Is there a relationship between Inflation and Corporate Profits? I think so. But I do not know of anyone talking about the relationship, so I will.
The point I want to make is that corporations control prices. They set prices. They are not just price-takers. Corporations will change prices with an eye on their profits. In the aggregate, we will see changes in inflation. I will also finish by saying that the Fed feels the Fed rate can rise because firms still have a large profit cushion with which to absorb a rate increase.
Let's set up the relationship between inflation and corporate profits.
First, see corporate profits as a corporate profit rate.
Corporate profit rate = Corporate profits/GDP
Then, get a nominal interest rate.
Mixed nominal interest rate = 0.56*effective Fed rate + 0.44*10-year treasury rate
To get this equation I optimized the fit of many nominal rates to the analysis, see graph #3 below. It gives the highest R Squared for the exponential trend line in graph #3 below. (rates used were effective Fed rate and treasuries at intervals of 3 months. 1 year, 3 years, 5 years and 10 years.) The treasuries at 3 months, 1 year, 3 years and 5 years dropped out as non-influential. Only the effective Fed rate and the 10-year treasury showed influence with the coefficients in the equation, 0.56 and 0.44 respectively. I used solver in Excel to maximize the fit.
This graph compares the mixed nominal rate with the Fed rate.
I will use the orange line as the mixed nominal rate for the analysis below.
Now that we have a nominal interest rate, we need to get the real interest rate.
Real interest rate = Mixed nominal rate - inflation rate
Inflation rate = CPI without food and energy
I do not use expected inflation. As Krugman & Wells wrote in their Economics book, 2015 edition...
"The expectations of borrowers and lenders about future inflation rates are normally based on recent experience." page 729
Corporations will borrow money, lend money or simply invest their own money as long as the opportunity cost of money is covered. Of course they seek the best returns, but the opportunity cost must be covered first.
When a corporation invests money, they only need to make more than the cost of the real interest rate, which is the nominal rate minus core inflation. Here is a graph of the difference between the corporate profit rate and the real rate.
Graph #2 shows that there is normally enough of a profit rate for a positive difference in favor of corporations to beat the real rate. The Volcker recession of the 80's pushed firms to the edge so that they would slow down inflation.
Which brings us to firms controlling inflation.
When firms are pushed against the lower bound of the real rate, they will maintain enough inflation to not fall below the cost of the real rate. Inflation will actually push the real rate farther down. But there are forces that do not like inflation... namely the banks. The return on their loans will be nibbled away by inflation.
Yet if the profit return on investment starts to go below the cost of the real rate, firms will raise prices in the aggregate. We saw this happen during the Volcker recession from graph #2 where the plot did not fall much below the zero lower bound.
Yes, inflation was falling during the Volcker recession, but at a pace controlled by firms to keep their profit rates above the cost of the real rate... in the aggregate of course.
Notice in graph #2 how the profit rate has been building a bigger and bigger cushion over the cost of the real rate since the 80's. Inflation has been dropping over that time. There is less pressure over time for firms to create inflation to protect their profit rates in the aggregate. So much so, that deflation starts to come into the picture. Maybe firms have enough room to actually cut prices to gain market share and still keep a nice profit rate.
To see this another way, the next graph pulls out inflation from graph #2 and puts it on the y-axis. Corporate profit rate minus the mixed nominal rate are on the x-axis. The down-sloping straight dark red line now represents the zero lower bound of the real cost of money which was the horizontal x-axis in graph #2. So the data points want to stay to the right of the dark red straight line.
Graph #3... quarterly date since 1958. (note: The bright red exponential trend line has its R squared optimized with the coefficients for the Fed rate and 10-year treasury, 0.56 and 0.44 respectively.)
The #1 in graph #3 points to where Volcker set in motion his recession in the second half of 1980. The data points were getting ready to fall in a Southeasterly direction. But nominal rates began to rise pushing the data points to the left. Inflation did not change, but the plot moved directly toward the lower bound of the real rate. Firms began to contract. A recession started. The #2 points to where the plot fell along the real rate boundary. Profit rates held pretty steady during that time. It was the nominal interest rates and inflation that fell together at a pace to keep aggregate profit returns above the real rate boundary barely.
Now as the plot in graph #3 goes Southeast down along the real rate boundary, an economy could just slide into deflation, but it doesn't. Why? There is resistance near the 0% inflation line. Actually firms can increase their profits by going to the right away from the real cost boundary. The farther away from the real cost boundary, the more profits firms enjoy.
Ono top of that, the Federal Reserve wants to keep a 2% inflation target, which firms love. Firms are fine with a low inflation rate, but the Fed keeps dropping the Fed rate trying to get firms to raise inflation. But firms are fine with low inflation. As well, as firms stay close to the 2% inflation target, they are able to increase their profits even more.
There is a some temptation by many firms to keep prices low in order to battle for market share, but firms in the aggregate are simply enjoying very high profit rates since the crisis. But the increased relative temptation to hold down prices contributes to what seems like "stubbornly" low inflation. It's just that firms are not concerned about profits enough to raise prices.
Look at #3 in graph #3. It points to where inflation jumped up a bit . You can also see this in graph #2 where the plot went so high to a maximum at the end of 2011.
Firms may not need to raise prices; they are far from the real cost lower boundary. Yet firms can increase their profit cushion over the cost of the real rate by raising prices. It is likely that the uncertainty in 2011 and 2012 prompted firms to maximize their profit rates as much as possible. Yet, even though the uncertainty has backed off, firms are still enjoying an environment of high profit rates over the real cost of money. They have been taking advantage of the situation in my opinion.
Graph #3 implies that inflation is low because firms have much weaker price pressures with such high profit rates over the real cost of money. So it seems logical that the Fed still wants to raise the Fed rate which would still raise the Mixed nominal rate used above. Firms have lots of profit cushion to absorb the Fed rate increase.