Let's pause briefly and assess where we are in our development of the Keynesian model. For starters, we have one curve: the consumption function that slopes upward and its slope is flatter in the aggregate production curve. Do you remember what the slope of the consumption function is? Please jot down an answer now before moving on. The slope of the consumption function is the marginal propensity to consume. Do you remember that key detail? Now, in our closed economy model where we leave out net exports, we also have other curves that, by Keynesian assumptions, are horizontal lines. These are the investment expenditure and the government expenditure functions. So, here is a very key point. If we vertically sum these curves, we arrive at the aggregate expenditures function and, because the investment and government expenditure functions are both horizontal lines, that means that the slope of the aggregate expenditures function will be the same as the consumption function. Let me repeat that. The slope of the aggregate expenditures function has the same slope as the consumption function because the investment expenditures and government expenditures functions are both horizontal lines. Now, this complete aggregate expenditures curve is illustrated in this figure. In this example, the full employment output is $900 billion. However, the economy is stuck at a recessionary output of $800 billion where the aggregate expenditures curve, AE, crosses the 45-degree line of the aggregate production curve, AP. In other words, this figure shows us a recessionary gap, and the beauty of the Keynesian model is that it helps us determine how fiscal policy can, quite precisely, close that recessionary gap. Before I demonstrate that, however, we first need to master one more key concept, that of so-called Keynesian expenditure multiplier or the Keynesian multiplier for short. In this key definition, the Keynesian expenditure multiplier is the number by which a change in aggregate expenditures must be multiplied in order to determine the resulting change in total output. Let me repeat that because it is so important. The Keynesian expenditure multiplier is the number by which a change in aggregate expenditures must be multiplied in order to determine the resulting change in total output. So, for example, if you want to change total output by $200 billion and the Keynesian multiplier is 4, you will need to increase aggregate expenditures by $50 billion. And that's the simple arithmetic the Keynesian fiscal policy is based on. Now, as a general observation, we can say that the Keynesian expenditure multiplier is always greater than 1. This is because income is respent, and not just once, but many times after the initial increase. This figure shows, in very fine detail, how the multiplier process can thereby deepen a recession. Please study this figure carefully before we move on to an explanation. Looking at the figure, here, we see that in Step 1, there is an aggregate demand shock which leads to $100 billion in unsold goods from a reduction in aggregate demand. Now, in Step 2, firms respond by cutting back on employment or wages. This in turn leads, in Step 3, to a reduction in income followed by a reduction in consumption in Step 4. Of course, this reduction in consumption triggers a cutback in sales and further cutbacks in employment and the process continues. Now, here's the key point and it relates directly to the idea of the Keynesian multiplier. The ultimate impact of this initial aggregate demand shock on total spending can be determined by computing the change in income and consumption at each step of the circular flow. So, how do we make what appears to be such a complex calculation in a simple way? Well, in the Keynesian model, it can be easily shown mathematically that the Keynesian expenditure multiplier is simply the reciprocal marginal propensity to save. Let me repeat this key formula and do commit it to memory now. The Keynesian multiplier is calculated simply by dividing 1 by the marginal propensity to save or MPS. Now, take a minute to figure out how we may rewrite this formula for the Keynesian multiplier in terms not of the marginal propensity to save but rather the marginal propensity to consume or MPC. Do give this a try now while we pause the presentation. So, if the Keynesian multiplier is simply 1 divided by the MPS, we can also express the Keynesian multiplier as 1 divided by 1 minus the MPC. Do you see that? If so, let's move on now. But if not, please go back in the presentation and review the math and logic of this. Okay, let's work out some examples to really nail this. So, please calculate the Keynesian multiplier for the following values of the marginal propensity to consume: 0.5, 0.75, 0.8, and 0.9. And, as you do so, please also note the relationship between the calculated multiplier and the size of the MPC itself. In particular, does the multiplier rise as the MPC rises or does it move in the opposite direction? Think about why this relationship may be so and write down a few thoughts now before moving on. This exhibit provides the multiplier for MPCs of 0.5, 0.75, 0.8, and 0.9 while illustrating the first five steps of the multiplier. You can see that the bigger the MPC, and the less people are saving, the larger will be the multiplier and the more effective fiscal policy will be. That should be very intuitive and this is also an observation that is consistent with our earlier discussion of leakages from an economy where savings represent a major leakage. In this case, the more thrifty a society is, the less effective fiscal policy may be. It's a well-known paradox in macroeconomics known as the paradox of thrift. It's the idea that in attempting to save more individually, individuals wind up saving less because their collective savings behavior results in a slower economy, reduced income, and, therefore, lower savings. And with that startling paradox, this module now comes to a close. So, take a well-deserved rest and, when you're ready, let's move on to the next module.