Question

Suppose the marginal propensity to consume out of disposable income is \(0.8\), the marginal tax rate is \(0.5\) and the marginal propensity to import is \(0.8\). Draw a diagram showing the 45 -degree line and the aggregate demand schedule using the diagram in which planned injections equal planned leakages. (a)How does this diagram differ from those earlier in the chapter? (b) What is the size of the multiplier? (c) Illustrate graphically the effect of a shift in aggregate demand using the diagram in which planned injections equal planned leakages.

Short answer

The diagram includes additional leakages such as taxes and imports, impacting the multiplier. The multiplier is 1.11.

Step-by-step solution

Identify Key Variables

Identify the key variables from the problem: Marginal Propensity to Consume (MPC) is 0.8, Marginal Tax Rate is 0.5, and Marginal Propensity to Import is 0.8. These will be used to determine the key economic relationships and multipliers.

Calculate Marginal Propensity to Save

Determine the Marginal Propensity to Save (MPS). Since MPC is 0.8, MPS can be calculated as \( MPS = 1 - MPC = 1 - 0.8 = 0.2 \). This helps to establish a foundation for calculating the multiplier.

Calculate Effective Marginal Propensity to Leak

Calculate the overall leakage from the economy. The marginal leakage rate includes savings, taxes, and imports. It can be calculated as:\[ MPL = MPS + (t \times MPC) + (MPI) = 0.2 + (0.5 \times 0.8) + 0.8 = 1.4 \]

Calculate the Multiplier

Use the calculated marginal leakage rate to find the multiplier using the formula:\[ Multiplier = \frac{1}{MPL - (1 - t)} = \frac{1}{1.4 - (1 - 0.5)} = \frac{1}{0.9} \approx 1.11\]

Draw the 45-Degree Line Diagram

Draw a diagram with real output (or GDP) on the x-axis and aggregate demand on the y-axis. Plot a 45-degree line where output equals aggregate demand. The line represents equilibrium where output equals demand.

Plot Aggregate Demand Schedule

Using the previously calculated multiplier, graph the aggregate demand schedule, showing the relationship between real output and aggregate demand. The aggregate demand curve should be steeper than the 45-degree line, reflecting the multiplier effect.

Compare Diagram to Previous Models

The primary difference from earlier diagrams is the inclusion of the higher leakage due to the high propensity to import and tax rate, reflected in the aggregate demand steepness relative to the 45-degree line.

Illustrate Effect of Shift in Aggregate Demand

Illustrate the effect of a shift in aggregate demand due to an external shock, such as government spending. Show the aggregate demand curve shifting parallel to its original position, indicating a change in planned injections.

Key concepts

Marginal Propensity to Consume (MPC)

Marginal Propensity to Consume, or MPC, is a term used to describe the portion of additional income that a household is likely to spend rather than save. If you receive an extra dollar of income, MPC tells us how much of that dollar you will typically use to buy goods and services, rather than put into savings.

In our problem, MPC is given as 0.8. This means for every extra dollar received, 80 cents would be spent on consumption. The remaining 20 cents would be saved. This ratio is critical in understanding consumer behavior and how income changes translate into changes in consumption patterns.

• MPC is always a number between 0 and 1.
• An MPC closer to 1 indicates higher consumer spending relative to saving.
• A higher MPC leads to a stronger multiplier effect, amplifying economic activities.

Understanding MPC helps economists predict changes in aggregate demand when incomes fluctuate, as consumption is a huge component of overall economic activity.

Marginal Propensity to Save (MPS)

Marginal Propensity to Save (MPS) complements the concept of MPC. MPS is the fraction of additional income that a household saves instead of consuming. Simply put, it is the portion of income not spent when personal income increases.

To calculate MPS, we use the formula:\[ MPS = 1 - MPC \]In the exercise, where MPC is 0.8, the calculation yields:\[ MPS = 1 - 0.8 = 0.2 \]This means that 20% of any additional income changes would typically be saved by households.

• An MPS closer to 1 indicates a tendency to save rather than spend.
• Like MPC, MPS is always a value between 0 and 1.
• A higher MPS can dampen the multiplier effect because less income is circulated back into the economy through spending.

Understanding MPS helps explain how savings behavior affects the economy as a whole, influencing the total savings and investment within a country.

Aggregate Demand

Aggregate Demand (AD) represents the total demand for goods and services within an economy at a given overall price level and in a given time period. It is an essential concept in macroeconomics, as it reflects the total spending by households, businesses, and the government.

Aggregate demand is affected by various factors, including household income, government policies, and external economic conditions. In the exercise, the calculation of the multiplier effect demonstrates how changes in spending can lead to larger changes in aggregate demand.

• AD comprises consumer spending, investment by businesses, government spending, and net exports.
• Understanding AD helps illustrate how economic policies or external changes affect an economy's overall size and performance.
• The aggregate demand curve is plotted in a graph to visually represent the relationship between output and AD.

In the graphical representation, AD is usually plotted against the 45-degree line to show equilibrium points, where the total output equals aggregate demand. When shifts occur in AD due to changes such as government spending or taxes, it highlights the effect on the economy's equilibrium.