Visualizing the Model

Recall, we have two interacting relationships between income and expenditure, namely

2. C = 500 + 0.7*Y

and

Y = C + 1000

We can express these relationships in a table or visualize them as a diagram. Here is a diagram based on the data in the linked table.

Figure 2: Income and Expenditure in the Example

In the figure, income is measured on the horizontal axis and components of expenditure are measured on the vertical axis. The consumption function is shown by the dark green line. Total expenditure (consumption plus investment, in this model) is shown by the lighter green line. The 45 degree line, shown in blue, has been put in to make it easier to compare income (horizontal axis) with expenditure (vertical axis).

Now, let's consider a few possibilities: what if ... ?

What if income is 3000?: An income of 3000 leads people to spend 2600 on consumption. Adding that to 1000 of investment we get a total expenditure of 3600 -- expenditure 600 more than income. (Check the Table if that's not clear on the diagram). But we know that's not right -- income and expenditure have to be the same. So 3000 cannot be an equilibrium income.
What if income is 7000?: An income of 7000 leads people to spend 5400 on consumption. Adding that to 1000 of investment we get a total expenditure of 6400 -- expenditure 600 less than income. That's not right, either -- so 7000 cannot be an equilibrium income.
What if income is 5000?: An income of 5000 leads people to spend 4000 on consumption. Adding that to 1000 of investment we get a total expenditure of 5000 -- eureka! Income equals expenditure, and we have found the equilibrium income for the example.

So we conclude that we have equilibrium where the total expenditure line intersects the 45 degree line, that is, where income equals total expenditure.

Next: More Generally, ...