# Derive consumption function from saving function with proper explanation.

Derivation of consumption from saving function can be explained using the following diagram.

In the given diagram, the upper panel shows saving function, that is $S=\overline{)S}+sY$, where $\overline{)S}$ indicates savings at zero level of income, which is equal to $-\overline{)C}$, that is consumption at zero level of income. This is because at zero level of income, the consumer uses his savings for autonomous consumption. This determines point C, the starting point of consumption function.

Now, when savings are zero, Y= C+S --> Y = C+0 --> C=Y. This is because at zero level of savings, the entire income of consumer is used in consumption. The points A( where Y=C) & B (where S=0) depict break-even point of the consumer.

Starting from point C and passing through point A, consumption function can be derived as a straight line in the lower panel.

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