A2 Economics: Two ways of calculating the equilibrium level of income

Went through an A2 multiple-choice question on calculating the equilibrium level of income with my A2 class. There are two ways that it can be worked out. Here is the question:

In a closed economy with no government C = 30 + 0.8 Y and I = 50, where C is consumption, Y is income and I is investment.

What is the equilibrium level of income?

A 64                B 80              C 250               D 400

Below is the most common way of working the question out:

Y = C + I

Y = 30 + 0.8Y + 50

0.2Y = 80

Y = 400

Here is the other way that you should be able to work out the equilibrium

Remember: Savings = Income – Consumption

S = Y – C

S = Y – (a + cY)

S = Y – a – cY

S = -a + (1-c) Y

So if we put the figures into the equation you get:

50 = -30 + (1-0.8) Y

50 = -30 + 0.2Y

80 = 0.2Y

Y = 400