Question

Suppose the \(M P C\) is \(.90\) and the \(M P I\) is \(.10\). If government expenditures go up \(\$ 100\) billion while taxes fall \(\$ 10\) billion, what happens to the equilibrium level of real GDP? Use the following equations for exercises 16-18. $$ \begin{aligned} C &=\$ 100+.8 Y \\ I &=\$ 200 \\ G &=\$ 250 \\ X &=\$ 100-.2 Y \end{aligned} $$

Short answer

Answer: The new equilibrium level of real GDP is $7,600 billion.

Step-by-step solution

Update the Consumption and Imports Functions

Since MPC is 0.9 and MPI is 0.1, the new consumption function will be: $$ C = \$ 100 + 0.9 Y $$ Additionally, since taxes fall by $10 billion, the disposable income will increase, leading to an increase in consumption. Thus, the new consumption function will be: $$ C = \$ 110 + 0.9 Y $$ The new imports function (M) will be: $$ M = 0.1 Y $$

Update the Government Expenditures

The government expenditures increased by \(100\) billion, so the new government spending will be: $$ G = \$ 350 $$

Substitute the Equations into the Aggregate Expenditure Equation

Now, we will substitute the new consumption function, investment function, new government expenditures, and exports into the Aggregate Expenditure Equation: $$ Y = (\$110+0.9Y)+(\$200)+(\$350)+(\$100-0.1Y) $$

Simplify and Solve for the New Equilibrium Level of Real GDP

By simplifying and solving for \(Y\), we can find the new equilibrium level of real GDP: $$ Y = 0.9Y + 0.1Y + \$760 $$ $$ 0.1Y = \$760 $$ $$ Y = \$7,600 $$ The new equilibrium level of real GDP is \(\$7,600\) billion.

Key concepts

Marginal Propensity to Consume

Understanding the Marginal Propensity to Consume (MPC) is crucial for grasping how changes in consumers' income levels affect their spending habits and, by extension, the wider economy. The MPC is the ratio of the change in consumption to the change in disposable income. In other words, it measures the proportion of additional income that households are likely to spend on consumption rather than save. For example, if the MPC is 0.9, it means that for every extra dollar of income, people will spend 90 cents and save the remaining 10 cents.

When the MPC is high, as in the given exercise, an increase in income leads to a significant rise in consumption, which can have a powerful effect on aggregate demand and real GDP. Conversely, a lower MPC means that any change in income results in a smaller change in consumption, dampening its impact on the economy. The MPC is a key component in the multiplier effect, which we see when government expenditures increase, causing a multiplied increase in the equilibrium level of GDP due to the cyclical nature of money spent and re-spent in the economy.

Government Expenditures

Government expenditures are a fundamental component of a country's overall economic activity. These expenditures include all spending by government bodies and can be categorized into various types, such as infrastructure, healthcare, education, and defense. Government spending can directly increase aggregate demand, as it represents immediate consumption of goods and services, injecting money into the economy.

In our exercise, when government expenditures rise by \(100 billion, this acts as an injection into the economy, increasing the aggregate expenditure. This action, combined with a \)10 billion tax cut, which effectively raises households' disposable income, spurs a greater level of consumption. Since every dollar spent by the government can lead to a greater than one dollar increase in real GDP—owing to the multiplier effect—the impact of changes in government expenditures on economic activity can be potent, particularly when the MPC is high. An understanding of the way government spending influences economic output is essential for students to appreciate how fiscal policy can be used to steer an economy toward desired outcomes.

Aggregate Expenditure Model

The Aggregate Expenditure (AE) model is a cornerstone of macroeconomic analysis that helps clarify how spending in an economy influences the level of real GDP in the short run. The AE model is the total amount of spending in the economy and is made up of four components: consumption (C), investment (I), government spending (G), and net exports (X - M).

The equilibrium level of real GDP occurs where the aggregate expenditure equals the actual GDP, meaning that all goods and services produced are purchased, with no excess inventory. As depicted in the exercise, an increase in government spending and a decrease in taxes directly affect the aggregate expenditure. The AE model equation is adjusted by substituting in the updated values for consumption, investment, and government spending, which then allows us to solve for the new GDP equilibrium. By studying this model, students can see how various factors, including changes in government policy, can affect the overall level of economic activity and analyze the potential magnitude of these changes on the equilibrium GDP.