Which equation depicts the consumption function?

Question

ScanSolve AI Tutor · Accepted Answer

The consumption function illustrates the relationship between consumption and income.

Identify the variables on the axes.
The vertical axis represents "Consumption spent" (C), and the horizontal axis represents "Income" (Y).
Identify the components of the consumption function from the graph.
The consumption function is typically a linear equation of the form $C = a + bY$ .
- The y-intercept represents autonomous consumption, which is the consumption that occurs even when income is zero. In the graph, this is labeled as A. So, $a = A$ .
- The slope of the consumption function represents the marginal propensity to consume (MPC), which is the change in consumption for a given change in income. In the graph, the slope is indicated by the triangle labeled B. This means B represents the MPC. So, $b = B$ .
Substitute these components into the general consumption function equation.
Substituting $a = A$ and $b = B$ into $C = a + bY$ , we get:
$C = A + BY$
Compare with the given options.
- a. $Y = C + AB$ (Incorrect form)
- b. $C = A + B$ (Incorrect, does not include income Y)
- c. $Y = AC + B$ (Incorrect form)
- d. $C = A + BY$ (Matches the derived consumption function)
The equation that depicts the consumption function is $C = A + BY$ .

The final answer is $\boxed{\text{d. C=A+BY}}$ .

Answer