Why drafting IDF soldiers makes no sense: or, why a volunteer army will always outperform a conscript army:
Whether a conscript army will out-perform a volunteer army depends on how you define success. If you define success from the perspective of the government, then a conscript army will outperform. But if you define success from the perspective of the governed populace, then a volunteer army will outperform. Let me explain:
There are two costs associated with hiring soldiers, the monetary and the psychological. Let's deal with each cost separately:
First, let us ignore psychological costs, and look only at monetary costs.
When soldiers are drafted, the monetary cost remains the same as when they are paid enough to convince them to volunteer, but the cost is hidden. For example, suppose you have someone who is making $50,000 in his private job. In order to convince him to voluntarily enlist, you must pay him at least $50,000 as a soldier. So there is an obvious, explicit monetary cost of $50,000 to convince him to volunteer. If you draft him, you don't have to pay him any money, so it appears like you're saving the expense. But in reality, the same expense is incurred, because the economy is losing a job which produced $50,000 for society. This is an opportunity cost; even if you don't pay him, society is still losing the value of his productivity, which is equal to how much you would have paid him. (Again, we are ignoring psychological costs for now.) So either way, the same cost of $50,000 is incurred whether you draft someone or pay him enough to convince him to voluntarily enlist. But if you draft him, that cost is hidden and unseen.
In fact, under the draft, the cost is even higher, because you draft the wrong people. You might draft someone who makes $100,000 while leaving un-drafted someone who makes only $20,000. If you were paying people to voluntarily enlist, the person who makes $20,000 would volunteer first, which is exactly what we want; we want the less productive members of society to be the first to enlist. We want to draft those people who have the least to lose, who have the lowest opportunity cost of being drafted. But if you draft people under a lottery, you might draft the highest-paid people while leaving the lesser-paid people un-drafted, so you're misallocating scarce and valuable labor. You might draft a doctor into the army as a foot soldier while leaving a homeless bum un-drafted. If you were to pay people to volunteer, you would ensure that only the right people enlist, the people who have the least to lose by joining the army.
But the government is glad to hide the costs, even if this increases the costs, because by hiding the costs, the populace is less likely to oppose the war. If the people knew what the war really cost, they might oppose it. But by drafting soldiers, the government is able to conceal the true costs of war, even as it increases the cost of the war, thus preventing the populace from revolting.
Now, for the psychological costs:
So far, we assumed that the only thing needed to convince someone to enlist voluntarily, is to pay him more than he makes at his job. But obviously, this is not true. Everyone also has psychological values. For example, a gung-ho patriot might be willing to pay for the privilege of fighting, while a pacificist might need to be paid a quadrillion dollars even to agree to be the cook. These psychological costs ARE real. To convince people to join voluntarily, you must pay them enough that the wage you pay them for being a soldier, minus the psychological costs of volunteering (which for a patriot might be negative), is greater than however much they are being paid at their private job (which also includes psychological costs). So suppose the patriot makes $100,000 at his job, and evaluates the cost of serving in the army at negative $30,000. Therefore, to convince him to enlist, you must pay him $70,000. Meanwhile, suppose an average Joe makes $50,000 at his job, and evaluates the cost of serving in the army at $10,000. You must pay him $60,000 to convince him to enlist. And as I said, the private job also includes psychological values. Suppose someone makes only $20,000, but he works at a charity, and attaches a psychological value of $1 million to his charitable work. And suppose the psychological cost to him of fighting in the war is $10,000. Therefore, to convince him to enlist voluntarily, you must pay him $20,000 (for his wages from his job) plus $1 million (the value of his work to him) plus $10,000 (the cost of fighting), which equals $1,030,000.
But of course, when you draft soldiers, the psychological costs are completely ignored. They still exist - the soldiers who are drafted still incur the psychological costs, which are as real as monetary costs - but you never see them. Once again, the government is glad, because this prevents revolt. The soldiers grumble at their incurred psychological costs, but the government doesn't care, and the populace gets taxed less than they otherwise would and they do not feel the psychological costs, so they do not object either.
So conscripted armies are better at fighting wars from the government's perspective. But volunteer armies are better from the perspective of the governed populace (if only they learned economics to understand their true interests!). (However, I am homogenizing the "governed populace" as if it had a unitary interest. I am assuming that the governed populace only wants to fight defensive wars at least-cost. If so, then a volunteer army is best. But if some sector of the populace enjoys offensive wars, and does not care about the cost as long as somebody else pays it, then conscript armies make sense.)
"Something else to add: most modern conscripted forces still pay nominal salaries to soldiers, so they costs are even greater than your example, as they include opportunity costs for the conscripts labor in the non-military market, and the explicit costs of their salary"
Not quite, or not necessarily. I think you're fallaciously double-counting.
This is true IF the taxpaying populace would not want the war if they knew how much it cost. In that case, the salaries paid to the conscripts would be simply wasted. And if the populace would want the war if only it were cheaper, but does not want it at its full cost, then the populace suffers a loss, but not a whole loss. Suppose the populace values the war at $30,000 per soldier, but every soldier costs $50,000. Then the populace loses $20,000 per soldier, not the entire $50,000. It's no different than if you are forced to buy something for $10 which you would have voluntarily bought only for $6. Your loss is $4, not $10.
But suppose the populace does truly want the war even at its full cost. In that case, the populace would be willing to pay the costs of hiring any soldiers at their market rate. So if the conscripts are paid only a fraction of their market rate, this means that the populace is still getting what it wants, at a fraction of the monetary cost, even. The loss here is to the soldiers, who have their psychological disutility only partially compensated. Suppose the case of the person who would need to be paid $60,000 to induce him to volunteer. And suppose the populace really would be willing to pay him in full, so the populace is not suffering any uncompensated loss. If as a conscript, he is paid only $20,000, then the populace is indifferent, while the conscript suffers a psychic loss of $40,00.
So the point is this: if the conscript is partially paid a fraction of what his market rate, then we must avoid double-counting this loss. The conscript's psychic loss is therefore partially defrayed, and the extra cost to society of paying the conscript is counterbalanced by a reduced psychic loss to the conscript. And while society might not be willing to pay the full cost of the war, it might have been willing to pay some of the cost, because it values the war somewhat, though less than its cost, so the value of the war - though less than the cost of the war - nevertheless partially defrays the cost of the war.
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