The relation between average product and marginal product is one of several that reflect the general relation between a marginal and the corresponding average

The relation betweenaverage productandmarginal productis one of several that reflect the general relation between a marginal and the corresponding average. The general relation is this:

If the marginal is less than the average, then the average declines.

If the marginal is greater than the average, then the average rises.

If the marginal is equal to the average, then the average does not change.

This general relation surfaces throughout the study of economics. It also applies to average andmarginal cost, average andmarginal revenue, average andmarginal propensity to consume, and well, any other average and marginal encountered in economics.

Making Tacos

Average and Marginal Product

The graph at the right for the hourly production of Super Deluxe TexMex Gargantuan Tacos (with sour cream and jalapeno peppers) illustrates the relation between average product and marginal product.

Marginal Greater Than Average: For the first few quantities ofvariable input(workers), marginal product is rising and lies above average product. This is consistent with an increasing average product. If Waldo (proprietor of Waldo's TexMex Taco World) hires an additional worker in this early stage of production, then the marginal product (that is the extra contribution) of this worker is greater than that of the existing workers. This, as such, increases the average for all workers.

Even after thelaw of diminishing marginal returnskicks in, and marginal product declines, average product continues to increase because the marginal exceeds the average.

Marginal Equal To Average: The point of intersection between the marginal product and average product curves is also the peak of the average product curve. If the productivity of the marginal worker is equal to the average productivity of the existing workers, then the average does not change.

Marginal Less Than Average: Once the marginal product curve moves below the average product curve, then the average product curve declines. As Waldo hires an additional worker in the middle of this range, the marginal product of this worker is less than that of the existing workers, which pulls down the overall average.

The Law of Diminishing Marginal Returns

This average-marginal relation for production is closely tied to the law of diminishing marginal returns. Marginal product declines with the onset of diminishing marginal returns. The "hump shape" of the marginal product curve reflects first increasing marginal returns then decreasing marginal returns.

For this reason, the "hump shape" of the average product curve is attributable, indirectly, to the law of diminishing marginal returns and the "hump shape" of the marginal product curve. Increasing marginal returns means marginal product is rising and because average product necessarily starts at zero (zero production means zero average product), marginal product lies above average product and causes it to rise, as well.

With the onset of decreasing marginal returns, marginal product declines. However, for this initial part of the marginal product decline, average product continues rising because marginal product is still greater. After marginal product falls enough to meet up and intersect average product, average product peaks. As marginal product, again guided by the law of diminishing marginal returns, continues to decline and falls below average product. This causes the decline of average product.

In essence, the average product curve plays catch-up to the marginal product curve, sort of follow the leader. At first, marginal product rises, so average product tags along like an annoying younger sibling. Then marginal product decides to fall, so average product chases after it. Because marginal product is guided by the law of diminishing marginal returns, so too is average product.

Mps - Marginal perpencity to save. Which is each dollar a household saves.Mpc - marginal perpencity to consume. Dollars spent

1-mpc=mps

Apc - average perpencity to consumeAps - average to save.The average propensity to save (APS) indicates what thehousehold sectordoes with income. The APS indicates the portion of income that is used forsaving. If, for example, the APS is 0.1, then 10 percent of income goes for saving.The standard formula for calculating average propensity to save (APS) is:

APS=saving

income

Saving Schedule

Top of Form

Bottom of Form

A saving schedule, such as the one presented to the right, provides data that can be used to run through a few APS calculations. The first column in this schedule presents household income, ranging from $0 to $10 trillion. The second column presents saving, ranging from -$1 to $1.5 trillion. The task at hand is to derive the average propensity to save at each income level.The average propensity to save is calculated by dividing saving in the second column by income in the first column. Beginning near the top of the schedule, if household income is $1 trillion, then saving is -$0.75 trillion, giving an average saving of -0.75.

Running the numbers through the APS formula gives:

APS=saving

income=-$0.75

$1=-0.75

Similar calculations can be performed for each income level. For example, if income from $4, then saving is also $0 trillion and the APS is equal 0 ($0/$4). If income is $8 trillion, the saving is $1 trillion and the APS is equal to 0.13 ($1/$8). To display all average propensity to save values, click the [APS] button.The prime conclusion from a quick look at the numbers is that APS increases as income increases. The APS is -0.75 for $1 trillion of income, then increases to 0.15 for $10 trillion of income. In other words, APS is not constant.

The APS increases due toautonomous savingandinduced saving. Autonomous saving is the -$1 trillion of saving that takes place if income is zero. Induced saving is the increase in saving that occurs due to an increase in income.

Because saving is negative when income is zero, saving is necessarily less than income at low income levels, meaning the APS is less than one. Moreover, while saving is induced as income increases. The increase in saving increases the APS from its initial negative value into the positive range.

The average propensity to save is one of four related measures. The other three areaverage propensity to consume,marginal propensity to save, andmarginal propensity to consume.

Average Propensity to Consume: This is the proportion of household income that is used for consumption. Abbreviated APC, this is really nothing more than average consumption. Together with the average propensity to save, it indicates how a given level of income is divided between consumption and saving.

Marginal Propensity to Save: This is the change in saving resulting from a change in income. Abbreviated MPS, this indicates the proportion of additional household income that is used for saving. It is the flip side of the marginal propensity to consume, and thus also quantifies the fundamentalpsychological law. The MPS is the slope of the saving line, which enters into theinjections-leakages model. Themultiplieris also related to the MPS.

Marginal Propensity to Consume: This is the change in saving resulting from a change in income. Abbreviated MPC, this indicates the proportion of additional household income that is used for saving. It quantifies the fundamental psychological law and is the most important of these four measures. The MPC is the slope of the saving line, key to the slope of the aggregate expenditures line, and affects the magnitude of the multiplier.