TL:DR the sign is right, but the magnitude looks far too small.

Suppose that monopoly power (as measured by the markup of price over marginal cost) has been increasing over time. What effect would that increase in monopoly power have on the equilibrium (real) rate of interest?

Let's start with a very simple model. Assume a technology: C+I=Y=F(K,L) and dK/dt=I-dK, where K is the stock of capital goods measured in physical units, I is the flow of new capital goods produced, d is the physical depreciation rate, so dK/dt is net investment, L is employment, C is consumption goods produced, and Y is total goods produced.

It is important to understand that C+I=Y is not, in this case, merely an accounting identity. It is an engineering relationship that tells us that the PPF for producing capital and consumption goods is a straight line (with a slope of minus one). That's because we are measuring C and I in physical units, not in value units.

Start with perfect competition. Let the price of the consumption good be the numeraire (we set it equal to one). The linear PPF between C and I determines the price of the capital good at one. Pk=1. Profit-maximisation ensures the equilibrium (real) rental rates on labour and capital goods are equal to their marginal products: W = MPL (= dY/dL) and R = MPK (= dY/dK). And the (real) interest rate is given by: r= R/Pk - d = MPK - d.

Now introduce monopoly power, so that price is a markup m over Marginal Cost: P = (1+m)MC = (1+m)W/MPL = (1+m)R/MPK. Assume that the degree of monopoly power (and so the markup of price over marginal cost) is the same for investment goods as consumption goods, so their relative price is unaffected, and remembering that the consumption good is numeraire, we get:

W = MPL/(1+m) and R = MPK/(1+m) and r = MPK/(1+m) - d

For a given employment of capital and labour (and so a given MPK), an increase in the degree of monopoly power m across the whole economy causes a reduction in the (real) interest rate. The intuition is simple: increased monopoly power causes lower (real) rentals on capital goods (just like it causes lower (real) wages), and in equilibrium the interest rate must fall to match the lower rate of return on buying capital goods and renting them out.

Let's do a back-of-the-envelope estimate to see how big this effect might be.

Assume initially d=10%, m=0%, r=5%, so MPK=15%. To reduce r to 0%, we would need to increase m from 0% to 50%. That means it would take a very big increase in monopoly power to explain why real interest rates have fallen to near 0%.

[Update: that same increase in monopoly power would also cause (global) wages to fall by 33%, which looks implausibly large. Plus, if markups had increased by that large an amount, I think I would have heard empirical IO economists shouting it from the rooftops.]

Let's try another one. Assume there is a 5% risk-premium, so a 5% safe interest rate translates into a 10% risky interest rate from buying capital goods. So initially d=10%, m=0%, r=10%, so MKP=20%. To reduce r to 5% (so the safe interest rate falls to 0%), we would need to increase m from 0% to 33.3%. That's a little bit more plausible, but still quite large.

[Update 2: Hugo Andre in comments says that 4% is a more plausible number for depreciation than the 10% I assumed, which makes the size of the increase in monopoly power needed to get a big enough effect on interest rates even more implausibly large.]

What would it take to make the effect bigger?

1. I have done my calculations taking employment of labour and capital as given (so MPK is given).

1a. If the labour supply curve slopes up, the fall in real wages due to increased monopoly power would reduce employment of labour, reducing MPK, which would mean a bigger fall in the rate of interest. But if the labour supply curve is very inelastic, this effect will be small.

1b. If saving (and hence investment) is a positive function of the rate of interest, the fall in the rate of interest due to increased monopoly power will reduce the stock of capital over time, increasing MPK over time, which would mean a smaller fall in the rate of interest. So that effect goes the wrong way.

2. We could assume that there is a bigger increase in monopoly power in the investment goods sector than in the consumption goods sector, so that the price of capital goods rises relative to consumption goods, which would reduce the interest rate by more. But that's a purely ad hoc assumption, which I have no independent reason for believing.

3. We could relax the assumption of a linear PPF between consumption and investment goods, and replace it with the standard assumption of a curved PPF where the price of capital goods is an increasing function of investment (so the supply curve of new capital goods slopes up). If saving (and hence investment) is an increasing function of the rate of interest, a fall in the rate of interest due to increased monopoly power would reduce Pk, which would partly offset that fall in the rate of interest. So that effect goes the wrong way too.

4. ?

Hmmm. I think the answer to my question is a tentative partial "yes", but I don't think the effect of increased monopoly power is big enough to explain more than a part of the decline in equilibrium interest rates ("secular stagnation").

[Addendum: I started writing this post after reading a Mark Thoma post about a Nick Bunker post about a Dietz Vollrath post. Then I read those posts.

Dietz says: "If firms are gaining market power – meaning they can charge a higher markup – then this implies that they will use inputs less efficiently from a social perspective. Each individual firm is producing less than the amount they would under competition (with costs = marginal costs), and so we are not getting everything we can out of our inputs. If market power has increased, this exacerbates that issue, and so measured productivity – the efficiency of input use – will fall."

That is not correct in aggregate. Consider an economy that produces apples and bananas only. If apple producers gain market power, while banana producers stay competitive, so the price of apples rises relative to bananas, then it is true that too few apples and too many bananas will be produced. But if both apple and banana producers gain market power equally, then the relative price stays the same. It is true that real wages will fall, and so employment will fall too if the labour supply curve slopes up, but that says nothing about the social efficiency of production given that (inefficiently low) level of employment.

Though Dietz's main point in that post, about measured productivity growth, is I think correct and important.

Nick Bunker says: "But Vollrath’s market power explanation for falling productivity growth, alongside the falling share of national income going to wage earners, is supported by some evidence. Work by Massachusetts Institute of Technology graduate student Matt Rognlie, for example, found evidence of higher markups."

On a quick skim, the only relevant bit of Matt's paper I could find is on page 16: "The long-term U-shape in p may also indicate some changes in market power or the scope for monopoly profits. To the extent that the rents giving rise to pure profits can sometimes be shifted to workers, fluctuations in p could in principle reflect changes in worker/firm bargaining power or the role of unions. In practice, however, the U-shape path for p is difficult to interpret along these lines: p is lowest in the 1980s, a decade that certainly was not known for union strength." ("p" is supposed to be Greek "pi", or capital's share in income, and the bold emphasis was added by me.)

Let's just say "maybe" to the idea that monopoly power has been increasing over time.]