Question

Suppose in an economy the income from the private sector is $$\$ 1,550$$ million. The government in this country may choose either to levy a \(5 \%\) sales tax or to levy an income tax to finance its expenditures. It balances its budget. What is the National Product of this economy, its National Income, and its Disposable Income under both proposed tax systems?

Short answer

Under the 5% sales tax system, the National Product (NP) can be calculated using the given private sector income and the equation \(1,550 = 0.95 * NP\). Solving for NP, we find that the National Product is \(1,631.58 million\). Since there is no income tax, the Disposable Income is equal to the National Income, which is also \(1,631.58 million\). In the case of the income tax system, the National Product is equal to the private sector income plus government expenditures. We also know that the tax revenue is equal to the income tax rate multiplied by the National Income (NI). By setting up the equations and plugging in the values, it will be possible to determine the values of NP and Disposable Income under this tax system. In conclusion, the National Product, National Income, and Disposable Income under the two tax systems can be calculated using the given information and equations. The 5% sales tax system results in \(1,631.58 million\) for both the National Product and Disposable Income. The income tax system requires further calculations to determine these values.

Step-by-step solution

Understand the terms

National Product: The total value of goods and services produced by a country's residents in a given year. National Income: The sum of all income in the economy, including wages, rents, interest, and profits. Disposable Income: The amount left over after taxes have been deducted, which individuals can spend on consumption or save.

Calculate National Product under Sales Tax

In this tax system, the government levies a 5% sales tax. Since the government balances its budget, the tax revenue from the sales tax equals government expenditures. Let's denote the National Product as NP. The equation can be expressed as: \[NP = private\_sector\_income + government\_expenditures\] Since the sales tax is on the transactions, the private sector receives 95% of the National Product. \[private\_sector\_income = 0.95 * NP\] We know that the private sector income is $1,550 million, so we can find NP. \[1,550 = 0.95 * NP\]

Calculate National Product under Income Tax

Now, let's denote the National Income as NI. For the income tax system, the government's tax revenue is directly taken from the National Income. From the balanced budget, the equation can be expressed as: \[government\_expenditures = tax\_revenue\] We know that the private sector income is $1,550 million. \[NI - tax\_revenue = 1,550\] It's important to note that since it's an income tax, the tax rate will be applied to the National Income to calculate the tax revenue. \[tax\_revenue = income\_tax\_rate * NI\] Now, we need to find the National Product (NP) by plugging the values back into the equation mentioned in step 2. \[NP = private\_sector\_income + government\_expenditures\]

Calculate Disposable Income under both tax systems

Disposable Income can be calculated as National Income minus tax revenue. For the sales tax system: \[disposable\_income = national\_income\] For the income tax system: \[disposable\_income = (1 - income\_tax\_rate) * national\_income\] Now, we have all the information needed to find the values of National Product, National Income, and Disposable Income under both tax systems.

Key concepts

National Product

The National Product is a crucial concept in understanding the overall economic performance of a country. It refers to the total value of all goods and services produced by the residents of a country within a specific time period, typically a year.
In the context of our exercise, calculating the National Product involves understanding how government revenues are generated and how they contribute to the overall economic output.

• Under a sales tax system, the National Product can be calculated by adding the income from the private sector to the government expenditures.
• The private sector receives a percentage of the National Product, and here, it's 95%, suggesting the remaining 5% is the revenue from the sales tax used for government spending.
• To find the National Product, rearrange the equation: \[ \text{NP} = \frac{\text{Private Sector Income}}{0.95} \]Since it's given that the private sector income is $1,550 million, you can calculate the exact National Product value by solving: \[ 1,550 = 0.95 * \text{NP} \]

This careful computation shows the direct impact of tax policy on national income accounting.

Disposable Income

Disposable Income is an important aspect as it indicates the amount of money that individuals have available to spend and save after taxes. It is crucial for understanding consumer behavior and overall economic health.
In our scenario, disposable income is affected differently under the two tax systems, sales tax and income tax.

• For the sales tax, disposable income remains the same as the National Income because sales taxes are applied to transactions rather than directly on income, thus not directly reducing an individual's income.
• However, with an income tax, disposable income is reduced by the amount of the income tax collected. Therefore, to calculate disposable income under income tax:\[ \text{Disposable Income} = \text{National Income} - \text{Tax Revenue} \]
• Alternatively, you can also express this as:\[ \text{Disposable Income} = (1 - \text{Income Tax Rate}) * \text{National Income} \]

Understanding how disposable income varies between these systems helps in comprehending the potential for consumer spending and savings.

Sales Tax vs Income Tax

The decision between imposing a sales tax or an income tax impacts both individuals and the economy as a whole in different ways.
In the given context, the economy has the option to choose between these two tax systems to fund government expenditures while maintaining a balanced budget.

• A sales tax is applied to goods and services during transactions. This means everyone pays the same percentage on their purchases, which can be considered regressive as everyone pays the same rate regardless of income level.
• Under the income tax system, earnings are directly taxed. Taxes collected in this manner can be influenced by the income bracket, providing a more progressive taxation structure where higher earners pay more.
• The choice between these taxes affects disposable income differently, as examined previously. With sales tax, disposable income is not directly reduced, whereas, with income tax, the amount consumers can spend after taxes decreases.

Evaluating the implications of each tax system is vital for policymakers aiming to design equitable and efficient fiscal policies.