Economia

Any A-Level economics student can probably tell you that the marginal propensity to consume (MPC) is the proportion of a rise in national income that is consumed (provided that they’ve learnt the topic, of course). But ask them to show this mathemathically and you’ll probably get blank stares. This shouldn’t be a surprise given the lack of mathematics weaved into pre-university economics courses, where theory is given primary focus.

But that doesn’t mean that your O-Level calculus course (yes, that’s all you’ll need) should go wasted. It really isn’t difficult to mathematically derive the MPC from a consumption function. So, let’s try it.

1. Consider a simple consumption function of: C = 100 + 0.7Y, where C = Consumption and Y = Income.
2. Remember that in mathematics-speak, the MPC can be considered as the rate of change of consumption with respect to income. So, this means that the MPC can be found be differentiating the consumption function.
3. Thus, formula-wise, MPC = dC/dY.
4. Using the formula on the function in (1), you will get MPC = 0.7.

Yeap, that’s it. Simplistic perhaps, but what do you expect from something this simple?