The Product or Value Added Method

2.2.1 The Product or Value Added Method

The Core Problem: Why We Cannot Simply Add Up All Outputs

When we want to measure the total value of goods and services produced in an economy over a year, the most natural thought is to collect the value of everything every firm produces and add it up. But this straightforward approach leads to a serious error.

Consider a simple economy with only two kinds of producers: farmers (who grow wheat) and bakers (who make bread). The farmers grow wheat using only human labour — no other inputs. They sell some of this wheat to the bakers, who use it as their only raw material to produce bread.

Suppose in a year the farmers produce wheat worth Rs 100. They sell Rs 50 worth of this wheat to the bakers. The bakers use all of that wheat during the year and produce bread worth Rs 200.

If we naively add the value of production of both sectors, we get:

Rs 100 (farmers) + Rs 200 (bakers) = Rs 300

But this is wrong. The farmers' entire Rs 100 is genuinely their contribution — they used no purchased inputs. The bakers, however, bought Rs 50 worth of wheat to make their bread. The Rs 200 worth of bread is not entirely their own creation; part of that value came from the wheat they purchased.

Double Counting

If we add Rs 100 and Rs 200, the Rs 50 worth of wheat gets counted twice. First, it appears as part of the farmers' output. Second, it appears again as the imputed value of wheat inside the bread the bakers produced. This is the mistake of double counting.

To avoid it, we must subtract the value of the wheat the bakers bought from other firms. The net contribution of the bakers is:

Rs 200 – Rs 50 = Rs 150

So the true aggregate value of goods produced in this economy is:

Rs 100 (farmers' net contribution) + Rs 150 (bakers' net contribution) = Rs 250

Value Added Defined

The term used for the net contribution made by a firm is its value added.

The raw materials a firm buys from another firm and completely uses up in production are called intermediate goods. Therefore:

The value added of a firm is distributed among its four factors of production: labour, capital, entrepreneurship, and land. This means the wages, interest, profits, and rents paid out by the firm must add up exactly to its value added.

Value added is a flow variable — it is measured over a period of time (typically a year).

The Wheat-Bread Example in Table Form

The textbook presents this example as Table 2.1:

All values are expressed in money terms, evaluated at market prices.

Extending the Chain of Production

The same logic applies when we add more players. Suppose the farmer uses fertilisers or pesticides to grow wheat. The value of those inputs must be deducted from the value of the farmer's output. Or suppose the bakers sell their bread to a restaurant. The restaurant's value added would be calculated by subtracting the value of the bread (its intermediate good) from the value of its own output.

Gross Value Added vs Net Value Added

We have already encountered the concept of depreciation, also called consumption of fixed capital. Capital used in production undergoes wear and tear, so the producer must undertake replacement investment to keep the value of capital constant. Replacement investment equals depreciation.

If we include depreciation in value added, we get Gross Value Added (GVA). If we deduct depreciation from gross value added, we obtain Net Value Added (NVA). Net value added excludes the wear and tear that capital has undergone.

Numerical example from the textbook: A firm produces Rs 100 worth of goods per year. It uses Rs 20 worth of intermediate goods and experiences Rs 10 worth of capital consumption (depreciation).

Gross value added = Rs 100 – Rs 20 = Rs 80 per year

Net value added = Rs 100 – Rs 20 – Rs 10 = Rs 70 per year

The Problem of Unsold Stock: Inventories

When calculating value added, we take the value of a firm's production. But a firm may not sell everything it produces. It may have unsold stock at the end of the year. Conversely, a firm might start the year with some unsold stock from the previous year, produce very little during the year, and meet demand by selling from that initial stock.

Also, a firm buys raw materials from other firms. The part that gets used up is an intermediate good. What about the part that remains unused?

In economics, the stock of unsold finished goods, semi-finished goods, or raw materials that a firm carries from one year to the next is called inventory. Inventory is a stock variable — it is measured at a point in time.

If the value of inventories is higher at the end of the year than at the beginning, inventories have accumulated. If it is lower, inventories have decumulated.

The symbol $\equiv$ stands for identity. Unlike equality ($=$), an identity always holds, no matter what values the variables take. For example, $2 + 2 \equiv 4$ is always true. But $2 \times x = 4$ is only true when $x = 2$ — it is an equation, not an identity.

Since production of the firm $\equiv$ value added + intermediate goods used, we can also write:

Numerical example from the textbook: A firm starts the year with unsold stock worth Rs 100. During the year it produces Rs 1,000 worth of goods and sells Rs 800 worth. The difference between production and sales is Rs 200 — this is the change in inventories. The inventories at the end of the year are:

Rs 100 (initial) + Rs 200 (change) = Rs 300

Notice that change in inventories takes place over a period of time, so it is a flow variable.

Inventories as Investment

Inventories are treated as capital. An addition to the stock of capital of a firm is called investment. Therefore, a change in inventory is treated as investment.

There are three major categories of investment:

1. Inventory investment — the rise in the value of inventories of a firm over a year
2. Fixed business investment — additions to machinery, factory buildings, and equipment employed by firms
3. Residential investment — additions to housing facilities

Planned vs Unplanned Changes in Inventories

Changes in inventories can be either planned or unplanned.

Unplanned accumulation: Suppose a firm produces shirts. It starts the year with an inventory of 100 shirts. It expects to sell 1,000 shirts during the year, so it produces 1,000 shirts, expecting to end the year with 100 shirts in inventory. But sales turn out to be unexpectedly low — only 600 shirts are sold. The firm is left with 400 unsold shirts. It ends the year with 400 + 100 = 500 shirts. The unexpected rise of 400 shirts is an example of unplanned accumulation of inventories.

Unplanned decumulation: If sales had been 1,050 shirts instead of the expected 1,000, the firm would sell all 1,000 shirts it produced plus 50 shirts from its inventory. This unexpected reduction of 50 shirts is unplanned decumulation of inventories.

Planned accumulation: Suppose the firm wants to raise its inventories from 100 shirts to 200 shirts during the year. Expecting sales of 1,000 shirts, it produces 1,000 + 100 = 1,100 shirts. If sales are actually 1,000, the firm ends up with 200 shirts in inventory — exactly what it planned. This is planned accumulation.

Planned decumulation: If the firm wants to reduce inventories from 100 to 25 shirts, it would produce 1,000 – 75 = 925 shirts. It plans to sell 75 shirts out of its initial inventory. If sales are indeed 1,000, the firm ends with the planned 25 shirts. This is planned decumulation.