Chapter 10: Problem 27

What are the main components of the national savings and investment identity?

Short Answer

Expert verified

The main components of the national savings and investment identity are private savings \((S_{private} = Y - T - C)\), public savings \((S_{public} = T - G)\), and investments (I). The identity is given by the equation \(S_{national} = S_{private} + S_{public} = I\), which can be simplified to \(Y - C - G = I\), stating that the total income in an economy, minus consumption and government spending, is equal to the total investment.

Step by step solution

Define Private Savings

Private savings refers to the amount of income that is saved by households after consumption and taxes. It is the difference between disposable income (income after taxes) and consumption expenditures. In a formula, private savings can be represented as: \[S_{private} = Y - T - C\] Where \(S_{private}\) is private savings, \(Y\) is national income, \(T\) is taxes, and \(C\) is consumption.

Define Public Savings

Public savings is the amount of income that the government saves, which is the difference between tax revenue and government spending. It is expressed as a surplus or deficit, depending on whether or not the government takes in more tax revenue than it spends on goods and services. Public savings can be represented as: \[S_{public} = T - G\] Where \(S_{public}\) is public savings, \(T\) is taxes, and \(G\) is government spending.

Define Investments

Investments, in the context of the national savings and investment identity, refer to the spending done by firms and the government on capital goods such as new factories, equipment, and infrastructure. This type of spending aims to enhance productive capacity and contribute to long-term economic growth. Investment is often represented as "I" in economic identities.

Relate the Components to Form the National Savings and Investment Identity

The national savings and investment identity states that the sum of private savings and public savings is equal to investment. In formula form, it can be represented as: \[S_{national} = S_{private} + S_{public} = I\] Substituting the formulas for private and public savings from steps 1 and 2, we have: \[(Y - T - C) + (T - G) = I\] Simplifying the equation, we get: \[Y - C - G = I\] This equation states that the total income in an economy, minus consumption and government spending, is equal to the total investment. This identity is useful for understanding the relationship between savings, investment, and overall economic performance.

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