Question

An economy has a marginal propensity to consume of \(0.5,\) and \(Y^{*},\) income- expenditure equilibrium GDP, equals \(\$ 500\) billion. Given an autonomous increase in planned investment of \(\$ 10\) billion, show the rounds of increased spending that take place by completing the accompanying table. The first and second rows are filled in for you. In the first row, the increase of planned investment spending of \(\$ 10\) billion raises real GDP and \(Y D\) by \(\$ 10\) billion, leading to an increase in consumer spending of \(\$ 5\) billion \((M P C \times\) change in disposable income) in row \(2,\) raising real GDP and \(Y D\) by a further \(\$ 5\) billion. a. What is the total change in real GDP after the 10 rounds? What is the value of the multiplier? What would you expect the total change in \(Y^{*}\) to be based on the multiplier formula? How do your answers to the first and third questions compare? b. Redo the table starting from round 2 , assuming the marginal propensity to consume is \(0.75 .\) What is the total change in real GDP after 10 rounds? What is the value of the multiplier? As the marginal propensity to consume increases, what happens to the value of the multiplier?

Short answer

Question: Analyze the effects of an increase in investment on real GDP and income distribution, given a marginal propensity to consume (MPC) of 0.5. Calculate the total change in real GDP after 10 rounds of spending, and compare the results to a scenario where the MPC is increased to 0.75. Answer: With an MPC of 0.5, the total change in real GDP after 10 rounds of spending is approximately \(\$20\) billion. When the MPC is increased to 0.75, the total change in real GDP after 10 rounds of spending increases to approximately \(\$37.75\) billion. This indicates that as the marginal propensity to consume increases, the value of the multiplier also increases, leading to a greater total change in real GDP after rounds of spending.

Step-by-step solution

Identify the Given Parameters

In this exercise, we are given the marginal propensity to consume (MPC) of 0.5, income-expenditure equilibrium GDP (\(Y^*\)) of \(\$500\) billion, and an autonomous increase in planned investment of \(\$10\) billion.

Find the Multiplier Formula

The multiplier formula is given by: \(k = \frac{1}{1-MPC}\)

Calculate the Value of the Multiplier

Using the MPC of 0.5, we can find the multiplier: \(k = \frac{1}{1-0.5} = 2\)

Calculate the Rounds of Increased Spending

Using the given investment increase of \(\$10\) billion and the multiplier of 2, we can calculate the increase in real GDP after 10 rounds of spending. Round 1: \(10 * (0.5)^0 = 10\) \\ Round 2: \(10 * (0.5)^1 = 5\) \\ Round 3: \(10 * (0.5)^{2} = 2.5\) \\ Round 4: \(10 * (0.5)^{3} = 1.25\) \\ Round 5: \(10 * (0.5)^{4} = 0.625\) \\ Round 6: \(10 * (0.5)^{5} = 0.3125\) \\ Round 7: \(10 * (0.5)^{6} = 0.15625\) \\ Round 8: \(10 * (0.5)^{7} = 0.078125\) \\ Round 9: \(10 * (0.5)^{8} = 0.0390625\) \\ Round 10: \(10 * (0.5)^{9} = 0.01953125\)

Calculate Total Change in Real GDP

To find the total change in real GDP after 10 rounds, we sum the amounts of the increased spending calculated in Step 4: \(10 + 5 + 2.5 + 1.25 + 0.625 + 0.3125 + 0.15625 + 0.078125 + 0.0390625 + 0.01953125 = 19.98046875\), approximately \(\$20\) billion. To check the agreement of the calculated values with the multiplier formula, we multiply the increase in investment (\(\$10\) billion) by the multiplier (\(2\)): \(10 * 2 = \)\$20$ billion. The answers to the first and third questions match, as the total change in real GDP is approximately \(\$20\) billion in both cases. PART B

Alter the Marginal Propensity to Consume

As per the question, we change the marginal propensity to consume to 0.75.

Calculate the New Multiplier

Using the new MPC of 0.75, we calculate the new multiplier: \(k = \frac{1}{1-0.75} = 4\).

Calculate the Rounds of Increased Spending

Using the new MPC of 0.75 and the new multiplier of 4, we can proceed to calculate the increase in real GDP after 10 rounds of spending, starting from round 2 (since round 1 remains unchanged). Round 1: (unchanged) \(10 * (0.75)^0 = 10\) \\ Round 2: \(10 * (0.75)^1 = 7.5\) \\ Round 3: \(10 * (0.75)^{2} = 5.625\) \\ Round 4: \(10 * (0.75)^{3} = 4.21875\) \\ Round 5: \(10 * (0.75)^{4} = 3.1640625\) \\ Round 6: \(10 * (0.75)^{5} = 2.373046875\) \\ Round 7: \(10 * (0.75)^{6} = 1.77978515625\) \\ Round 8: \(10 * (0.75)^{7} = 1.3348388671875\) \\ Round 9: \(10 * (0.75)^{8} = 1.001129150390625\) \\ Round 10: \(10 * (0.75)^{9} = 0.7508468627929688\)

Calculate the Total Change in Real GDP

Add the amounts from Step 8: \(10 + 7.5 + 5.625 + 4.21875 + 3.1640625 + 2.373046875 + 1.77978515625 + 1.3348388671875 + 1.001129150390625 + 0.7508468627929688 = \$37.747559967\) The total change in real GDP after 10 rounds is approximately \(37.75\) billion.

Analyze the Effects of Changing MPC

Comparing the results of part (a) and part (b), we can see that as the marginal propensity to consume increases, the value of the multiplier (\(k\)) also increases (from \(2\) to \(4\)). This increase in the multiplier leads to a greater total change in real GDP after 10 rounds of spending (\(\$20\) billion to \(37.75\) billion).

Key concepts

Marginal Propensity to Consume

The Marginal Propensity to Consume (MPC) is a key economic metric that reflects the percentage of additional income that households in an economy are likely to spend on consumption rather than saving. Simply put, it measures the tendency to spend rather than save a given increase in income.
The MPC value, which ranges between 0 and 1, is fundamental to understanding consumer behavior and economic spending patterns. For example, if the MPC is 0.5, it implies that for every additional dollar earned, 50 cents is used for consumption while the rest is saved.
The concept of MPC plays a crucial role in calculating the investment multiplier, which indicates how much economic output will be generated from a particular increase in investment. In exercises involving the investment multiplier, MPC helps in understanding the ripple effect of spending throughout the economy.

• The MPC is derived from income-expenditure data.
• It is used to predict changes in consumption due to changes in income.
• Government and policymakers often use it to shape fiscal policies.

Understanding the MPC helps in deciphering consumer confidence levels and can also relate closely to economic growth patterns.

Real GDP

Real GDP, or Real Gross Domestic Product, represents the total value of all goods and services produced in an economy, adjusted for inflation, over a specific period. This adjustment for inflation distinguishes Real GDP from nominal GDP, thereby providing a more accurate reflection of an economy's size and growth.
Real GDP is an essential tool for economists who wish to analyze standard of living over time, make economic comparisons between different years, and develop forecasts for future growth. It accounts for purchases made for individual consumption, business investments, government spending, and net exports.
In the context of investment and the multiplier effect, changes in Real GDP are examined to determine how investments translate into tangible economic output. Maintaining a stable and growing Real GDP is often a central aim of economic policies.

• Real GDP provides a comprehensive measure of economic productivity.
• It excludes inflation effects to ensure consistency over time.
• High Real GDP growth is typically indicative of a prosperous economy.

Understanding Real GDP allows stakeholders to evaluate how effectively an economy can meet the needs of its population.

Income-Expenditure Equilibrium

Income-Expenditure Equilibrium refers to a situation where the total of an economy's output, or GDP, is equal to the aggregate spending by its households, businesses, and government. This balance signifies that the economy is in a state where supply meets demand.
When income aligns with expenditure, we find ourselves in a stable economic environment, where the level of planned investment equals actual savings, and there is neither excess demand nor excess supply. In this context, adjustments in investment or consumer confidence can shift this equilibrium, thus affecting economic stability.
In economic modeling, understanding the income-expenditure equilibrium helps to predict changes that might occur due to varying factors like changes in investment, consumption patterns, or governmental policies. Economic indicators that deviate from this equilibrium may prompt adjustment measures.

• It assures efficient allocation of resources.
• Reflects balanced economic growth.
• Assists in making macroeconomic policy decisions.

Grasping how this equilibrium works aids economists in evaluating the impact of economic interventions and policies on overall growth.

Economic Modeling

Economic Modeling involves the methodical use of mathematical equations and data to represent various aspects or components of the economy. These models aim to simplify complex economic realities to accurately predict and analyze economic behaviors and outcomes.
From assessing the impact of fiscal policies to gauging the effects of changes in consumer confidence, economic models serve as crucial tools for academics, policymakers, and business leaders. They allow users to run simulations and project future economic scenarios based on different variables such as consumer spending habits, tax policies, and international trade.

• Models can predict economic trends and setbacks.
• They are used extensively in policy formulation.
• Provide a quantitative framework for testing economic theories.

While immensely beneficial, interpreting the results of economic models requires an understanding of their assumptions and limitations. They offer a framework to dissect how variables such as the marginal propensity to consume can impact broader economic outcomes.