As mentioned earlier, the ratchet effect occurs when either
	- The advantage of innovation is short lived and thus exceeds the
		cost (intra-work competitive ratchet)
	- The short term advantage of reporting falsely low capabilities
		of production outweighs the loss of benefits (inter-work
		planned ratchet)

(How would the former work wrt university model?)

We'll deal with the latter here, though on a macroscopic level they are both
the same.

In any planned economy, the prime information source of how much can be
produced by a given organization will have to be the predictions of that
organization itself. Secondary sources like statistics or networking may be
able to generate a rough estimate, but we'll deal with that later (upper
and lower bounds).

The organization thus has an incentive to lie if it can cut back on production
and gain the same rewards, and/or if it can cut back on its estimate, store
the surplus and either sell it on a black market or lie in the other direction
if they are doing less well and pad the inability with their earlier stored
surplus.

Denote p(x) the cost of producing the amount x, and r(x, L) the reward 
function where L is the claimed amount possible to produce. Also denote Q the
real amount possible to produce.

Also, the planners must create a reward function for any set x,y so that
r'(x, y) has a maximum at x = y. If the maximum > x, then the producer may
overproduce, and if the maximum < x, he may underproduce, assuming the producer
wants to maximize r(a,b)/p(a) for set b and selectable a. We also assume that
these reward functions are all over equal quality, and that they are degraded
on lower quality production.

Then, the organization has an incentive to lie if (but not only if):
	1. r(x, x)/p(x) > r(y, y)/p(y) where y > x
		Corresponds to a direct liar - if the rewards per production
		unit is greater with less production if the organization can
		convince this amount is the correct quota.
	2. r(y-x, y-x)/p(y) + r(x+z, x+z)/p(z) > r(y, y)/p(y) + r(z, z)/p(z)
		This is the hoarding liar -- he hides away some of his
		production for the future.

Consider a square wave reward function. In it the producer is rewarded with
RA if his production amount is greater than or equal to the quota, and RB 
otherwise, with RA > RB

Then we see that, RA and RB being equal for both, r(a,a) = RA for any "a".
Thus for 1., we get if RA/p(x) > RA/p(y) where y > x, then the organization
has an incentive to lie. And since the derivative of p() presumably is >= 0
(we're not producing waste here), so must p(y) > p(x), and hence RA/p(y) <
RA/p(x), which means there's an incentive to lie. (There is not, however, an
incentive to hoard)

It's actually surprising that the Russian command economy, implementing the 
square wave function as a reward guide, worked as well as it did. One paper
[1] mentions that informal readjustments were made by the dictator to offset
the nature above.

-

Let us collapse the reward function with a new function R(x) = r(x, x),
which assumes producers will choose an optimum by either telling the truth
or lying, and then produce just that much. This is a reasonable assumption,
given that r'(x, y) maximizes at x = y.

Furthermore, for simplicity, assume p(x) is linear in x up to x=Q. This is 
probably not true, but is a good approximation. It is also more reasonable
than that p(x) is totally linear (after all, past a certain level a producer
must purchase new equipment etc), but gives the same result as no producer
would lie about his quota so that L > Q.
	(We should refine this because the producer may upgrade his facility
	 and then Q is changed. So the planner cannot know Q. If he did, he
	 could set RQ(x) = r(x,Q) and there would be no problem.)

In order to defeat 1. above, then R(x) < R(x+a) for some a will insure that
it is not advantageous to lie if the planner will never ask for more than x+a
units. Generalized, if R(x) < R(x+a) for any positive a, it is not an advantage
for the producer to lie.

This can be done if we know the nature of the production function p(x). Then
r(x,y) should be arranged on the horizontal scale (x) so that it peaks for
x = y, and on the vertical scale so that R(a)/p(a) is increasing for a up
until the planner's optimal choice, after which it falls.

Now the producer has an incentive to increase his estimate because this will
put him on a higher point at the R(a)/p(a) curve, but not beyond the planner's
optimum or Q, whatever comes first, because of diminishing returns. The only
problem here may come into existence if the producer tries to make his stuff
too cheaply, but that deals with quality; there should be a lagged factor
based on quality -- perhaps a power sum of some kind. Measuring "quality" will
be more easy in a public R&D model than in a restricted one.

The planner can encourage growth by tweaking the reward curve to account for
the cost of expansion, if he knows the details. But if he does, then he can
more easily just add these details into the main plan explicitly.

-

In a market economy, as long as there are many competitors, R(x) is set by
consumer demand and is communicated by prices. The organization then 
manufactures as many as required to maximize R(x)/p(x). When there are few 
competitors, R(x) is now controlled partly by the organization/s left, and they
set it just high enough to not make consumers revolt.

[1] "Coercion, compliance, and the collapse of the Soviet command economy",
Harrison, M., University of Warwick.