(1) If P deserves x at t, then there is something P did prior to t in vittue of which x is deserved.
(2) One's income is determined by the price of one's labor on the market.
(3) The price of one's labor is determined by the demand for one's labor on the market.
So, (4) one's income is determined by the demand for one's labor on the market.
(5) Suppose x is P's income.
So, to reiterate, (1) if P deserves x at t, then P did something prior to t in virtue of which she deserves x.
But, (6) P did not do anything to create demand for her labor on the market.
Therefore, (7) P does not deserve x.
That is, because you didn't have anything to do with demand being what it is, you don't deserve the price you command for your labor on the market.
There are a number of problems with this particular argument. The first problem is premise (1). I don't believe desert is always backward looking. People can, for example, deserve love, not for anything they have done, but because of the way it could transform them. (Christians, do you hear me?) Similarly, people can deserve a chance or an opportunity, although they haven't done anything yet to earn it. But let's set that aside.
It strikes me that (6) just has nothing to do with anything relating to desert. What I did prior to t to deserve x (whatever the value of x is) was complete my end of a contract that was entered into voluntarily by the relevant parties within a system of just rules. It just doesn't matter what I did to fix the particular value of x. If S agreed to pay me x for completing my end of a contract, and I complete my end of the contract, then I deserve x from S. THIS IS OBVIOUS and if an argument implies the contrary, then we have a ready reductio of the argument.
The question Anderson seems to raise is: how is it that I could possibly deserve, say, $67,456.84 per year rather than $23,764.45 per year when I have so little to do with determining the conditions under which my labor commands either amount?
And the answer is easy. The same way I can deserve a silver medal in Olympic tennis, even though I had so little to do with determining the existence of the Olypmics, or the rules of tennis, or the quality of my pool of competitors. My reward is fixed by a combination of my performance, chance, and the rules of the games. The existence of chance or my lack of responsibility for the rules simply does not bear on what I deserve in this context.
Do you know what's annoying? Computer programmers who were making $90,000 per year because of the labor shortage in computer programmers, and who are now whining because they get $50,000, or can't find work at all because of some eager low-cost chap in Bangalore. Why is this annoying? Because computer programmers don't deserve to get any particular amount of money for their labor. They deserve to get whatever is specified by a fair contract within a just system of rules. If the number shifts, it has nothing to do with what the programmer deserves. The programmer, or whomever, deserves whatever the value of of the variable happens to be, but they don't deserve that the value of the variable be anything in particular.
Some further thoughts.
Does Anderson's argument imply that I would be making a fundamental mistake if I argued to my boss that I deserve a raise because everyone else doing the same job is being paid more?
How close does Anderson get to committing the Fundamental Redistributivist Error (the FRE), which is the very common but nonetheless logically horrifying error of inferring from the fact that P doesn't deserve x to the conclusion that there exists someone who is morally authorized strip x from P. Somebody ought to write an article about the manifold expressions of FRE titled “How Not to Argue For Taxes.”
Now, I myself believe that there are conditions under which the state is legitimate, and under which it may justly redistribute holdings. However, I think it's a lot harder to show that there is someone who is morally authorized to use coercion to take stuff than it is to show that people deserve what is specified in a fair contract when they complete their end of it.