Question

Explain graphically the determination of equilibrium GDP for a private economy through the aggregate expenditures model. Now add government purchases (any amount you choose) to your graph, showing their impact on equilibrium GDP. Finally, add taxation (any amount of lump-sum tax that you choose) to your graph and show its effect on equilibrium GDP. Looking at your graph, determine whether equilibrium GDP has increased, decreased, or stayed the same given the sizes of the government purchases and taxes that you selected.

Short answer

• The equilibrium GDP is shown in the graph below:

The equilibrium GDP is Y, where total spending (consumption and gross investment) intersects the income (GDP) curve.

• The effect of government purchases is shown below:

The inclusion of government expenditure increases the equilibrium level of GDP.

• The effect of lump-sum taxes on the total spending is as follows:

The taxes reduce the equilibrium level of income.

• The final GDP level is higher than the initial equilibrium level of GDP (without government expenditure and taxes); hence, equilibrium GDP increases.

Step-by-step solution

Step 1. Equilibrium GDP for a private economy

A private economy does not have any interaction with foreign economies. Equilibrium GDP for a private economy is the spending generated from consumption and gross investment expenditure that is just enough to purchase the output produced by that economy.

Equilibrium GDP = C + I_g' or

Equilibrium GDP = a + bY + I_g'

The 45-degree line shows the level of output. The above graph shows that the intersection of the output line and total spending curve gives the equilibrium level of income, which is Y.

Step 2. Injection of government purchases into the economy

When the government expenditure is included, the total spending increases as shown below:

According to the above graph, the economy’s total spending has increased because of government expenditure, as shown by the upward shift in the spending graph. The new equilibrium is achieved when this new spending curve intersects the 45-degree line at Y’ income level. This new level of income is greater than Y (without government expenditure).

Hence, government expenditure increases the equilibrium level of income.

Imposition of lump-sum tax in the economy

The lump-sum taxes are imposed on the prices per unit. Therefore, lump-sum taxes reduce the disposable income of the households and, as a result, private consumption decreases.

Due to lump-sum taxes, the total spending curve shifts downward (green line). This decrease in spending results in a fall in the equilibrium level of GDP from Y’ to Y”.

Step 4. Final position of the equilibrium GDP

As per the above graphs, the equilibrium GDP has increased significantly as the total spending curve shifts upward due to the large government expenditure producing new equilibrium GDP Y’.

The taxes reduce the disposable income of households, and, therefore, the private consumption falls, which lowers the economy’s total spending. Reduction in the size of total spending depends upon the size of taxes.

If the curve shift was below the level when only government expenditure was included (red line) and above the initially closed economy spending (dark blue line), the new equilibrium, that is, Y” (intersection of this curve and 45-degree line), will still be higher than the initial level of equilibrium income given by Y. Hence, the final equilibrium GDP has increased.