The Mechanism for Achieving Macroeconomic Equilibrium with the Help of the Keynes Cross

To avoid significant losses from the decline in production, an active state policy is needed to regulate aggregate demand. Therefore, Keynesian economic theory is often called the theory of aggregate demand.

Actual investments include both planned and unplanned investments. The latter are unforeseen changes in investments in inventories (TMZ). These unplanned investments function as a leveling mechanism that aligns actual savings and investments and establishes macroeconomic equilibrium.

Planned expenditures are the amount that households, firms, the government and the outside world plan to spend on goods and services. Real costs differ from planned costs when firms are forced to make unplanned investments in inventories in the face of unexpected changes in sales levels.

The planned flow function E = C + I + G + Xn is depicted graphically as a function of consumption C = a + b (Y – T), which is “shifted” upwards by the value I + G + Xn.

In this case, for the sake of simplicity of analysis, it is assumed that the value of net exports is autonomous from the dynamics of total income Y. Therefore, net exports are fully included in the value of autonomous expenditures (a + I + G + Xn).

The value of autonomous costs will be equal to (a+ I + G + g) taking into account the net export function

where Хn is net exports;

g – autonomous net export;

m’ is the marginal propensity to import;

Y is income.

The marginal propensity to import is the share of the increase in spending on imported goods in any change in income:


where ΔM is the change in import costs;

ΔY is the change in income.

As total income rises, imports increase as consumers and investors increase their spending on both domestic and imported goods. And exports from a given country do not depend directly on the value of its total income Y, but depend on the dynamics of the total income of the country importing these goods and services. Therefore, the relationship between the dynamics of the total income of a given country Y and the dynamics of its net exports Xn is negative, which is fixed by a minus sign in the function of net exports.

Obviously, the line of planned expenditure will cross the line on which the actual and planned expenditures are equal to each other (i.e. line Y = E) at one point A (see Figure 8.12). The above drawing was called the Keynes Cross. On the line Y = E, the equality of actual investment and savings is always observed. At point A, where income is equal to planned expenditures, equality of planned and actual investments and savings is achieved, that is, macroeconomic equilibrium is established.

If the actual output of Y1 exceeds the equilibrium Y0, it means that buyers purchase fewer goods than firms produce, i.e. AD<AS. Unsold products take the form of TMZ, which are increasing. The growth of inventories forces firms to reduce production and employment, which ultimately reduces GNP. Gradually, Y1 is reduced to Y0, that is, income and planned expenses are equalized. Accordingly, an equilibrium of aggregate demand and aggregate supply (i.e., AD = AS) is achieved.

Conversely, if the actual output of Y2 is less than the equilibrium Y0, then this means that firms produce less than buyers are willing to purchase, i.e. AD>AS. Increased demand is met by unplanned drawdowns in firms’ inventories, which creates incentives to increase employment and output. As a result, GNP gradually increases from Y2 to Y0 and the AD = AS equilibrium is reached again.