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Notes -
On the mainstream theories
I don't see how the Monetarist model can be seen as contrived. It is the simplest model and the one most in line with standard economic principles without bells and whistles. All prices are relative and we can think of the "price" of money relative to other goods. Money is a (durable) good with well-defined demand and supply. (Sure, the demand and supply functions must be described in "real" rather than "nominal" terms, because dollars are valued according to what they can buy not just for themselves). Demand and supply determine the relative price of money. If supply is increasing relative to demand—a monetary expansion— the price of money will be going down and we have inflation. Granted, there are a lot of important details: what should count as money, how substitutable bank deposits and cash are, how should we aggregate them into a single composite measure of total money; but the core of the framework is just that. Just basic supply and demand analysis.
The New Keynesian model recognizes this, but it gets hidden in their "cashless limit" so that the standard textbook version has no mention of money quantities at all. But it is there in the background. The contrived parts of the New Keynesian model comes from their decision to select and rule out certain types of equilibria and not being careful with working directly with the limit version of the model rather than solving the model first and taking the limit later.
On the discount rate
The fact that the discount rate matters for saving decisions does not mean that the discount rate changes with the environment. If the government has some expansionary fiscal policy, my budget constraints will change and I might substitute consumption intertemporally even if my discount rate is the same.
In the theory of (consumption-based) asset pricing, economists generally talk about the stochastic discount factor which takes into account the marginal utility in the future (in the different possible futures, hence stochastic). For instance, changes in this stochastic discount factor are used to explain the changes in the value of the stock market. But the idea there is that my rate of time preference between 1 utility unit today and 1 utility unit tomorrow remains the same, I just have a different rate of preference between 1 unit of consumption today and 1 unit of consumption tomorrow. If this is your point, then it makes sense. But it is not a point that is missed by the mainstream theories, it is literally taught in the first-year classes of any mainstream school.
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