Simple Keynesian model of income determination

When determining equilibrium, we take consumption equal to:

$$\begin{equation*} C =a_{0} +a_{1} YD \end{equation*}$$

where $$\displaystyle a_{0}$$ is the autonomous consumption or minimum consumption that would take place even in absence of income. What could be the consequences on equilibrium income if the autonomous consumption $$\displaystyle a_{0}$$ was negative?

• Side note: equations like this one are usually fitted to current levels of consumption and income (i.e. trillions of dollars). In such a regression it is possible for the intercept to be negative, but no one expects that to hold true if income theoretically fell to zero. Dec 18, 2021 at 14:19

I cannot see any way to have negative autonomous consumption. I believe autonomous consumption's extreme is zero if there's a kind of superheroes who don't need water, electricity and food to live and they save everything they earn. But in a case like this, there's no reason for having aggregate supply at all as nobody will buy the goods in first place.

• Yes, you are right. It doesn't seem like a plausible case in reality but like a few hypothetical cases if we consider hypothetically, autonomous consumption was ever negative how could it impact the equilibrium?
– SDM
Jan 28, 2017 at 12:24
• Also, when we talk about autonomous consumption we are assuming that the consumer s are borrowing to carry on their consumption and since it's a static model, can we assume that the consumers are lending at that particular time and thus, autonomous consumption is negative?
– SDM
Jan 28, 2017 at 12:34
• I suppose we talk about Aggregate Demand/Supply Equilibrium. In this case, $AD=C+I+G+NX$. If the economy is closed we just remove $NX$ from the formula. The autonomous consumption is just the constant term of $C$. If the constant decreases, then $AD$ shifts to the left (just look it mathematically since everything is linear). Jan 29, 2017 at 0:26
• If your economy is closed, the aggregate borrowing cannot exceed savings in first place. However, if your economy is open and you borrow to consume, then $MPC$ and/or $Y_d$ will increase, not autonomous consumption. Check en.wikipedia.org/wiki/Autonomous_consumption Jan 29, 2017 at 0:36
• Even at an autonomous consumption of zero, it would be difficult to make any simulations, unless you have government money to compensate. Dec 13, 2021 at 13:39
1. Consumption cannot be negative because of how it is defined. Consumption measures people's spending on goods or services. Spending, like weight or distance cannot be negative.

2. If we forget about point 1 just as a thought experiment, the effect of negative $$a_0$$ on output would be just:

$$\frac{dY}{da_0 }= M\cdot\frac{da_0}{dt}$$

where $$M$$ is the multiplier (in most 101 textbook $$M= \frac{1}{1-MPC}$$ - where MPC is the marginal propensity to consume).

So if $$a_0$$ falls by 1% the output falls by $$M\%$$.

If $$a_0$$ would be sufficiently small it could even make output negative - but again that is nonsesical. Output, consumption, investment and government spending cannot be negative.