Question

In an economy with no government and no foreign sectors, autonomous consumer spending is \(\$ 250\) billion, planned investment spending is \(\$ 350\) billion, and the marginal propensity to consume is \(2 / 3\). a. Plot the aggregate consumption function and planned aggregate spending. b. What is unplanned inventory investment when real GDP equals \(\$ 600\) billion? c. What is \(Y^{*}\), income-expenditure equilibrium GDP? d. What is the value of the multiplier? e. If planned investment spending rises to \(\$ 450\) billion, what will be the new \(Y^{*}\) ?

Short answer

In summary, we were able to find the consumption function, calculate planned aggregate spending, calculate unplanned inventory investment, find the income-expenditure equilibrium GDP, and the multiplier. The consumption function is given by \(C = \$250 + (2/3)Y\). The planned aggregate spending is \(PAS = \$600 + (2/3)Y\). The unplanned inventory investment is -\$400 billion. The income-expenditure equilibrium GDP (\(Y^*\)) is \$1800 billion, and the multiplier is 3. If investment spending increases to \$450 billion, the new equilibrium GDP (\(Y^{*'}\)) is \$2700 billion.

Step-by-step solution

Identify the Consumption Function Formula

The Consumption Function (C) is given by the formula: \(C = C_0 + MPC \cdot Y\), where \(C_0\) is autonomous consumer spending, MPC is the marginal propensity to consume, and Y is the real GDP. Step 2: Find the Consumption Function (C)

Plug in the Given Values

Using the given values for autonomous consumer spending (\(C_0 = \$250\) billion), planned investment spending (\(350\) billion), and the marginal propensity to consume (MPC = \(2 / 3\)), we can find the consumption function (C): \(C = \$250 + (2/3)Y\). Step 3: Plot the Aggregate Consumption Function (C)

Draw the Consumption Function Graph

To draw the aggregate consumption function (C) graph, plot the consumption function (\(C = \$250 + (2/3)Y\)) on the vertical axis against real GDP (Y) on the horizontal axis. Step 4: Find Planned Aggregate Spending (PAS)

Identify Planned Aggregate Spending Formula

Planned Aggregate Spending (PAS) is the sum of the consumption function and planned investment spending: \(PAS = C + I\), where I is planned investment spending. Step 5: Calculate Planned Aggregate Spending (PAS)

Plug in the Given Values

Using the consumption function identified in Step 2 and the given planned investment spending value (\(I = \$350\) billion), we can calculate Planned Aggregate Spending (PAS): \(PAS = (\$250 + (2/3)Y) + \$350 = \$600 + (2/3)Y\). Step 6: Plot Planned Aggregate Spending (PAS)

Draw the PAS Graph

To draw the planned aggregate spending (PAS) graph, plot the planned aggregate spending function (\(PAS = \$600 + (2/3)Y\)) on the vertical axis against real GDP (Y) on the horizontal axis. Step 7: Unplanned Inventory Investment

Identify Unplanned Inventory Investment Formula

Unplanned inventory investment occurs when there is a difference between the actual GDP (Y) and Planned Aggregate Spending (PAS), and it can be found using the formula: Unplanned inventory investment = GDP - PAS. Step 8: Calculate Unplanned Inventory Investment

Plug in the Given Values

Given that the real GDP = \(\$600\) billion, we can now find the unplanned inventory investment using the formula: Unplanned inventory investment = \(\$600\) - PAS. PAS = \(\$600 + (2/3)(\$600)\). Unplanned inventory investment = \(\$600 - (\$600 + (2/3)(\$600)) = -\$400\) billion. Step 9: Income-Expenditure Equilibrium GDP (\(Y^*\))

Find Equilibrium Condition

At income-expenditure equilibrium, the total spending (C+I) equals the total output (Y): \(Y^* = C + I\). Step 10: Calculate \(Y^*\)

Solve for Equilibrium GDP

Using the equilibrium condition and the consumption function and investment spending, we can find \(Y^*\): \(Y^* = \$250 + (2/3)Y^* + \$350\). Solve for \(Y^*\) to get \(Y^* = \$1800\). Step 11: Find the Multiplier

Identify the Multiplier Formula

The multiplier is given by the formula: Multiplier = \(\frac{1}{1 - MPC}\). Step 12: Calculate the Multiplier

Plug in the Given Values

Using the given marginal propensity to consume (MPC = \(2 / 3\)), we can find the multiplier: Multiplier = \(\frac{1}{1 - (2/3)} = 3\). Step 13: New \(Y^*\) If Investment Spending Increases

Adjust for New Investment Spending

Given the new planned investment spending (\(I = \$450\) billion), we can calculate the new income-expenditure equilibrium GDP (\(Y^{*'}\)): \(Y^{*'} = C + I' = \$250 + (2/3)Y^{*'} + \$450\). Solve for \(Y^{*'}\) to get \(_{*'} = \$2700\).

Key concepts

Understanding the Consumption Function

The consumption function plays a critical role in understanding how consumer spending behaves in relation to income levels in an economy. This function can be expressed mathematically as:\[C = C_0 + MPC \cdot Y\]where:

• \(C\) is the total consumption.
• \(C_0\) is the autonomous consumer spending.
• \(MPC\) is the marginal propensity to consume, denoting the additional amount consumed when income increases by one unit.
• \(Y\) is the real GDP or income.

Autonomous consumer spending, \(C_0\), is the baseline level of consumption when income is zero. It's the spending necessary for basic survival, regardless of income. Meanwhile, the MPC dictates how much additional consumption occurs with increases in income.
For example, with an \(MPC\) of \(\frac{2}{3}\), individuals will spend \(\frac{2}{3}\) of any additional income. Therefore, if income rises by \\(300, spending will increase by \\)200.
The consumption function is the backbone of Keynesian economics, helping to forecast potential economic outcomes by predicting consumer behavior.

Exploring Marginal Propensity to Consume

Marginal Propensity to Consume (MPC) is a vital economic indicator that shows how much the consumption will increase when income rises by one additional unit. The MPC is calculated as:\[\text{MPC} = \frac{\Delta C}{\Delta Y}\]where:

• \(\Delta C\) is the change in consumption.
• \(\Delta Y\) is the change in income.

An MPC value between 0 and 1 suggests that a portion of additional income will be saved, while the rest will be spent. For example, an MPC of \(\frac{2}{3}\) implies that for every extra dollar earned, \\(0.67 will be spent, and the remaining \\)0.33 will be saved.
This is crucial in understanding consumer behavior and can help determine the effectiveness of economic policies aiming to stimulate spending.
A high MPC indicates a tendency to spend more with increased income, which can spur economic growth. Conversely, a lower MPC suggests more savings, leading to slower short-term economic growth but potentially fostering greater investment in the long run.

Understanding the Multiplier Effect

The multiplier effect is a phenomenon where an initial increase in investment leads to a more significant increase in overall economic output. It is a concept that helps explain how economies reach income-expenditure equilibrium. The multiplier is computed using the formula:\[\text{Multiplier} = \frac{1}{1 - \text{MPC}}\]This formula shows that the size of the multiplier is directly related to the MPC. If people are more inclined to spend additional income, the multiplier will be larger.
For instance, with an MPC of \(\frac{2}{3}\), the multiplier would be \(3\). This means an initial increase in investment by, say, \\(1 results in a \\)3 increase in the overall economic output.
The multiplier effect helps understand the impact of fiscal policies like government spending or tax cuts. It shows why such measures can significantly influence GDP and economic growth. By increasing consumption, investments can multiply across the economy, leading to higher aggregate demand. Understanding this can be highly beneficial for policymakers when designing economic interventions.