If national income increases from $410 to $430 billion and the marginal propensity to save is 0.25, then savings will increase from $5 to billion.

1. Break Down the Problem

We need to determine the increase in savings resulting from an increase in national income. The given data indicates:

• Initial national income: $Y_1 = 410$ billion
• New national income: $Y_2 = 430$ billion
• Marginal propensity to save (MPS): $MPS = 0.25$

2. Relevant Concepts

The increase in savings can be calculated using the formula: $\Delta S = MPS \times \Delta Y$ where $\Delta S$ is the change in savings and $\Delta Y$ is the change in national income.

3. Analysis and Detail

First, we calculate the change in national income: $\Delta Y = Y_2 - Y_1 = 430 - 410 = 20 \text{ billion}$

Next, we apply the MPS to find the change in savings: $\Delta S = MPS \times \Delta Y = 0.25 \times 20 = 5 \text{ billion}$

4. Verify and Summarize

The increase in savings, as calculated, indicates that savings will increase by $5$ billion. The initial savings were $5$ billion, hence the new savings would be: $\text{New Savings} = \text{Initial Savings} + \Delta S = 5 + 5 = 10 \text{ billion}$

Final Answer

Savings will increase from $5 billion to$10 billion.