31 Jan 2018

A Numerical Example on Corporate Tax Cuts and Wage Increases

Economics 7 Comments

In my last post I mentioned that a lot of economists are puzzled that corporations are announcing wage hikes right when the tax cut goes through. I’ve now jotted down some numbers to show exactly what I mean.

But before I dive in, let me say what I think the fundamental problem is: The way professional economists (especially in academia) think about firms and production, there is no corporate net income. So it shouldn’t be surprising if they miss what may seem obvious to the layperson.

(Let me stress again that I’m not making fun of the economists here. These are all really smart people. I’m pointing out that standard models of perfect competition with “zero profit” don’t typically include the explicit earning of interest as a return to financial capital. Instead, interest is conceived as a return to the physical productivity of capital equipment. I’ve mentioned this problem before, when I was trying to help some Texas Tech students get ready for their first-year qualifying exams.)

So my “take” here is to ask: Why do corporations need net income in the first place? It’s because the shareholders need a return on their invested equity. If they thought they would get a 0% return, then they’d be better off putting their funds in bonds.

You can either think of it as a very short-term thing, where there is no such thing as pure arbitrage. No matter what the corporation invests in, there’s a chance it will fail. So ex ante, the corporation needs to expect to earn a positive return, even for a timeless transaction. Competition *won’t* drive revenues down to explicit out of pocket costs for factors.

Or, you can think of it with certainty, but then you need to include the time element. That’s what I’ll do here. (And someone tell me if you think I’m botching how accountants in the real world would handle this type of calculation vis-a-vis the tax authorities.)

So, suppose there’s no corporate tax. There’s constant returns to scale. There is just one input, labor. If a corporation pays a wage w, it gets an intermediate product, and then it takes 12 months to market and finally sell it for $110 to the final consumer.

If we suppose that the shareholders require a 10% return on their equity, then in equilibrium it must be that the wage is $100. The corporation would report (right?) net income of $10 for each unit produced. But we economists would say, “That’s not pure profit, that’s just accounting profit. It’s the interest return on invested financial capital.”

OK what if the corporate tax rate is 35%? Then the wage paid is about $95 (rounding down). The product sells for $110, so before-tax net income is $15. But the corporation only keeps 65% of it, i.e. $9.75. And a $9.75 interest earning on the invested $95 works out to a 10.3% rate of return.

Now what if they lower the corporate tax rate to 21%? Then the wage paid jumps to $98 (rounding up). The product sells for $110, so before-tax net income is $12. The corporation keeps 79% of it, i.e. $9.48. That’s a 9.7% rate of return.

So, if you are OK with my rounding to the nearest dollar, we see that cutting the corporate income tax rate from 35% to 21% immediately boosts wages by $3/$95 = 3%. This has nothing to do with investing in physical capital equipment and boosting productivity. This is just the new equilibrium wage needed to keep the rate of return on shareholder equity the same.

What am I missing, friends?

7 Responses to “A Numerical Example on Corporate Tax Cuts and Wage Increases”

  1. Harold says:

    Some thoughts. Both arguments appear sound at first glance, which is interesting if not very helpful.

    My (limited) experience is that when common sense arguments come against economic models, the models are right IF we accept the assumptions. You have offered another model which is apparently at odds with models generally used by economists.

    In your 100% example,” I think I can come up with a pretty standard neoclassical model in which corporations don’t want to hire workers…”

    Is there a distinction between number of workers and pay rates? There may be fewer employees, but this is not the same as wages going down. In the articles it was pointed out that Wal-Mart “also announced plans to cut roughly 10,000 jobs by closing about 10% of its 660 U.S. Sam’s Club warehouse stores….” so there is not necessarily a net gain t workers in these wage hikes. This distinction may be critical – are we talking about wage rates or total wages paid to workers?

    As I said, economic models are often accurate if we accept the assumptions. In your model an assumption is that there is only one input, labor, so the owners have nowhere else to spend their money. Say we introduce some machines as well, does your analysis then look more like the other one? The owners can either spend it on paying labor more, which will bring them no more returns, or on better machines, which will increase their profits.

  2. Transformer says:

    I’m not getting why the wage rate has to jump immediately. In the short term the value of share holder equity could increase to maintain the 10% return, or the return could temporarily go above 10% until market forces take things back to equilibrium.

    • Transformer says:

      But I do agree that the market forces that eventually raise wages do not necessarily have anything to do with investing in physical capital equipment and/or boosting productivity.

  3. DZ says:

    Presumably you’re inferring that once taxes fall, above-equilibrium equity returns will attract market participants to that industry, bidding up wages and returning equity returns to equilibrium. However if the tax rate falls for _all_ industries, there’s no incentive for market participants to shift from industry to industry…meaning increased investment will have to either be from foreign investment or from individuals choosing to save more instead of consume. If it’s a closed economy, the latter is the only option i.e. for lower taxes (and the consequent higher returns) to result in increased saving…which isn’t entirely intuitive to me.

  4. Bob Murphy says:

    You guys are right that I’m building in assumptions about elasticity etc. You’re right, we could imagine that since the US is huge, in the new equilibrium the after-tax rate of return rises somewhat, drawing forth more savings, and that workers’ wages aren’t as much higher as my initial calculations suggested, but that the higher quantity of labor employed also translates into higher output and lower unit prices for consumers too.

    But, I was just trying to isolate the fact that there could easily be an immediate reaction in factor prices to the corporate tax cut. You don’t need to rely solely on the mechanism of increased investment leading to higher productivity of labor.

  5. Tel says:

    If we suppose that the shareholders require a 10% return on their equity, then in equilibrium it must be that the wage is $100. The corporation would report (right?) net income of $10 for each unit produced. But we economists would say, “That’s not pure profit, that’s just accounting profit. It’s the interest return on invested financial capital.”

    This doesn’t seem quite right, because a given investment decision is irrevocable even after new information becomes available later … for example, suppose a company issues additional shares to raise money to build a new factory. A shareholder buys the shares with the expectation of a 10% return, and the factory gets built.

    Well now the building is completed, new information comes along… and it turns out there’s a windfall gain because for whatever reason this factory produces much more than expected. The shareholder might be in a position to demand 13% return, even though previously they would have settled for 10%. Having a time preference of 10% does not imply you would decline to pick up a dollar left lying on the table.

    Generally the price of those shares will go up and shareholders will receive a capital gain so that if sold on the open market the return looks like 10% again, but if the original shareholder refuses to sell (therefore never realizes the capital gain) they end up with a 13% return, which was better than originally expected.

    These shareholders could of course decide to offer the windfall gain to the employees, but it seems to me that only the competitive pressure of new capital investments and more factories being built by other people would put pressure on the shareholders to go back to accepting a 10% return.

  6. Khodge says:

    One thing that is missing, but suggested in your analysis and maybe not relevant, is that the bonus is spread out through whichever year it is paid so it looks, to the employee, like a single lump sum but to the company as 4 quarters of salary.

    I think this may be in your post but I’m not sure: a bonus rushed through at the end of the year (again, possibly accrued back to last year if early this year) would be used to reduce income for last year’s taxes, lowering the tax rate in what may have been a very profitability year. (Without having read the argument by the referenced economists, I would guess this was where their arguments were going.)

    I would suspect that the answer would be in knowing the size of the companies giving the bonus…if it is large to medium size, we are talking about barriers to entry, much like those same companies pushing for an increase in the minimum wage.

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