The savings function derived from the consumption function c=-a+by isa...
Saving function equation. As saving function is co
rollary of consumption function, we can derive the correspondine savine function from consumption function equation, straight C space equals space straight C with bar on top space plus space bY by s
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The savings function derived from the consumption function c=-a+by isa...
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.
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