My last post was on the false trade-off between social policies and growth. In particular, I took a shot at an essay by Michael Strain, but his essay is simply a good example of an argument that gets made very often: social policies will lower growth. I said this was wrong, and a number of responses I got questioned my reasoning. So this post is meant to spell out the logic more clearly, and point out why precisely I think that Strain's argument (and others like it) is flawed. Consider this an uber-response to comments on the site, some e-mails I got, and the discussion I had with my neighbor (who probably won't read this, but whatever).

First, we need to be clear that we have to distinguish the effect of social policies on innovation from the effect of social policies on growth in GDP. They need not be identical, which I'll get too in more detail below. So to begin, let's think about the effect of these policies on innovation, which is what Strain and others acknowledge is the source of improvements in living standards.

I'm an economist, so I think of the flow of innovations as responding to incentives. When the value of coming up with a new idea goes up, we get more new ideas. Simple as that.

What's the value of an idea? That depends on the flow of net profits that it generates. The profits of owning an idea are

$$\pi = (1-\tau)(\mu-1)wQ$$

where ${\tau}$ is the tax rate'', and this tax rate is meant to capture both formal taxation and any other frictions that limit profits (e.g. regulations).

${\mu>1}$ is the markup that the owner can charge over marginal cost for their idea. ${(\mu-1)>0}$ is therefore the difference between price and marginal cost. The more indispensable your idea, the higher the markup you can charge. For instance, there are big markups on many heart medications because your demand for them is pretty inelastic. The markup on a new type of LCD TV is very low because there are lots and lots of almost identical substitutes.

${w}$ is the marginal cost, which here we can think of as the wage rate you pay to run the business that produces the good or service based on your idea. ${Q}$ is the number of units'' of the idea that you sell (pills or TVs or whatever). Together, ${wQ}$ represents market size''. If the wage rate or quantity purchased go up, then your absolute profits rise. The effect of ${Q}$ makes sense, but why do profits rise when wages rise? Because of the markup. If your costs are higher, the price you can charge is higher too.

The profits from an idea are the incentive to innovate. So anything that makes ${\pi}$ goes up should generate more ideas. My issue with Michael Strain's article, and others like it, is that when they think of progressive social policy'', they think only of the cost ${\tau}$ of funding that policy. So there is a direct trade-off between funding these social policies and innovation (and possibly growth).

My point is that those social policies have direct, positive, effects on market size, ${w}$ and ${Q}$. Profits should be written as

$$\pi = (1-\tau)(\mu-1)w(\tau)Q(\tau).$$

If we raise ${\tau}$ to pay for social policies that educate people or raise their living standards, there is a positive effect on market size. The wage goes up, either directly because we have higher-skilled workers, or indirectly because they have some kind of viable outside option.

Further, the size of the market increases because people appear to have non-homothetic preferences. That is, they buy a few essential goods no matter what. They only spend money on other goods once those essentials are dealt with. With non-homothetic preferences, the distribution of income matters a lot to the size of the market for your idea. If lots of people are very poor, or if the cost of essentials is very high, then they have little or no money to spend on your idea, and ${Q}$ is small. If you provide them with more income or make essentials cheaper, they have more income to spend on your idea, and ${Q}$ goes up.

To be clear, I think that the positive effects of ${\tau}$ on ${w}$ and ${Q}$ outweigh the direct negative effect of ${\tau}$. That's what I mean when I say progressive social policies are good for innovation, and why I said that there is not a direct trade-off between funding social policies and innovation (and possibly growth).

That doesn't mean that funding social policies is always positive. There is a Laffer-curve type relationship here, and if ${\tau}$ were too high the incentives to innovate would go to zero and that would be bad. But the innovation-maximizing level of ${\tau}$ is not zero.

As an aside - there are plenty of costs that comparies or innovators have to pay that would have no direct benefit for wages or ${Q}$. Think of useless red tape regulations. I'm all for getting rid of those. But getting rid of red tape is not something that requires us to sacrifice social policies. It does not cost anything to remove red tape.

But wait, there's more. The speed of innovation in an economy - ${g_A}$ - is going to be governed by something like the following process

$$g_A = \frac{R(\pi,H)}{A^{\phi}}$$

where ${R(\pi,H)}$ is a function that describes how many resources we put towards innovation, like how much time is spent doing R&D, or how much is spent on labs. That allocation depends on profits, ${\pi}$, which dictate how lucrative it is to come up with an innovation. But it also depends on the stock of resources available to do innovation, and here I think specifically of the amount of human capital available, ${H}$. Social policies can not only raise ${\pi}$ indirectly, but can directly act to raise ${H}$. Education spending is the obvious case here. But policies that lower uncertainty (income support, health care coverage) allow people to either undertake risky innovation projects themselves, or work for those who are pursuing those projects, because they don't have to worry about what happens if the risk fails to pay off. Social policy can act directly to raise ${H}$. Which means that social policies can, for two reasons, raise the growth rate of innovation, ${g_A}$. Even if the effect on profits is zero, innovation can still rise because the stock of innovators has been increased.

Aside: The term on the bottom, ${A^{\phi}}$, is a term that captures the effect of the level of innovation, ${A}$, on the growth rate, ${g_A}$. If you are of the Chad Jones semi-endogenous growth opinion, then ${\phi>0}$, and this means that the growth rate will end up pinned down in the long run, and social policies will have a positive level effect on innovation. If you are of the opinion that ${\phi=0}$, then policies have permanent effects on the growth rate. It isn't important for my purposes which of those is right.

What does this mean for GDP growth? I said in the prior post that it isn't clear that GDP growth is the right metric. We really want to encourage innovation, not necessarily GDP growth. Why? Because growth in GDP, ${g_Y}$, is just

$$g_Y = g_A + g_{Inputs}.$$

If we raise ${g_A}$, then what happens to ${g_Y}$ depends on what happens to ${g_{Inputs}}$. We might imagine that ${g_{Inputs}}$ remains constant, so ${g_Y}$ rises when ${g_A}$ goes up. But there is no reason we couldn't have ${g_{Inputs}}$ fall while ${g_Y}$ remains constant. What if we take advantage of innovations to only work 30 hours a week? Then GDP growth could remain the same, ${g_{Inputs}}$ falls, and yet we're all better off. Or if innovation allows us to dis-invest in some capital (parking garages?) while still enjoying transportation services (self-driving cars?). GDP may not grow any faster, but we'd be better off by using fewer inputs to produce the same GDP growth rate.

The point is that the right metric for evaluating the effect of social policies is not GDP growth per se, it is the rate of innovation. It is ${g_A}$ that dictates the pace of living standard increases, not ${g_Y}$. In lots and lots of models, we presume that growth in inputs is invariable, but that doesn't mean it is how the world actually works.

Strain completely ignores the possible positive impacts of social policies on the growth of innovation, and that is what I'm saying is wrong about his essay. We can have a reasonable discussion about what the right level of ${\tau}$ is to maximize the growth rate of innovation, but that answer is not mechanically zero. There is no strict trade-off between innovation growth and social policies. Which means there is even less of a strict trade-off between GDP growth and social policies.