Question

(More difficult) \({ }^{9}\) Consider an economy in which the consumption function takes the following simple algebraic form: $$ C=300+0.75 D I $$ and in which investment (I) is always \(\$ 900\) and net exports are always \(-\$ 100\). Government purchases are fixed at \(\$ 1,300\) and taxes are fixed at \(\$ 1,200 .\) Find the equilibrium level of GDP, and then compare your answer to Table 1 and Figure 2 . (Hint: Remember that disposable income is GDP minus taxes: \(D I=Y-T=Y-1,200\).)

Short answer

Answer: The equilibrium level of GDP in this economy is 2,800 dollars.

Step-by-step solution

Key Definitions and Concepts

In this problem, we have the following components of the economy: - Consumption function (C): C = 300 + 075DI - Disposable income (DI): DI = Y - T = Y - 1200 - Investment (I): 900 dollars - Net exports (NX): -100 dollars - Government purchases (G): 1,300 dollars - Taxes (T): 1,200 dollars The equilibrium level of GDP is the point at which the total demand for goods and services (C + I + G + NX) is equal to the total output (Y) in the economy.

General Equation for Equilibrium GDP

To find the equilibrium level of GDP, we will equate total demand to total output: $$ Y = C + I + G + NX $$

Substitute Given Values

Now, we will substitute the given values in the equation for finding the equilibrium level of GDP: $$ Y = (300 + 0.75 (Y-1200)) + 900 + 1300 - 100 $$

Solve for Equilibrium GDP

Now, we need to solve this equation to find the equilibrium level of GDP (Y): $$ Y = 300 + 0.75 (Y-1200) + 900 + 1300 - 100 $$ $$ Y = 300 + 0.75Y - 900 + 900 + 1300 - 100 $$ $$ Y - 0.75Y = 300 - 900 + 1300 $$ $$ 0.25Y = 700 $$ $$ Y = 2800 $$ Thus, the equilibrium level of GDP in this economy is 2,800 dollars.

Key concepts

Consumption Function

Understanding the consumption function is essential to grasp how consumer expenditure varies with changes in disposable income. In macroeconomics, the consumption function is the relationship between consumption and the disposable income of households. The formula provided in the exercise, \( C = 300 + 0.75DI \), is an example of a consumption function. In this expression, the term '300' represents autonomous consumption, which is the consumption that occurs regardless of income; think of it as the basic level of consumption necessary for survival. The coefficient '0.75' is known as the marginal propensity to consume (MPC), which quantifies the additional consumption resulting from an additional dollar of disposable income.

The higher the MPC, the more likely consumers are to spend their income rather than save it. Students can improve their understanding of how equilibrium GDP is influenced by recognizing that any change in disposable income will affect consumption proportionally, based on the MPC. This understanding can be further enhanced by considering how a change in autonomous consumption or the MPC would affect the overall consumption and thus the equilibrium level of GDP.

For example, if the autonomous consumption increases, for the same level of disposable income, total consumption will be higher. Conversely, if the MPC decreases, it means that for each dollar of disposable income, less is being spent on consumption, which could lead to lower equilibrium GDP, all else being equal.

Disposable Income

Disposable income, often denoted as DI, is a crucial concept in understanding consumer behavior and calculating the equilibrium level of GDP. It's defined as the income that households have available for spending and saving after accounting for income taxes. In the exercise, the disposable income is calculated as \( DI = Y - T \), where 'Y' represents gross domestic product (GDP) and 'T' is the fixed taxes amounting to \(1,200. Thus, \( DI = Y - 1,200 \).

The role of disposable income in the consumption function directly influences the total demand in an economy. As disposable income increases, consumers generally have more money to spend on goods and services, thus raising consumption (C). In the exercise, students should note that a \)1 increase in GDP (before taxes) results in a $0.75 increase in consumption, based on the given MPC of 0.75.

It's beneficial for students to simulate scenarios where the level of taxation changes to see the cascading effects on disposable income, consumption, and ultimately, the equilibrium GDP. A higher tax level, for instance, would reduce disposable income, consumption, and potentially equilibrium GDP in an economy with a similar structure to the one provided.

Macroeconomic Equilibrium

The concept of macroeconomic equilibrium is about balancing aggregate demand with aggregate supply. It's the point in an economy where the quantity of goods produced (GDP) equals the total quantity of goods demanded by households, businesses, government, and foreign buyers. From the perspective of the exercise, equilibrium GDP is calculated by setting total demand \( C + I + G + NX \) equal to total output \( Y \).

Breaking it down, each component of the equation represents a sector of the economy: 'C' for household consumption, 'I' for investment by businesses, 'G' for government purchases, and 'NX' for net exports. At equilibrium, there is no tendency for the economy to change unless an external shock or policy change occurs.

For learners, it is crucial to understand that equilibrium is a theoretical state when all else remains constant. In real economies, fluctuations happen frequently, and equilibrium levels shift accordingly. By studying equilibrium, students can better understand the delicate balance of economic forces, the potential impact of policy changes, such as a change in government spending or taxes, and how these can shift the equilibrium GDP up or down. Additionally, understanding how investment and net exports contribute to overall demand can refine students' perspectives on international trade and economic growth strategies.