Explanation:

1. Consumption Function:
The consumption function is represented by the equation c = -a + bY, where c is consumption, Y is income, a is autonomous consumption, and b is the marginal propensity to consume.

- The term -a represents autonomous consumption, which is the level of consumption that occurs even when income is zero.
- The term bY represents the consumption that is based on income. The marginal propensity to consume (b) determines the proportion of income that is consumed.

2. Savings Function:
The savings function is derived by subtracting consumption (c) from income (Y). Therefore, the savings function can be represented as S = Y - c.

- Substituting the consumption function into the savings function, we get S = Y - (-a + bY).
- Simplifying the equation, we get S = Y + a - bY.
- Combining like terms, we get S = (1 - b)Y + a.

3. Deriving the Savings Function:
To derive the savings function from the given consumption function c = -a:

- Start with the consumption function c = -a.
- Subtract the consumption function from income: Y - c.
- Simplify the equation: Y - (-a).
- Combining like terms, we get Y + a.
- Therefore, the savings function derived from the consumption function c = -a is S = Y + a.

4. Correct Answer:
The correct answer is option 'B' - S = -a(1 - b)Y.

- Comparing the derived savings function S = Y + a with the given options, we can see that option 'B' matches the derived equation.
- In option 'B', we can rewrite -a(1 - b) as -a + ab, which matches the derived equation Y + a.
- Therefore, option 'B' - S = -a(1 - b)Y is the correct answer.