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The formula used to calculate marginal propensity to consume is change in consumption divided by change in income, or, MPC = ∆C/∆Y. To make this calculation, you first must determine the change in income and the resulting change in spending (consumption). If someone's income increases by $5,000 and their spending increases by $4,500, the calculation would be made in this way:

MPC = 4,500/5,000. MPC = .9 or 90%

Keynes formally introduced the concept of MPC in his 1936 book, The General Theory of Employment, Interest, and Money. Keynes argued that all new income must either be spent, as with consumption, or invested, as with savings.

Keynes understood that the classical thinking which held that supply would create its own demand did not always work. He noted that the main problem was a lack of aggregate demand. He believed that government spending could add to aggregate demand and that this fiscal stimulus would create a multiplier effect. This effect would result from increases in income and consumer spending that caused a chain reaction of spending by various other beneficiaries of the spending.

Take an employee of ABC Company. They receive a raise in salary. Their spending goes up as a result. What is MPC in this instance? Since the formula for MPC is change in consumption divided by change in income, you must first determine those two changes.

For change in income, the salary rose from $65,000 to $75,000. The change is $10,000 ($75,000 minus $65,000).

For change in consumption, determine levels of spending before and after the salary increase. Before the increase, the employee spent $60,000 of the $65,000 on goods and services. They put the remaining $5,000 into savings. After the salary raise to $75,000, they spent $65,000 on goods and services. The change in consumption is $5,000 ($65,000 minus $60,000).

To calculate marginal propensity to consume, insert those changes into the formula:

MPC = ∆C/∆Y

MPC = 5,000/10,000

MPC = .5 or 50%

This means the individual spent 50% of their added income on goods and services.

An MPC equal to one means that a change in income (∆Y) led to the same proportionate change in consumption (∆C). That is, a person spent 100% of the additional income on goods and services and saved none of it.

An MPC less than one means that a change in income produced a proportionally smaller change in consumption. A person spent less than the added income received.

An MPC equal to zero means that a change of income led to no change in consumption. So, a person spent none of the change in income and, instead, put it into savings.

An MPC that is higher than one means that additional income led to spending that surpassed the amount of additional income.

A 'mesh' (also called a loop) is simply a path through a circuit that starts and ends at the same place. For the purpose of mesh analysis, a mesh is a loop that does not enclose other loops.

Similar to nodal analysis, mesh analysis is a formalized procedure based on KVL equations. A caveat: mesh analysis can only be used on 'planar' circuits (i.e. there are no crossed, but unconnected, wires in the circuit diagram.)

Steps:

1. Dependent Voltage Sources

Solution: Same procedure, but write the dependency variable in terms of mesh currents.

2. Independent Current Sources

Solution: If current source is not on a shared branch, then we have been given one of the mesh currents! If it is on a shared branch, then use a 'super-mesh' that encircles the problem branch. To make up for the mesh equation you lose by doing this, use the mesh current relationship implied by the current source (i.e. I 2 − I 1 = 4 m A {\displaystyle I_{2}-I_{1}=4mA} ).

3. Dependent Current Sources

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