Problem 66 - Single Variable Calculus

Question

Suppose that the average wage earner saves \(9 \%\) of his or her take-home pay and spends the other \(91 \%\). What is the estimated impact that a proposed \(\$ 30\) billion tax cut will have on the economy over the long run because of the additional spending generated by the proposed tax cut? Note: This phenomenon in economics is known as the multiplier effect.

Step-by-Step Solution

Answer

The estimated impact that the proposed $30 billion tax cut will have on the economy over the long run because of the additional spending generated by the proposed tax cut is approximately \$303.3 billion due to the multiplier effect.

Step 1: Calculate the total amount saved and spent after tax cut

First, find out the amount of money that will be saved and spent after the tax cut. Since the tax cut is \$30 billion, we will need to find 9% and 91% of this amount. Amount saved: \(0.09 \times 30 \: billion = 2.7 \: billion\) Amount spent: \(0.91 \times 30 \: billion = 27.3 \: billion\)

Step 2: Calculate the spending multiplier

The spending multiplier, also known as the marginal propensity to consume (MPC), is the proportion of extra income that is spent on consumption. In this case, MPC is equal to the percentage spent of the original income, which is 91%. MPC = 0.91

Step 3: Calculate the multiplier effect

The multiplier effect represents the ratio of change in spending on consumption and the change in spending due to an initial change in income. In this case, the multiplier effect (ME) can be calculated using the following formula: ME = \( \frac{1}{1 - MPC} \) ME = \( \frac{1}{1 - 0.91} \) ME = \( \frac{1}{0.09} \) ME = 11.11

Step 4: Calculate the overall increase in spending

Now that we have the multiplier effect, we can calculate the overall increase in spending due to the proposed tax cut by multiplying the initial amount spent with the multiplier effect. Overall increase in spending = Initial amount spent * ME Overall increase in spending = \(27.3 \: billion \times 11.11\) Overall increase in spending = \(303.3 \: billion\) Therefore, the estimated impact that the proposed \$30 billion tax cut will have on the economy over the long run because of the additional spending generated by the proposed tax cut is approximately \$303.3 billion due to the multiplier effect.

Key Concepts

Marginal Propensity to Consume

Understanding the marginal propensity to consume (MPC) is crucial in economics to comprehend how households are likely to spend additional income. The MPC measures the percentage of extra income that individuals spend on goods and services, as opposed to saving it. For instance, if workers receive a pay increase, the MPC indicates what proportion of that pay rise they will use for consumption. The value of MPC is between 0 and 1. If the MPC is 0.91, as shown in the original exercise, it means that for every dollar of increased income, 91 cents are spent.

Knowing the MPC allows economists and policymakers to predict the effect of fiscal policies, like tax cuts, on the overall economy. When people have a high MPC, tax cuts can significantly stimulate demand in the economy because more money is being circulated and spent rather than saved. Conversely, a lower MPC would mean that most additional income gets saved, diminishing the potential stimulative effect on the economy.

Economic Impact of Tax Cuts

Tax cuts can have a broad range of impacts on an economy. Their effectiveness largely depends on factors like current economic conditions, how taxpayers use their additional disposable income, and the overall monetary policy environment. When the government implements a tax cut, as proposed in the exercise, they are essentially leaving more money in the hands of individuals and businesses.

With a high marginal propensity to consume, as indicated by the 91% spending rate, the economic impact of tax cuts can be substantial. Consumers are likely to increase their spending on goods and services, leading to higher demand. This demand stimulates businesses to increase production, potentially leading to job creation and more investment. In a stagnating or contracting economy, such fiscal stimulus can help reinvigorate economic activity. However, it's important to understand that if an economy is already at full capacity, the increase in demand may lead to inflationary pressures instead of boosting growth.

Calculation of Spending Multiplier

The spending multiplier is a fundamental concept in macroeconomics, representing the ratio of a change in output to the initial change in spending that caused it. To calculate the spending multiplier, we use the formula:
\( ME = \frac{1}{1 - MPC} \)
where ME stands for 'Multiplier Effect' and MPC is the 'Marginal Propensity to Consume'. For example, with an MPC of 0.91, the spending multiplier would be:\( \frac{1}{1 - 0.91} = 11.11 \). This means that for every dollar of new spending introduced into the economy (such as through a tax cut), there is an 11.11-dollar increase in overall economic output.

The power of the spending multiplier is seen in its ability to amplify the effects of fiscal policy. In the exercise's context, a \(30 billion tax cut could lead to a \)303.3 billion increase in economic activity over the long run, significantly impacting employment, investment, and economic growth. The accuracy of the spending multiplier model depends on the constancy of the MPC and other economic variables remaining stable post the initial fiscal action.