By "c=a level" I mean situation when all consumption by households equals to autonomous spending, more or less. I assume no counter-cyclical policies(including automatic stabilizers). I also assume that no suprise positive shocks (like new resources, new technology) will happen midway.
Suppose there is a recession. And as it's typical for a recession, it starts as a slump in planned investment spending. As a consequence, aggregate disposable income of households decreases. Households decrease their aggregate consumption in response. It increases unplanned inventories investments by firms, consequently making firms to decrease their planned investment spendings (because they produce less).
Rinse, repeat. Economy gets caught in a feedback loop. And if I understand the acceleration principle correctly (I understand it as "If consumption decreases, then planned investment spending decreases even more. If consumption increases, then planned investment spending increases even more"), this is not a negative feedback loop, but a positive feedback loop. In other words, each cycle becomes only stronger (Households consume less, it causes firms to invest even less, it causes households to restrict their consumption even stronger than before, etc.) Without counter-cyclical government intervention (I count as counter-cyclical intervention automatic stabilizers aswell), or positive shocks in the midway, the whole thing will stop only when it will hit the wall, and the wall is autonomous spending. Households will stop tightening their belts when consumption spending will equal autonomous spending.
Do I understand everything correctly (the end results and the whole mechanism how we get where)? Or did I misunderstand something?