The consumption function is the relationship between the disposable income that the household sector of an economy has and the amount that that sector consumes. It is typically stated as a linear equation and is therefore graphed as a line.
The slope-intercept form of a line can be given as
Y = b + mx
In this form, y is the value along the y-axis, b is the y-intercept, x is the value along the x-axis, and m is the slope of the line. In other words, b tells us where the line crosses the y-axis (when x is equal to 0) and m shows us how steep the line is. These two factors tell us the shape of the line.
The consumption function can be expressed in slope-intercept form. It can be expressed as
Consumption = autonomous consumption + MPC*disposable income.
Therefore, there are two factors that affect the shape of the line on the graph. These are autonomous consumption and MPC.
Autonomous consumption is the amount that people would spend if they had no disposable income. This is the amount that they would simply have to spend on necessities. On the graph, it is the point where the consumption line crosses the y-axis. It is the amount of consumption when disposable income is zero.
The MPC is the marginal propensity to consume. This is the percentage of disposable income that people spend. When people get money, they will spend some of it and save the rest. The MPC tells us how much they will spend and how much they will save. The MPC tells us the slope of the consumption curve. If the MPC is high, the line will rise steeply. If it is lower, the line will be flatter.
So, the consumption function is the mathematical relationship between disposable income and consumption. The shape of the line derived from this relationship is determined by the level of autonomous consumption and by the MPC.