Question

$$\begin{array}{cc} \underline{\text { Disposable income after taxes }} & {\underline{\text { Net Savings }}}{\$ 8,000} & 100 \\ \$ 9,000 & 250 \end{array}$$ What is the marginal propensity to consume in the range $$\$ 8,000-\$ 9,000$$ for the family given in the figure?

Short answer

The marginal propensity to consume (MPC) in the range of \(\$8,000-\$9,000\) for the family can be calculated using the following steps: 1. Calculate the change in disposable income: \(\Delta \text {Disposable Income} = \$9,000 - \$8,000 = \$1,000\) 2. Calculate the change in net savings: \(\Delta \text {Net Savings} = 250 - 100 = 150\) 3. Calculate the consumption for each disposable income: - Initial Consumption = \(\$8,000 - 100 = \$7,900\) - Final Consumption = \(\$9,000 - 250 = \$8,750\) 4. Calculate the change in consumption: \(\Delta \text {Consumption} = \$8,750 - \$7,900 = \$850\) 5. Calculate the marginal propensity to consume (MPC): \(\text {MPC} = \frac{\Delta \text {Consumption}}{\Delta \text {Disposable Income}} = \frac{\$850}{\$1,000} = 0.85\) Hence, the marginal propensity to consume for the family in the given range is \(0.85\).

Step-by-step solution

Calculate the change in disposable income

We are given the range of disposable income as \(8,000 to \)9,000. To find the change in disposable income, we can subtract the initial disposable income from the final disposable income:\[ \Delta {\text{Disposable Income}} =\$9,000 - \$8,000\]

Calculate the change in net savings

We are given the net savings corresponding to the disposable incomes. Subtract the initial net savings from the final net savings to find the change in net savings:\[ \Delta {\text{Net Savings}}= 250 - 100\]

Calculate the consumption for each disposable income

We can find consumption by subtracting net savings from the disposable income. The formula for calculating consumption is:\[ {\text{Consumption}}={\text{Disposable Income}}-{\text{Net Savings}}\] For initial disposable income:\[ {\text{Initial Consumption}}=\$ 8,000 - 100\] For final disposable income:\[ {\text{Final Consumption}}=\$ 9,000-250\]

Calculate the change in consumption

Subtract the initial consumption from the final consumption to find the change in consumption:\[ \Delta {\text{Consumption}} = [(\$ 9,000-250)] - [(\$ 8,000-100)]\]

Calculate the marginal propensity to consume (MPC)

The marginal propensity to consume (MPC) is the ratio of change in consumption to the change in disposable income. Calculate the MPC using the formula:\[ {\text{MPC}} = \frac{\Delta {\text{Consumption}}}{\Delta {\text{Disposable Income}}}\] Plug in the values obtained from Steps 1 and 4 into the equation:\[ {\text{MPC}} = \frac{[\$ 9,000-250) - (\$ 8,000-100)]}{(\$ 9,000-\$ 8,000)}\]

Key concepts

Disposable Income

Disposable income is the amount of money that an individual or family has left after paying taxes. It represents the funds available to spend on goods, services, and savings. The equation to find disposable income is quite simple:
Disposable Income = Total Income - Taxes
Understanding disposable income is crucial because it acts as a foundation for personal financial planning. It dictates how much a family can allocate towards essential expenses, leisure activities, or savings. When disposable income increases, options for spending and saving rise proportionately, impacting overall lifestyle choices.

Net Savings

Net savings refer to the amount of money that remains after all expenditures have been subtracted from disposable income. It's essentially the segment of income that individuals choose to set aside rather than spend. You can find net savings using this straightforward formula:
Net Savings = Disposable Income - Consumption
Net savings are significant because they indicate the ability and willingness of individuals to save income for future use, like emergencies or long-term goals. Having healthy savings can provide a financial cushion against unexpected expenses and contribute to the accumulation of wealth over time.

Consumption Calculation

Understanding how to calculate consumption is essential for grasping how individuals allocate their disposable income. Consumption is simply what is spent from disposable income after savings are taken out. We use the following equation to find consumption:
Consumption = Disposable Income - Net Savings
This calculation helps in assessing the spending behavior of individuals. It reveals the proportion of income that is utilized for immediate needs and pleasures, giving insights into economic health and consumption patterns within an economy. By examining consumption levels, economists can predict potential demands for goods and services.

Economic Problem Solving

Economic problem solving involves using data and mathematical equations to understand and address economic behaviors and trends. A key part of economic problem solving is the calculation of marginal propensity to consume (MPC), which measures the change in consumption resulting from a change in income. The formula for calculating MPC is:
MPC = \( \frac{\Delta \text{Consumption}}{\Delta \text{Disposable Income}} \)
By determining the MPC, economists and policymakers can predict how changes in income levels might influence consumer spending habits. This helps in policy formation, forecasting economic growth, and managing inflation effectively. The knowledge of how different variables impact each other plays a critical role in crafting strategies that aim to foster economic stability and growth.