The Keynesian model is based on the belief that demand drives the economy and that a shortfall in demand causes recessions and depressions. According to Keynes, if we can find ways to stimulate consumption and other forms of spending, we will solve the problem.
The Marginal Propensity to Consume (MPC)
Keynes discussed the Marginal Propensity to Consume (MPC). The MPC indicates how much of any additional earnings a person consumes. If the government increases spending by $1,000, and if the recipients of the $1,000 decide to spend $800 to purchase goods (let’s say, a used car), then the marginal propensity to consume is 800/1,000, or .8, or 80%.
The Multiplier and the Significance of the Multiplier
This additional spending of $800 turns into additional income for the person who sold the product (the used car). If this person’s MPC is also 80%, then spending (for instance, on a television) increases by 80% of $800 or $640. This creates income for the person who sold the television. This person spends her/his MPC of the $640 on goods, and so forth. If the MPC is 80% for everyone in this economy, then the total amount of additional spending in the entire economy is: $1,000 (the initial government spending) + $800 (on the used car) + $640 (on the television) + … = $5,000.
This mathematical sum ($1,000 +$800 + $640 + ….) is 5 times $1,000, or $5,000. The factor 5 in this equation is called “the multiplier.” The $1,000 is the increase in government spending and is called the “initial spending.” The $5,000 is the increase in total spending in the economy.
The significance of the multiplier, according to Keynes, is that an initial amount of government spending ($1,000 in the above example) can create a total amount of spending in the economy equal to a multiple (5 in the above example) times the initial amount. Keynes argued that this additional spending is needed to increase the “equilibrium national income” (for our purposes, we can think of this as GDP). During a recession, or a recessionary gap, as Keynes called it, an increase in government spending will result in additional rounds of spending and income necessary to eventually reach full employment.
Thus, the equation for computing the total spending change in the economy is
The multiplier * the change in initial spending = change in the economy’s total spending (GDP) In the above example: 
Keynes’s formula for the multiplier is:
Multiplier = 1/(1MPC). In the above example:
Multiplier = 1/(1.8) = 1/(.2) = 5. A greater MPC leads to a larger multiplier. 
The Marginal Propensity to Save (MPS)
The counterpart to Keynes’s Marginal Propensity to Consume is the Marginal Propensity to Save (MPS). Savings is defined as income not consumed. If a person receives additional income of $100 and of that (s)he consumes $80, her/his savings must be $20. The MPC in this example is .80, or 80% and the MPS is .20, or 20%. The MPC and the MPS always add up to 100%, or 1. Furthermore, the MPS = 1 – MPC, so that the multiplier can also be written as
Multiplier = 1 / MPS.

Examples of How Changes in Government Spending Affect GDP
Example 1
Problem: Let’s say that we are experiencing a recession and the government increases spending by $25 billion. Let’s also assume that the MPC equals .75. By how much will equilibrium national income (GDP) increase?
Solution: Because the MPC equals .75, the multiplier equals 4:
Multiplier = 1 / (1 minus .75) = 1 / .25 = 4.
To get the increase in GDP, we multiply the multiplier by the increase in government spending:
Change in GDP = 4 * $25 billion = $100 billion.
This means that if GDP was, for example, $800 billion before the change, it will be $900 billion after the change.
Recessionary Gap
Example 2
Problem: Let’s say that we are experiencing a recessionary gap of $500 billion. A recessionary gap is how much GDP needs to increase from the current GDP in order to achieve full employment. Also assume that the MPC equals .90. How much will the government have to increase spending in order to close the recessionary gap?
Solution: We know that the increase in government spending times the multiplier equals the increase in GDP.
Remember that the change in government spending x the multiplier = the change in GDP.
The MPC is .9, so the multiplier is 10 (1 divided by 1 minus .9, or: 1 / (1.9)).
So: the change in government spending * 10 = $500 billion.
So: the change in government spending = $500 / 10 = $50 billion.
In other words, if the government increases spending by $50 billion, and the multiplier is 10, then GDP will increase by $500 billion. Since we need to add $500 billion to GDP to achieve full employment, we will have closed the recessionary gap.
Inflationary (Expansionary) Gap
Example 3
Problem: Let’s say that we are experiencing an inflationary (expansionary) gap of $200 billion. An inflationary gap is how much GDP needs to decrease from the current GDP in in order to eliminate inflation due to a GDP that is too high. Also assume that the MPC equals .80.
Solution: The change in government spending * the multiplier = the change in GDP. The multiplier is 1 / (1.8) = 5.
So: the change in government spending * 5 = $200 billion.
So: the change in government spending =$200 / 5 = $40 billion.
In other words, if the government decreases spending by $40 billion, and the multiplier is 5, then GDP will decrease by $200 billion. Since we need to lower GDP by $200 billion to achieve full employment without inflation, we will have closed the inflationary gap.
Video Explanation
For a video explanation and examples of how changes in government spending (and taxation) affect total spending in the economy, please visit:
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