 – ₹ 20 = ₹ 80 per year. The net value added will be, ₹ 100 – ₹ 20 – ₹ 10 = ₹ 70 per year.

Note : while calculating the value added we are taking the value of production of firm. But a firm may be unable to sell all of its produce. In such a case it will have some unsold stock at the end of the year. Conversely, it may so happen that a firm had some initial unsold stock to begin with. During the year that follows it has produced very little. But it has met the demand in the market by selling from the stock it had at the beginning of the year.

How shall we treat these stocks which a firm may intentionally or unintentionally carry with itself? Also, a firm buys raw materials from other firms. The part of raw material which gets used up is categorised as an intermediate good. What happens to the part which does not get used up?

In economics, the stock of unsold finished goods, or semi-finished goods, or raw materials which a firm carries from one year to the next is called inventory. Inventory is a stock variable. It may have a value at the beginning of the year; it may have a higher value at the end of the year. In such a case inventories have increased (or accumulated). If the value of inventories is less at the end of the year compared to the beginning of the year, inventories have decreased (de-cumulated). We can therefore infer that the change of inventories of a firm during a year production of the firm during the year – sale of the firm during the year.

The sign ‘≡’ stands for identity. Unlike equality (‘=’), an identity always holds irrespective of what variables we have on the left hand and right hand sides of it. For example, we can write 2 + 2 ≡ 4, because this is always true. But we must write 2 × x = 4. This is because two times x equals to 4 for a particular value of x, (namely when x = 2) and not always. We cannot write 2 × x ≡ 4.

Observe that since production of the firm ≡ value added + intermediate goods used by the firm, we get, change of inventories of a firm during a year ≡ value added + intermediate goods used by the firm – sale of the firm during a year.

For example, let us suppose that a firm had an unsold stock worth of ₹ 100 at the beginning of a year. During the year it had produced ₹ 1,000 worth of goods and managed to sell ₹ 800 worth of goods. Therefore the ₹ 200 is the difference between production and sales. This ₹ 200 worth of goods is the change in inventories. This will add to the ₹ 100 worth of inventories the firm started with. Hence the inventories at the end of the year is, ₹ 100 + ₹ 200 = ₹ 300. Notice that change in inventories takes place over a period of time. Therefore it is a flow variable.

Inventories are treated as capital. Addition to the stock of capital of a firm is known as investment. Therefore change in the inventory of a firm is treated as investment. There can be three major categories of investment.

• First is the rise in the value of inventories of a firm over a year which is treated as investment expenditure undertaken by the firm.
• The second category of investment is the fixed business investment, which is defined as the addition to the machinery, factory buildings, and equipments employed by the firms.
• The last category of investment is the residential investment, which refers to the addition of housing facilities.

Change in inventories may be planned or unplanned. In case of an unexpected fall in sales, the firm will have unsold stock of goods which it had not anticipated. Hence there will be unplanned accumulation of inventories. In the opposite case where there is unexpected rise in the sales there will be unplanned de-cumulation of inventories.

This can be illustrated with the help of the following example. Suppose a firm manufactures shirts. It starts the year with an inventory of 100 shirts. During the coming year it expects to sell 1,000 shirts. Hence it produces 1,000 shirts, expecting to keep an inventory of 100 at the end of the year. However, during the year, the sales of shirts turn out to be unexpectedly low. The firm is able to sell only 600 shirts. This means that the firm is left with 400 unsold shirts. The firm ends the year with 400 + 100 = 500 shirts. The unexpected rise of inventories by 400 will be an example of unplanned accumulation of inventories. If, on the other hand, the sales had been more  than 1,000 we would have unplanned de-cumulation of inventories. For example, if the sales had been 1,050, then not only the production of 1,000 shirts will be sold, the firm will have to sell 50 shirts out of the inventory. This 50 unexpected reduction in inventories is an example of unexpected de-cumulation of inventories.

What can be the examples of planned accumulation or de-cumulation of inventories? Suppose the firm wants to raise the inventories from 100 shirts to 200 shirts during the year. Expecting sales of 1,000 shirts during the year (as before), the firm produces 1000 + 100 = 1,100 shirts. If the sales are actually 1,000 shirts, then the firm indeed ends up with a rise of inventories. The new stock of inventories is 200 shirts, which was indeed planned by the firm. This rise is an example of planned accumulation of inventories. On the other hand if the firm had wanted to reduce the inventories from 100 to 25 (say), then it would produce 1000 – 75 = 925 shirts. This is because it plans to sell 75 shirts out of the inventory of 100 shirts it started with (so that the inventory at the end of the year becomes 100 – 75 = 25 shirts, which the firm wants). If the sales indeed turn out to be 1000 as expected by the firm, the firm will be left with the planned, reduced inventory of 25 shirts.

Taking cognizance of change of inventories we may write –

Gross value added of firm i

GVAi ≡ Gross value of the output produced by the firm i (Qi)
Value of intermediate goods used by the firm (Zi)

OR

GVAi ≡ Value of sales by the firm (Vi)
+ Value of change in inventories (Ai)
Value of intermediate goods used by the firm (Zi)

Second equation above has been derived by using: Change in inventories of a firm during a year ≡ Production of the firm during the year – Sale of the firm during the year.

It is worth noting that –

• the sales by the firm includes sales not only to domestic buyers but also to buyers abroad (the latter is termed as exports).
• all the above mentioned variables are flow variables. Generally these are measured on an annual basis. Hence they measure value of the flows per year.

Net value added of the firm i, NVAi ≡ GVAi – Depreciation of the firm i (Di)

If we sum the gross value added of all the firms of the economy in a year, we get a measure of the value of aggregate amount of goods and services produced by the economy in a year (just as we had done in the wheat-bread example). Such an estimate is called Gross Domestic Product (GDP). Thus GDP ≡ Sum total of gross value added of all the firms in the economy.

If there are N firms in the economy, each assigned with a serial number from 1 to N, then
GDP
Sum total of the gross value added of all the firms in the economy
GVA1 + GVA2 + · · · + GVAN

Thus, GVA stands for the sum total of gross value added of all the N firms. The net value added of the i-th firm (NVAi) is the gross value added minus the wear and tear of the capital employed by the firm.

Thus, NVAi ≡ GVAi – Di
Therefore, GVAi ≡ NVAi + Di

This is for the i-th firm. There are N such firms. Therefore the GDP of the entire economy, which is the sum total of the value added of all the N firms, will be the sum total of the net value added and depreciation of the N firms.

This implies that the gross domestic product of the economy is the sum total of the net value added and depreciation of all the firms of the economy. Summation of net value added of all firms is called Net Domestic Product (NDP).

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Bibliography : NCERT – Introductory Macroeconomics

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