That's exactly what I was saying. Keynes assumes he can reduce the world to Calc 101. Austrians/Chicagoans/etc don't.
As for why I think it's clear this reduction is not always valid, a simple hypothetical: suppose the stimulus targeted doctor-delivered medicine. There is no unemployment among doctors, so there is no pool of underutilized doctors to employ. It also takes about 8 years to train a doctor, so any effect that stimulus has on inducing construction workers (or others) to become doctors can only occur 8 years later.
Also, sticky wages don't immediately lead to the validity of AD or keynesianism. For example, suppose construction workers earned $30/hour before the bust and assume Keynesian wage stickiness. They will not take un-stimulated jobs at Walmart at $12/hour or even stimulated jobs at $24/hour and they will be unqualified for Sous Chef jobs at $30/hour or even a stimulated $35/hour. Unless there is some specific job out there that pays at least $30/hour and construction workers are qualified for it, they will simply remain unemployed. Thus, under some circumstances, Keynes own assumptions make his Calc 101 reduction invalid.
Lastly, there is no reason a housing bubble bursting would cause job losses only in construction. It would also harm realtors, mortgage brokers, bankers, etc. It would indirectly harm people who sell things to realtors, mortgage brokers and bankers. Thus, in the recalculation picture, we'd expect the biggest job losses in construction, real estate and mortgages, and correspondingly smaller job losses as you move outward through the economy from this epicenter.
As for why I think it's clear this reduction is not always valid, a simple hypothetical: suppose the stimulus targeted doctor-delivered medicine. There is no unemployment among doctors, so there is no pool of underutilized doctors to employ. It also takes about 8 years to train a doctor, so any effect that stimulus has on inducing construction workers (or others) to become doctors can only occur 8 years later.
Also, sticky wages don't immediately lead to the validity of AD or keynesianism. For example, suppose construction workers earned $30/hour before the bust and assume Keynesian wage stickiness. They will not take un-stimulated jobs at Walmart at $12/hour or even stimulated jobs at $24/hour and they will be unqualified for Sous Chef jobs at $30/hour or even a stimulated $35/hour. Unless there is some specific job out there that pays at least $30/hour and construction workers are qualified for it, they will simply remain unemployed. Thus, under some circumstances, Keynes own assumptions make his Calc 101 reduction invalid.
Lastly, there is no reason a housing bubble bursting would cause job losses only in construction. It would also harm realtors, mortgage brokers, bankers, etc. It would indirectly harm people who sell things to realtors, mortgage brokers and bankers. Thus, in the recalculation picture, we'd expect the biggest job losses in construction, real estate and mortgages, and correspondingly smaller job losses as you move outward through the economy from this epicenter.