Question

What is the effect on savings of a tax cut of 10billion? Is this inflationary or deflationary? Assume that the marginal propensity to consume is \(0.85\)

Short answer

The tax cut of 10 billion leads to an increase in disposable income by 10 billion. The marginal propensity to consume (MPC) of 0.85 implies that 85% of this increased disposable income will be spent on consumption, and the remaining 15% will be saved. Therefore, the change in consumption is 8.5 billion, and the change in savings is 1.5 billion. Since the change in consumption is greater than the change in savings, the tax cut is more likely to be inflationary. However, the actual effect on inflation depends on various factors, such as the state of the economy, monetary policy, and the output gap.

Step-by-step solution

Understand the relationship between consumption, savings, and taxes

The relationship between disposable income (income after taxes), consumption, and savings can be represented as follows: Disposable income = Consumption + Savings If taxes decrease, disposable income will increase. The increase in disposable income will be spent on consumption and savings according to the marginal propensity to consume (MPC).

Calculate the change in disposable income due to the tax cut

Given that the tax cut is 10 billion, the change in disposable income can be calculated as: ΔDisposable income = -ΔTaxes = 10 billion

Calculate the change in consumption and savings using the marginal propensity to consume (MPC)

The MPC is the ratio of the change in consumption to the change in disposable income. We are given that the MPC is 0.85, which implies that when disposable income increases, 85% of the increase will be spent on consumption, and the remaining 15% will be spent on savings. ΔConsumption = MPC × ΔDisposable income ΔSavings = (1 - MPC) × ΔDisposable income Plugging in the values, we get: ΔConsumption = 0.85 × 10 billion = 8.5 billion ΔSavings = (1 - 0.85) × 10 billion = 1.5 billion

Determine if the tax cut is inflationary or deflationary

An increase in consumption can lead to an increase in aggregate demand, which may cause inflation (if the economy is operating near full capacity) or reduce unemployment (if there is slack in the economy). On the other hand, an increase in savings can lead to an increase in investments, which might have a positive long-term effect on the growth of the economy. If ΔConsumption is greater than ΔSavings, then there is a higher chance for the tax cut to be inflationary, as people are spending more instead of saving. In this case, since ΔConsumption (8.5 billion) is greater than ΔSavings (1.5 billion), we can determine that the tax cut is more likely to be inflationary. However, the actual effect on inflation depends on the current state of the economy and other factors, such as the monetary policy and the output gap. For example, if the economy operates below full capacity, an increase in private consumption could be beneficial to close the output gap without causing significant inflation.

Key concepts

Tax Cut Effects

A tax cut essentially means the government is reducing the amount of taxes it collects from individuals and businesses. This action has a direct impact on people's disposable income available for spending and saving. When taxes decrease, individuals are left with more money in their pockets, leading to an increase in disposable income. A 10 billion tax cut implies an extra 10 billion added to peoples' disposable income collectively.

Tax cuts can have several effects on the economy:

• Increase in disposable income leading to higher consumer spending.
• Possibility of increased savings if individuals decide to save rather than spend.
• Potential stimulation of economic activity if the increase in consumer spending leads to higher demand for goods and services.

Thus, tax cuts can be a tool used to stimulate economic growth, although the ultimate effect depends on how recipients of the tax cut choose to utilize their increased disposable income.

Disposable Income

Disposable income is the amount of money individuals have available to spend and save after taxes have been deducted from their total income. It serves as a crucial indicator that affects consumption and savings patterns. When taxes are reduced, disposable income rises since less money is taken out for tax purposes, resulting in more income available for consumption and savings.

The increase in disposable income can be calculated using the concept of the change in taxes: \[-\Delta Taxes = \Delta \text{Disposable Income}\]In this scenario, a tax cut of 10 billion leads to an equivalent increase of 10 billion in disposable income. This increase then influences consumption and savings according to the marginal propensity to consume, dictating how much of this new income will be spent or saved.

Consumption and Savings

Understanding consumption and savings involves knowing how individuals allocate their disposable income. The marginal propensity to consume (MPC) is key in this regard; it indicates the proportion of additional income that will be spent rather than saved. For example, with an MPC of 0.85, 85% of any increase in disposable income will be spent on goods and services, while the remaining 15% is saved.

Using the formula: - \( \Delta \text{Consumption} = \text{MPC} \times \Delta \text{Disposable Income} \)- \( \Delta \text{Savings} = (1 - \text{MPC}) \times \Delta \text{Disposable Income} \)These formulas help determine how much of the increased income from a tax cut will go towards consumption and how much will be saved. With our example of a 10 billion tax cut and an MPC of 0.85, consumption increases by 8.5 billion, while savings increase by 1.5 billion. This distribution reflects individuals’ preference patterns between immediate spending and saving for future needs.

Inflationary Impact

The inflationary impact of a tax cut arises primarily through its effect on consumption and overall demand within the economy. When consumption increases significantly because of higher disposable income, it can lead to increased demand for goods and services. If the economy is close to full capacity, such an increase in demand can contribute to inflation, as producers may struggle to meet the higher demand without raising prices.

If \( \Delta \text{Consumption} \) exceeds \( \Delta \text{Savings} \), this suggests that more money enters the economy through spending than is withdrawn via savings. This could lead to inflationary pressures, especially in a tight economy where demand already approaches supply limits.

However, if the economy has slack, meaning it operates under its full capacity, this increase in consumption might actually help in utilizing idle resources, boosting production without necessarily causing high inflation. Thus, the actual inflationary result of a tax cut is complex and contingent on the economy's existing conditions along with other factors such as monetary policies and existing output gaps.