How to Calculate the Equilibrium Level of Income

by Ryan Menezes

The equilibrium income of an economy is the point where consumers' expected spending matches their actual spending. In other words, companies sell as much of their inventories as they plan to. When consumer's aggregate expenditures start to exceed the gross domestic product (GDP), the GDP rises, and when it exceeds aggregate expenditures, the GDP will drop. In either case, the nation's aggregate income will settle at an equilibrium. Calculate this equilibrium using the function that derives consumption from aggregate income.

Step 1

Add the economy's consumption, C, stated in terms of the aggregate income, Y, to the economy's investment, I, which exists independent of Y. For example, if the function determining consumption is C = $200b + 0.8Y, and investment is a constant $400b: $200b + 0.8Y + $400b = $600b + 0.8Y.

Step 2

Substitute this expression for C + I in the formula Y = C + I, which describes aggregate income in terms of consumption and investment. Continuing from the previous step, this produces the equation Y = $600b + 0.8Y.

Step 3

Subtract the statement of income. Continuing with the example from the previous steps, subtract 0.8Y, from both sides of the equation. In this case, this produces "Y - 0.8Y = $600b + 0.8Y - 0.8Y," or "0.2Y = $600b."

Step 4

Divide both sides of the equation by the coefficient of Y, which is in this case 0.2. This produces "0.2Y ÷ 0.2 = $600b ÷ 0.2," or "Y = $3,000b." The economy's equilibrium income is $3,000 billion or $3 trillion.

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