If all the people of the economy increase the proportion of income they save, the total value of savings in the economy will not increase - it will either decline or remain unchanged. This result is known as...........

The correct option is Paradox of Thrift.

The phenomenon described in the question is a central concept in Keynesian economics known as the Paradox of Thrift. It states that if everyone in an economy tries to save more of their income, it can lead to a decrease in total savings or leave it unchanged, rather than increasing it.

Here is a step-by-step explanation of why this occurs:

1. Reduction in Consumption: Savings and consumption are the two primary uses of disposable income. If households decide to save a higher proportion of their income, they must reduce the proportion they spend on consumption.

2. Decline in Aggregate Demand: Consumption is a major component of aggregate demand. When households spend less, the demand for goods and services in the economy falls.

3. Decrease in Production and Income: In response to lower demand, businesses reduce their production and lay off workers or cut hours. This leads to a decline in national income (GDP).

4. Impact on Total Savings: Total savings in an economy depends on both the rate of saving and the level of income. The relationship can be represented as:

$$S=sY$$

where $S$ represents total savings, $s$ is the marginal propensity to save (the proportion of income saved), and $Y$ is the national income.

While the saving rate ($s$) has increased, the overall national income ($Y$) has fallen. The decrease in income ($Y$) offsets the increase in the saving rate ($s$). As a result, the total value of savings ($S$) does not rise; instead, it either declines or remains unchanged.