# Stock and Flow variables

Both stock and flows are variables. Generally, most of the economic variables that are studied are categorized either as stock or flow variables. Both are quantities that may increase or decrease over time. However, there is a difference between them. Stock variables are those which are measured at a point of time. Flow variables are those which are measured in a period of time. A period is nothing but the difference between two points of time.

Let’s try to understand these concepts in detail with few examples.

## Stock variables

A stock is measured at one specific time, and represents a quantity existing at that point in time (say, March 31, 2004), which may have accumulated in the past. A stock (or “level variable”) in this broader sense is some entity that is accumulated over time by inflows and/or depleted by outflows. Stocks can only be changed via flows. Mathematically a stock can be seen as an accumulation or integration of flows over time, with outflows subtracting from the stock. Stocks typically have a certain value at each moment of time – e.g. the number of population at a certain moment, or the quantity of water in a reservoir.

### Examples of Stock Variables

1. Bank Account Balance

• Definition: The amount of money you have in your bank account at a specific moment.
• Example: If you have \$5,000 in your bank account today, that \$5,000 is a stock variable because it represents the accumulated balance at that particular point in time.

2. Population of a City

• Definition: The total number of people living in a city at a specific point in time.
• Example: The population of New York City on January 1st, 2024, is a stock variable because it measures the accumulated number of residents at that particular date.]

3. Inventory of Goods in a Warehouse

• Definition: The total quantity of goods stored in a warehouse at a specific moment.
• Example: If a warehouse currently holds 1,000 units of a particular product, that 1,000 units is a stock variable because it reflects the accumulated inventory at that moment.

## Flow variables

A flow variable is measured over an interval of time. Therefore, a flow would be measured per unit of time (say a year). Flow is roughly analogous to rate or speed in this sense. A flow (or “rate”) changes a stock over time. Usually we can clearly distinguish inflows (adding to the stock) and outflows (subtracting from the stock). Flows typically are measured over a certain interval of time – e.g., the number of births over a day or month.

### Examples of Flow Variables

1. Income

• Definition: The amount of money earned over a period of time, such as monthly or annually.
• Example: Your monthly salary of \$3,000 is a flow variable because it represents the income you receive over a specific period (one month).

2. Birth Rate

• Definition: The number of births per thousand people in a population per year.
• Example: A city with a birth rate of 15 births per 1,000 people per year has a flow variable describing the rate at which the population increases due to births.

3. Carbon Emissions

• Definition: The amount of carbon dioxide released into the atmosphere over a period of time, such as annually.
• Example: A country emitting 500 million tons of carbon dioxide per year has a flow variable describing the rate of carbon emissions over that period.

## Relationship between Stock and Flow Variables

It is important to note that often stock and flows are related. This is because a flow is actually the change in the stock.

• Savings (Stock) and Income (Flow)
• Example: If your savings account has \$5,000 (stock), and you deposit \$1,000 (flow) each month from your income (flow), your savings increase over time due to the accumulation of monthly deposits (flow).
• Population (Stock) and Birth Rate (Flow)
• Example: A city with a population of 1,000,000 (stock) experiences a birth rate of 20 births per 1,000 people per year (flow). Over time, the population grows as births exceed deaths (flow).

## Difference between Stock and FLow variables

 Distinctive Characteristics Stock Flow Definition It relates to the values of any variables at a certain point in time. It represents the values of the variables throughout a specific time period. Dimensions of time It does not have a temporal dimension. Flow is a notion with a temporal dimension. Nature It is of a static character. It has a dynamic character. Indicates The amount of any variable at any certain point during time is represented by stock. Flow denotes average rate of any variable at any given point during time. Reflection The status of overall economy at any given period is represented here. The changes within economic factors are displayed here over a period of time.

Understanding these concepts helps in analyzing how quantities change over time in various contexts, whether it’s financial, demographic, environmental, or industrial. In essence, stock and flow variables provide a structured way to analyze the dynamics of systems, whether economic, ecological, or social, by distinguishing between accumulated quantities and the rates at which they change. This distinction is critical for understanding causality, making predictions, and formulating effective strategies in a wide range of fields.

Stock and Flow variables
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