Trouble with the equation of exchange.

[DSGE]

that's obviously not true because Income necessarily equals expenditure. That's an identity. It always holds.

what about "cash on hand" ?

Outflows can derive, from Inflows; or from draw-down of current Stock:

A stock isn't income. If you draw down a a stock and spend it, the spending as a flow. Your spending (expenditure) is somebody else's income.

dS/dt = +I -O​

Seriously dude, your maths doesn't help things. It just makes shit more confusing. Just use your words unless absolutely necessary.

E.g. imagine nobody buys anything (Expenditures = zero); everybody could still have Income, if new Money entered the economy ("victorious general showers the masses with Money from campaign"):

Is that income people receive is also an expenditure from the general (or central bank or whoever).

It's an identity. You have to understand that that means it always holds. Always, invariably, never violated. The same way as sin^2(x) + cos^2(x) = 1. It's always 1, no matter what. If I arrive at some conclusion that sin^2(x) + cos^2(x) = 1 + 0.5*x; then I've fucked up. Income and expenditure are always equal. If you arrive at a conclusion otherwise, you've fucked up somewhere.

 

[Widdekind]

A stock isn't income.

yes, a Money-stock [$], is not a Money-flow [$/time]

If you draw down a a stock and spend it, the spending as a flow.

yes, depleting a stock [$], at some rate-of-Velocity [%/time], is a flow [$/time]

Your spending (expenditure) is somebody else's income.

but not my "hoarding"; i can receive Revenues (Rev), and "stash" some, replenishing my stock (S) of cash-on-hand (c.p. Demand-for-[holding-]Money), at the 'expense' of Expenditures (Exp)

Rev-Exp = dS/dt​

for an entire economy, "Revenue" is the rate of new Money creation (Inflow of Money into the economy from central banks) +dM/dt, whilst "Expense" is the rate of existing Money de-circulation, into central bank Reserves -dR/dt. Other "sources" of new Money include counterfeiting; other "sinks" of existing Money include destruction of currency ("burning bills", "using them for wallpaper"). For simplicity, i assume that central banks are the principal determiners of Money supplies.

you told me, that new Money (aside from new notes) is "created endogenously" when banks loan new "inside Money" into circulation (balanced by an equally new debt, c.p. matter & antimatter). So, more-than-less, rule-if-not-exception, +dM/dt represents the rate of debt creation, different from mining & minting new coinage (or plundering neighbors for theirs)... somehow it all connects, and it all is important to understand

 

[DSGE]

A stock isn't income.

yes, a Money-stock [$], is not a Money-flow [$/time]

If you draw down a a stock and spend it, the spending as a flow.

yes, depleting a stock [$], at some rate-of-Velocity [%/time], is a flow [$/time]

Your spending (expenditure) is somebody else's income.

but not my "hoarding"; i can receive Revenues (Rev), and "stash" some, replenishing my stock (S) of cash-on-hand (c.p. Demand-for-[holding-]Money), at the 'expense' of Expenditures (Exp)

Rev-Exp = dS/dt​

for an entire economy, "Revenue" is the rate of new Money creation (Inflow of Money into the economy from central banks) +dM/dt, whilst "Expense" is the rate of existing Money de-circulation, into central bank Reserves -dR/dt. Other "sources" of new Money include counterfeiting; other "sinks" of existing Money include destruction of currency ("burning bills", "using them for wallpaper"). For simplicity, i assume that central banks are the principal determiners of Money supplies.

you told me, that new Money (aside from new notes) is "created endogenously" when banks loan new "inside Money" into circulation (balanced by an equally new debt, c.p. matter & antimatter). So, more-than-less, rule-if-not-exception, +dM/dt represents the rate of debt creation, different from mining & minting new coinage (or plundering neighbors for theirs)... somehow it all connects, and it all is important to understand

I think maybe you're getting a little confused here. Income = Expenditure doesn't mean that any income you receive you necessarily spend afterward. Obviously you can just keep the money under your mattress. It means that at any point income was gained, an equally sized expenditure happened at the same time. And any time expenditure happens, an equally sized income is gained. Income = Expenditure is just looking at the same flow, the same transaction, but from the perspective of the different parties. When you gain income, somebody gave you that income. Your income was their expenditure. And whenever you spend money, your expenditure is necessarily also whoever you're buying from's income.

So the identity doesn't look at your stock of wealth, or money under the mattress or anything; it looks at what happens when an exchange takes place.

 

[Widdekind]

Income = Expenditure doesn't mean that any income you receive you necessarily spend afterward. Obviously you can just keep the money under your mattress. It means that at any point income was gained, an equally sized expenditure happened at the same time. And any time expenditure happens, an equally sized income is gained. Income = Expenditure is just looking at the same flow, the same transaction, but from the perspective of the different parties.

i was saying:

income-to-me less expenditures-from-me = (d/dt)[cash-under-my-mattress]​

you are saying:

income-to-me = expenditure-from-you​

i was looking at "economic actors"; you are looking at their trans-actions.

If you have a large collection of "economic actors", all "in a box"; and if, in some time period (dt), they mutually engage in some number (N) of pairwise transactions; then there will be N "incomes (from other actors)" and N "expenditures (to other actors)"; and both lists are identical. Where does saving (hoarding) & dis-saving (dis-hoarding) enter ?

 

[DSGE]

Income = Expenditure doesn't mean that any income you receive you necessarily spend afterward. Obviously you can just keep the money under your mattress. It means that at any point income was gained, an equally sized expenditure happened at the same time. And any time expenditure happens, an equally sized income is gained. Income = Expenditure is just looking at the same flow, the same transaction, but from the perspective of the different parties.

i was saying:

income-to-me less expenditures-from-me = (d/dt)[cash-under-my-mattress]​

you are saying:

income-to-me = expenditure-from-you​

i was looking at "economic actors"; you are looking at their trans-actions.

It's not what I'm saying. It's what the income-expenditure identity is saying. For what you're talking about you can't just use Y = C+I+G+X-M, because that identity relates to looking at a flow from different perspectives. Using Y = C+I+G+X-M+dm/dt doesn't make any sense. It's not a justified step.

Where does saving (hoarding) & dis-saving (dis-hoarding) enter ?

When we introduce money. Normally we don't introduce money until we absolutely have to, because the same money being used to buy different goods becomes totally confusing and bullshit. Just look at the flow of real goods and services. Look at it like a pure exchange economy, and then introduce money once you've got that model working perfectly and want to add an extra friction. You can't just dive in. Build your model from the ground up, adding money last.

 

[Widdekind]

When we introduce money. Normally we don't introduce money until we absolutely have to, because the same money being used to buy different goods becomes totally confusing and bullshit. Just look at the flow of real goods and services. Look at it like a pure exchange economy, and then introduce money once you've got that model working perfectly and want to add an extra friction. You can't just dive in. Build your model from the ground up, adding money last.

• imagine an economy with "N" actors
• consider two "NxN" matrices, one for Expenditures, the other for Incomes
• for every transaction, with money flowing from "a" to "b", in the Expenditures matrix, element (a,b) is decremented by the amount transacted, representing "a lost money to b"; whilst in the Incomes matrix, element (b,a) is incremented, representing "b gained money from a"
• then, the Expenditures matrix equals the negative, transpose, of the Income matrix (Exp = -Transpose(Inc))
• the diagonal elements represent net profits, equal to the difference, between the sums, of the elements in columns vs. rows (in "Exp", columns represent "all the money expended to", whilst rows represent "all the money expended from"; the difference is that actor's net gains/losses that period)
• if the Money-supply is increasing, so that everybody is (generally) stockpiling money, the the matrices will be lopsided, with "below diagonal elements" (generally) exceeding "above diagonal elements" (or conversely)

edit: i made a mistake above; in the black-and-white economy "flow chart", due to fractional-Reserve banking, the sum of loans into the "financial market" (savings, investments) may be much much less, than the sum of loans thereby generated, back out into the economy.