Fiscal Policy: A Numerical Example

According to the Keynesian diagnosis, unemployment is a result of inadequate aggregate demand. It follows that government can offset the inadequate aggregate demand by increasing its own purchases of goods and services, which are a component of aggregate demand. The government purchases will have a multiplier effect, increasing private spending and production by as much or more than the government's own spending. We might say the Keynesian diagnosis is complemented by a Keynesian prescription for economies suffering from recession: more government purchases. As usual, we will illustrate the reasoning with a numerical example. For this example, assume:

1. C = 250 + 0.7*Y

2. G = 250

3. I = 1000

Thus, autonomous spending is 250+250+1000=1500. As before, the multiplier is

= 3.333.

Equilibrium income is

3.333*1500 = 5000.

But (let us suppose) the government determines that there is about 16% unemployment. On this basis, they calculate that the economy would be at "full employment" if production were increased to 6000. The government proposes to do this by increasing government purchases above its present level of 250. How much new government purchases will be necessary to reach the target?

It will be less than 1000, since the increase in government purchases will have a multiplier effect. We'll have to do a bit of algebra to figure it out. Let X be (as usual!) the unknown increase in government purchases. Using the multiplier approach the increase in equilibrium income will be

= X*3.333.

We want the increase in equilibrium to be 1000, to get total production up to 6000; so we have

X*3.333=1000

Solving for X, the unknown, we get

X=1000/3.333 = 300

So, the government should increase its spending by 300 in order to get equilibrium income up to the target level of 6000.

Let's check the answer. Government purchases is up from 250 to 250+300 = 550. Autonomous spending is 250+550+1000=1800. Equilibrium income is 1800*3.333. (When I got out my calculator to make sure -- I'm not really that good at doing algebra in my head -- I got 5999.4. That's because the multiplier of 3.333... was rounded off).

In the Simple Keynesian Model economy, the government can fine-tune its spending to get the equilibrium income it believes corresponds to full employment. Here is the way it looks in a diagram:

The Graphic View