Question

When comparing Neoclassical and Keynesian ideals one will find a: “deeper oppositions between the two theories’ ways of linking individuals (as component parts of society) to society as a whole.” Explain how these two theories view individuals as parts of society.

Answer 1

tl;dr

Difference 1: Prices do not adjust freely, markets do not clear.

Difference 2: Classical model was closed with all economic behavior endogeneous, Keynesian model has Future Expectations about ROI (Return on Investment) as exogeneous

-----

It should be pointed out that the Neoclassical and Keynesian ideals aren't contemporary;

Keynes wrote his General Theory of employment, interest and money back in the 1930s in the Great Depression era, partly in opposition to the school of Classicals (Marshal, JB Say, Menger, Walras) who had a nice theory but no concretely useful suggestions on how to turn the economy around.

The neoclassical school is an umbrella term for mainstream modern economic thought, and represents an amalgamation of Classical, Keynesian and other ideas.

Digging deeper beyond the differences in terminology and concepts taught under each theory in a beginner economics course,

the core conflict is regarding the following proposition: Markets clear.

-----

Markets clear means there are no "excesses" or "deficits".

Free adjustment of the price mechanism (in a slider-like fashion, you can visualize it like the volume slider on your phone) over time closes such gaps between quantity supplied and quantity demanded.

The price mechanism will reflect both a change in demand conditions (e.g. if a product goes out of demand then its price goes down indicating that society's resources should be allocated elsewhere) and supply conditions (if an item becomes more expensive to produce then the exchange rate of that item with respect to other products in the economy should increase i.e. the price should go up)

thus by free adjustment of the price mechanism, an optimal allocation of society's resources is achieved by the decentralized action of economic agents (the Invisible Hand) rather than the coordinated activity of a centralized entity (Government intervention)

----

Keynes observed that in the real world, prices do not adjust so freely - and so markets do not necessarily clear.

e.g.

Labor market rigidities - the predominance of personal relationships, the need to provide job security, company incentive to retain employees to avoid the cost of retraining new employees - prevents the wage or labor recruitment from adjusting freely in response to market conditions.
Thus unions may cause underemployment by driving the wage above the marginal product of labor and keeping it fixed there through group bargaining power.

Capital market rigidities - the fact that capital cannot always be bought in an incremental quantity but rather is available in discrete "chunks" - make it so that capital may be unavailble for use by a firm even when the marginal product of capital at that firm exceeds the market real rental price.

and the price of output may also be rigid e.g. due to fear of inconvience caused to customers from frequent price change (menu costs)

----

As a consequence of these market rigidities, society fails to allocate its resources efficiently.

It is not necessarily the case that the classical model is "wrong";
since the assumption upon which the Classical model is predicated
(that prices adjust freely and so markets clear) is not satisfied,
we cannot say that the conditional relationship(s) proposed by the classicals is wrong

^ this understanding comes from Mathematical logic; if the antecedent P of a conditional statement "P implies Q" is not satisfied, then the conditional statement is non-falsifiable (because we have no evidence of what would have happened if P was satisfied) and the conditional statement must be accepted to be true (something like the idea of innocent until proven otherwise)

----

In particular think about a firm's production decision:

it's the decision to allocate investable funds into either
production/inventory
vs hold as money
vs put into the bank or a bond.

during the Great Depression, investable funds were indeed available but concentrated in the hands of the elite. Like all economic agents in theory these groups aren't concerned with societal welfare but rather personal profit.
So they refrained from investing into production because their expectations of the ROI on the investment were poor; nobody knew when the economy would turn around and people would be able to buy things again.

but this represents a situation of coordination failure (a technical term in game theory) since it is the the income provided by firms involved in production that goes around and comes back as receipts for purchases (what goes around comes around).

This circular flow of income - firms pay laborers wage for their time and effort, laborers use this wage to buy goods and services produced by firms - is analogous to the circulation of blood in our body; it represents the vital heartbeat and lifeblood that sustains an economy.

Just we feel weak when our blood pressure drops, so too economic slowdown can be attributed to the slowing down of this circular flow of income or exchange of Value.

During the Great Depression the economy slowed down because investors were myopic;
they didn't see that by witholding investment and dampening the cycle (kind of like dampening a fire by taking away the logs that sustain it) they were really harming themselves.

-----

At this juncture, we've concluded the primary discussion - the key "conflict" stems from a difference in assumptions.

A side-question that would be entertained is: so why is it that sometimes investors are optimistic (economic boom) and sometimes pessimistic (economic bust)?

Keynes proposed an answer exogeneous to the economic model: the presence of animal spirits, which unexpectedly and unpredictably alter the behavior of people on the individual and collective level.

One way of understanding these animal spirits is through the lens of Cialdini's Social Proof, or equivalently the Bandwagon Effect in microeconomics, or simply the everyday phrase "herd mentality" - investors are optimistic when other investors are optimistic.

If a sufficiently large number of investors - in a moment of Nihilistic disbelief - jumped ship, this would trigger a panic wave across all investors who would race to cut their losses. Economy plummets, and the prophecy becomes self-fulfilling; and in a way something like "two wrongs fix a right", government must step in to hedge the (negative) effect of (drop in) Investment on Aggregate Demand by increasing Public Expenditure

^ advice that is actionable, at a time when nobody else had anything but theory to offer; that is why Keynes is held as a genius. Despite being trained in the traditional mode of thinking, he was able to overcome dogma, dig deep into the root of the matter and identify which naughty assumption was causing the entire logical system to break down.

But why does that "sufficiently large number of investors" loose faith or jump ship in the first place? It's not specified within the model;

thus we can conclude upon another (finer) point of difference: the Classicals proposed a "closed" model where all economic behavior is endogeneous, whereas Keynes model was "open" in that Investment expectations (and by extension Investment behavior) is exogeneous.

-----