Legal incidence is irrelevant to economic incidence

That's plausible. But suppose the full tax were paid by the employer. That would lower the wage the firm would be willing to pay its workers; so even when a tax is paid solely by the firm, it still indirectly harms the workers.

Perhaps, though, the indirect harm will be less than the direct harm. It's not obvious. But by thinking carefully--i.e., by doing economics--we can see that, in fact, the indirect harm is exactly equal to the direct harm: it doesn't matter to the workers what fraction of the tax is directly paid by them, since the total cost of the tax, direct and indirect, is always the same.

To follow this reasoning, you need to understand the economic concepts of demand, supply, and EQUILIBRIUM.

Let's simplify. Instead of a payroll tax, consider a simple sales tax, say on widgets. And instead of a percentage tax, consider a per-unit tax, e.g., $1/widget.

• Case 0: No tax

Consider first the situation without any tax. Call the resulting market price P0, the quantity Q0. We assume the market is in equilibrium: the quantity demanded at P0 equals the quantity supplied:
D(P0) = S(P0)
• Case 1: Producer tax

Next, consider instituting a producer tax, $T per unit. Now the term "price" is ambiguous: we must specify whether we're referring to the price paid (PP1) or the price received (PR1).

For example,

• if the tax is $1 (T=$1)
• and the price paid by the consumer is $10.50 (PP=$10.50),
• then the price received by the firm will be only $9.50 (PR = PP - T = $10.50 - $1 = $9.50).
Now remember, we're trying to figure out whether it matters to consumers whether they or the firm are legally obligated to pay the tax. What that boils down to is, is the price paid higher when the consumer pays the tax or when the producer pays the tax--or, as I will argue, is the price paid the same, no matter who pays.

Demand depends on price paid, supply on price received. In equilibrium, the quantity demanded at the price paid equals the quantity supplied at the price received.
D(PP1) = S(PR1)

Under the producer tax, part of the the price paid is sent by the firm to the government; the rest the firm keeps as the price received:
PP1 = PR1 + T

• Case 2: Consumer tax

Next, consider instituting a consumer tax, $T per unit. Again we must distinguish between price paid (PP2) and price received (PR2). Part of the price paid is sent by the consumer to the government, the rest the consumer gives to the firm as the price received:
PP2 - T = PR2

Remember, what I'm trying to prove is that PP2=PP1: consumers pay the same price regardless of who pays the tax. So how can I show that PP2=PP1? Well, we always suppose the market is in equilibrium. By definition, PP1 is the equilbrium price paid under the producer tax; all I have to do is show that PP1 is also the equilibrium price paid under the consumer tax.

But that is almost obvious! Suppose that, under the consumer tax, the price paid is indeed PP1.
PP2=PP1.
What will the price received be? Clearly,
PR2 = PP2 - T = PP1 - T = PR1

If consumers pay the same price under both taxes, then firms will receive the same price. But we already know that PP1 and PR1 are an equilibrium. So we're done.

This page maintained by Steven Blatt. Suggestions, comments, questions, and corrections are welcome.