Is the Sraffian Critique of the Labor Theory of Value Correct?

1. Introduction. I've been reading (and re-reading) Steve Keen's Debunking Economics for a while now. He summarizes the Sraffian critique of the Labor theory of value (or its Marxist variant; I'll use the acronym "LTV" for short) using the following system:

28 units iron + 56 units labor → 56 units iron
16 units iron + 16 units labor → 48 units gold
12 units iron + 8 units labor → 8 units corn

It is assumed that it takes 5 units corn to sustain labor.

If we use the LTV, then we set the value created by 1 unit of labor to unity. Thus we have the system become

28 v_i + 56 = 56 v_i
16 v_i + 16 = 48 v_g
12 v_i + 8 = 8 v_c

where v_i is the value of 1 unit iron, v_g the value for 1 unit gold, and v_c the value for 1 unit corn.

Objection. This seems a bit too static...I'm not going to invoke particular interpretations of the LTV (*cough*TSSI*cough*), but it seems like we are mixing apples and oranges when we assume the value of the iron input is the same as the value of the iron output.

2. Determining Values. We can solve this system of equations to find that v_i = 2, v_g = 1, and v_c = 5.

In a more useful, although slightly misleading, form we write: 4 units gold = 2 units iron = 1 unit corn.

Sraffians leap to the conclusion "This isn't what Sraffa's model gives us!"

I would like to ask the simple question: "Wait, let us see: does this work?"

3. Reproduction. Let us start with the iron sector. It keeps 28 units for its own reproduction.

The iron sector sells 12 units to the corn sector. For how much? Well, 12 units of corn = 6 units corn.

The iron sector sells 16 units to the gold sector, for 32 units gold (wow!).

To finish this up, the gold sector needs (¹⁄₅) × 5 units corn, i.e., 1 unit corn. So it buys 1 unit corn from the corn sector for 4 units gold.

The corn sector keeps 1 unit of corn, and has 4 units gold.

We see that reproduction can occur.

4. Profits. The only "problem" I see: we don't have a "uniform rate of profits". What are the profits?

The iron sector has its profits consist of 2.5 units corn + 32 units gold.

The gold sector has its profits consist of nothing: it has no profits.

The corn sector has its profits be 0.5 units corn + 4 units gold.

I suppose, in closing, I have a controversial question (for both Marxists and non-Marxists): is there any reason we should expect a uniform rate of profit across all industries?

Addendum (February 5, 2014 at 7:05AM [PST]). It dawns on me in classical economics, the following conditions are equivalent:

1. The economy is in equilibrium
2. The rate of profits is uniform across all sectors
3. Commodities are exchanged at prices determined by their value (there is no markup, it's just the value expressed in units of money)

I suppose one could take this result and argue "Aha, this must mean Marx works in disequilibrium!" But the problem one must ask is: why would commodities be traded at their value? Perhaps this is the "proof by contradiction" Sraffians are going for...

References.

1. Steve Keen, Debunking Economics. First ed.,
Zed Press, 2001.
2. Ian Steedman, Marx after Sraffa. New Left Books, 1977.