No Such Thing as a Free Lunch: Principles of Economics (Part 113)

“A democracy cannot exist as a permanent form of government. It can only exist until the voters discover that they can vote themselves largesse from the public treasury. From that moment on, the majority always votes for the candidates promising the most benefits from the public treasury with the result that a democracy always collapses over loose fiscal policy, always followed by a dictatorship. The average age of the world's greatest civilizations has been 200 years. These nations have progressed through this sequence: From bondage to spiritual faith; From spiritual faith to great courage; From courage to liberty; From liberty to abundance; From abundance to selfishness; From selfishness to apathy; From apathy to dependence; From dependence back into bondage.”

― Alexander Fraser Tytler

The Government and Fiscal Policy

(Part B)

by

Charles Lamson

Equilibrium Output: Y = C + I + G

We know from the last several posts that equilibrium occurs where Y = AE---that is, where aggregate output equals planned aggregate expenditure. Remember that planned aggregate expenditure in an economy with a government is AE = C + I + G, so the equilibrium condition is:

equilibrium condition: Y = C + I + G

The equilibrium analysis in the last several posts apply here also. If output (Y) exceeds planned aggregate expenditure (C + I + G), there will be an unplanned increase in inventories---actual investment will exceed planned investment. Conversely, if C + I + G exceeds Y, there will be an unplanned decrease in inventories.

An example will illustrate the government's effect on the macro economy and the equilibrium condition. First, our consumption function, C = 100 + .75Y (introduced in part 108) before we introduced the government sector, now becomes

C = 100 + 75(Y - T)

Second, we assume that the government is currently purchasing $100 billion of goods and services and collecting net taxes (T) of $100 billion. In other words, the government is running a balanced budget, financing all of its spending with taxes. Third, we assume that planned investment (I) is $100 billion.

Table 1 calculates planned aggregate expenditure at several levels of disposable income. For example, at Y = 500, disposable income is Y - T, or 400. Therefore, C = 100 + .75(400) = 400. Assuming that I is fixed at 100, and assuming that G is fixed at 100, planned aggregate expenditure is 600(C + I + G = 400 + 100 + 100). Because output (Y) is only five hundred, planned spending is greater than output by 100. As a result, there is an unplanned inventory decrease of 100, giving firms an incentive to raise output. Thus, output of 500 is below equilibrium.

In Figure 2 we derive the same equilibrium level of output graphically. First, the consumption function is drawn, taking into account net taxes of 100. The old function was C = 100 + .75Y. The new function is C = 100 + .75 (Y - T) or C = 100 + .75(Y - 100), rewritten as C = 100 + .75y - 75, or C = 25 + .75Y. For example, consumption at an income of zero is 25 (C = 25 + .75Y = 25 + .75(0) = 25). The marginal propensity to consume has not changed---we assume it remains .75. Note that the consumption function in Figure 2 plots the points in columns 1 and 4 of Table 1.

Planned aggregate expenditure, recall, adds planned investment to consumption. Now, in addition to 100 in investment, we have government purchases of 100. Because I and G are constant at all levels of income, we add I + G = 200 consumption at every level of income. The result is the new payee curve. This curve is just a plot of the points in columns 1 and 8 of Table 1. The 45-degree line helps us find the equilibrium level of real output, which, we already know, is 900. If you examine any level of output above or below 900, you will find this equilibrium. Look, for example, at Y = 500 on the graph. At this level, planned aggregate expenditure is 600 but output is only 500. Inventories will fall below what was planned, and firms will have an incentive to increase output.

The Leakages/Injections Approach to Equilibrium As in the last several posts, we can also examine equilibrium using the leakages/injections approach. Look at the circular flow of income in Figure 1. The government takes out net taxes (T) from the flow of income---a leakage---and households save (S) some of their income---also a leakage from the flow of income. The planned spending injections are government purchases (G) and planned investment (I). If leakages (S + T) equal planned injections (I + G), there is equilibrium:

leakages/injections approach to equilibrium: S + T = I + G

To derive this, we know that in equilibrium, aggregate output (income) (Y) equals planned aggregate expenditure (AE). By definition, AE equals C + I + G, and by definition Y equals C + S + T. Therefore, at equilibrium:

C + S + T = C + I + G

Subtracting C from both sides leaves:

S + T = I + G

Note that equilibrium does not require that G = T (a balanced government budget) or that S = I. It is only necessary that the sum of S and T equals the sum of I and G.

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 456-458* 

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