Business Cycle, Multiplier and Accelerator

In the economy, we observe patterns of rising and falling growth that fluctuate around an upward-sloping line of best fit of LR potential growth.  We can start at the peak, or boom, then fall down during a recession (contractionary period) until hitting rock bottom at the trough and then rising again in recovery (or expansionary period) until reaching a new (usually higher) peak.  This is the business cycle.  At a boom, the difference between the actual growth (which the squiggly line represents) and the line of best fit (potential growth trend) is a positive output gap and at a trough, the distance is a negative output gap (where actual growth is less than potential growth).  During a downturn, we see a fall in aggregate demand which leads to unemployment.  This pattern reverses itself during and upswing.  A recession is technically defined as two consecutive quarters (three months plus three months) of negative GDP growth (-x%).

The multiplier, calculated by taking 1/1-the marginal propensity to consume or mpc), tells economists inevitably how big a governmental injection in monetary terms will be when expansionary fiscal policy occurs.  Basically, income for people becomes the income for other people when the original people spend it.  They can also save, be taxed and buy imports (all people), but some money will be consumed.  This occurs again and again over time until the multiplier effect runs its course.  This means a $10 million injection can turn into a $20 million injection if the pc is .5.

The accelerator describes how a small increase in aggregate demand can lead to a proportionally bigger increase in induced investment.  Induced investment occurs when firms actively add to the capital stock of the economy to meet increasing demand for their products.  This is contrasted with replacement investment which replaces capital that has depreciated over time and always takes place, even during recessions. 

Lastly, the marginal propensity to save (mps) measures the percentage of income saved by consumers, the marginal propensity to tax (mpt) measures the percentage of income taxed by the government and the marginal propensity to import (mpm) measures the percentage of income used by consumers to buy imports.  Algebraically, mpc + mps + mpt + mpm = 1.