“Introduction to Post-Keynesian Economics”, part 3: Growth Models

Jacob Keegan
10 min readNov 28, 2021

Today, we’ll finish off the book by covering chapter 5 and the conclusion. The previous two chapters can be found here.

Chapter 5. The Long Period: Old and New Growth Models

5.1 The Old Post-Keynesian Growth Models

Post-Keynesians are well known for their models of growth, first developed by Cambridge economists Kaldor and Robinson in 1956. To examine these models, we’ll need some definitions. K is the capital stock, the growth rate g = I/K, and the profit rate r = P/K. Next, we refer back to Kalecki’s profit equation from last chapter.

This last equation is known as the Cambridge savings equation. The mirror image of this is, of course, an equation for the growth of investment. Per Robinson, that equation is:

Where the last variable is the expected rate of profit, and the β coefficient decreases as the expected rate of profit increases. We can combine these two equations in the graph below:

Note the intersections of the original curves at L and H. Which of these in a stable equilibrium? Consider an arbitrary growth rate g_0 that is less than g_h*. As you can see from the graph, at this value the realized profit rate r_0 is greater than the expected profit rate. So in the next period, the expected profit rate and therefore the growth of investment is higher. This continues until H is reached, where expectations align with reality.

Next, let’s examine whether the paradox of thrift is preserved in the long run. A decrease in the propensity to save flattens the growth of savings curve, as shown by the dotted line on the graph. This establishes a new stable equilibrium, H’, which is clearly greater than H. So, the paradox is maintained: lower savings leads to higher growth and output.

One feature of these old models is questioned by Kaleckians and Sraffians: the implied positive relationship between the profit rate r and the costing margin θ or Θ [see part 1 here]. Post-Keynesians like Eichner and Wood justified this relationship by arguing that leading firms would increase the costing margin when higher growth was expected. But a higher costing margin means lower real wages. This negative relationship between real wages and growth is exactly what the Kaleckians and Sraffians reject.

In addition, Kaldor and Robinson’s model assumes no change in utilization rates in the long run. So, any adjustments between supply and demand are done through prices and costing margins, not quantities. This is in contrast to Keynes and Kalecki’s ideas on effective demand. So, new growth models were developed, often called Kaleckian growth models.

5.2 The new Kaleckian model

In these newer models founded on the principle of effective demand, the profit rate is exogenous instead of the utilization rate. All adjustments are now done through quantities. Say there’s an increase in aggregate income, either from higher capitalist consumption or higher real wages. As discussed in the previous chapter, this will increase output, and therefore capacity utilization in the short term. Capitalists will then increase investment in order to counteract the decrease in spare capacity. In short, higher effective demand leads to an increase in the growth rate in the long run. And as we’ll see, on the macro level, firms will fail to bring utilization back down to normal levels in the face of this increase in aggregate demand.

Let’s examine a simple form of this model with three equations. First is the aforementioned Cambridge savings equation. Second is a new investment growth equation:

As we can see, if the utilization rate (u) equals the normal utilization rate (u_n), firms will just want to invest to keep up with the growth in sales (α). But if u is greater (less) than u_n, they will want to invest more (less) to try and return to u_n.

Lastly is the following equation for the rate of profit:

Substituting this profit equation into the Cambridge savings equation, we also have a new savings growth equation in terms of utilization:

Say we start at an equilibrium growth rate g_0*. What is the long-run effect of a higher real wage, keeping productivity constant? Such an increase would require a decrease in the markup, and therefore in the profit share. The savings function above would also decrease, as depicted below by moving from the solid to the dotted line.

At first, growth would remain at g_0*. But with higher real wages comes higher sales, which firms will respond to with increased investment, moving the growth rate to g_1* at a higher rate of utilization. Recall also that only capitalists save here: so if the profit share decreases, then aggregate savings decreases. Yet, we’ve now seen that total output goes up. So, the paradox of thrift exists in this model.

Note that we can also combine the investment and Cambridge savings equations to get the effective demand profit rate: the profit rate at equilibrium.

As we have shown, higher real wages lead to a higher utilization rate in the long run. So, the denominator of this equation increases. We have a version of the paradox of costs in this model too: higher real wages lead to a HIGHER profit rate by inducing investment, though the profit share goes down.

The existence of these paradoxes “underline the shortcomings of an analysis that would rely solely on individual behaviour within microeconomic markets, while ignoring their macroeconomic consequences.” A single firm decreasing real wages increases their profit rates: but this doesn’t work for the economy as a whole.

5.3 Extensions and criticism of the Kaleckian model

The Kaleckian model above doesn’t have much of a role for supply-side conditions, so we’ll examine them in this section. Let’s discuss the natural growth rate: the sum of the rate of technical progress plus the labor force growth rate. If the natural growth rate is less (or greater) than the real growth rate, then unemployment will continuously increase (or decrease). Yet in the Kaleckian model, real growth rates reach an equilibrium independent of the natural growth rate. Yet in the real world, unemployment doesn’t continually increase or decrease. So, the model is incomplete.

Kaleckians have two responses to this. First is to argue that profit margins are endogenous to labor bargaining power, and that such power increases (or decreases) when the unemployment rate is low (or high). This fact can push the real growth rate to the natural growth rate. The second is more radical, arguing that the natural growth rate itself is an endogenous variable, ultimately dependent on effective demand. This means it is affected by hysteresis: the actual state of demand today will permanently alter the natural growth rate in the future.

What mechanisms can cause this endogeneity? First, a strong economy can increase the labor force participation rate, as employers desperate for workers increase pay and drop job requirements, enticing new folks into the workforce. Second, technical progress could also increase quicker: perhaps due to economies of scale, or increased investment leading to more innovation. This effect is called Verdoorn’s Law. [Empirically, a 10% increase in production is associated with a 4.5%–5% increase in productivity.] Given a constant markup, higher productivity means higher real wages. So, increasing real wages have even more beneficial long-term results than previously discussed.

“Contrary to neoclassical theory, and contrary in fact to what many Marxists and classical economists claim, there is no necessary inverse relationship between real wages and profit rates” in the Kaleckian model. Wage increases instead lead to increased profits, as growth is wage-led. But many Sraffian and Marxist economists dispute this, arguing that investment depends not only on the utilization rate, but also the profit share or the normal profit rate r_n. This would mean that the increase in consumption from higher real wages is offset to some extent by lower investment. In fact, it may offset the effect entirely, in which case an economy would be profit-led instead. To be clear, the paradox of thrift is still preserved: but the paradox of costs only holds for some values, depending on the effect of changes in real wages and profits on aggregate demand.

The Kaleckian model implicitly assumes a closed economy. Let’s relax that assumption, and examine a country’s balance of payments (BoP): the difference between all money flowing into the country in a particular period of time, and the outflow of money to the rest of the world. This has two parts: the capital account (reflecting net wealth) and the current account (reflecting net income). Crucially, the sum of all components of the BoP must be zero. Imports decrease the current account and increase the capital account, and exports do the opposite, for example. According to economists like Harrod and Kaldor, countries could grow faster if they were not constrained by their BoP. As countries grow, demand for imports increases. If demand for exports doesn’t keep up, then a country will run a current account deficit. This could be compensated by a capital account surplus, meaning more investment flowing into a country than out of it. But this isn’t sustainable in the long run, as more and more interest and dividends will have to be paid on that investment over time. The exception to this is the US dollar: since it’s stable and easy to convert between other currencies, foreign central banks hold them to help maintain their BoP. Crucially, no interest is paid on these holdings.

Thus, in the long run, the growth rate of a country depends on import and export demand. Stated formally, we have Thirwell’s Law:

This law has been verified empirically from 1960–1990 in all countries except the USA and Japan. In the former, growth has been higher than the law would predict, due to the aforementioned unique nature of the dollar. In the latter, growth has been lower than expected, due to accumulated current account surpluses.

Note an asymmetry here: countries who start running a current account deficit must eventually curtail their demand. But in the opposite case, countries do not need to boost demand. So in total, this constraint suppresses global aggregate demand. Some have suggested that an international monetary body like the IMF should force countries running current account surpluses to boost domestic demand, thus boosting demand for imports, and lessening the current account deficits of other countries.

Besides this external constraint to growth, there is the internal constraint of inflation. Marxist economists Gérard Duménil and Dominique Lévy have constructed a variant of the Kaleckian model with this constraint that undermines both the paradox of cost and thrift. By this model, when capacity utilization exceeds the normal level, inflationary pressures result. In response, the central bank (which aims to keep inflation low) will increase the benchmark rate, and therefore increase real interest rates. Eventually, this will slow investment and therefore growth. This resurrects the neoclassical ideas of lower savings leading to lower investment. But recall the cost curves from chapter 2: a higher utilization rate only means higher costs when a firm moves past full capacity, NOT normal capacity. Beyond that, Verdoon’s Law helps to offset any inflationary pressure from high demand.

Post-Keynesians instead believe that inflation is mainly the result of class conflict between workers, rentiers, and entrepreneurs over the distribution of income. For example, high profit rates may lead unions to demand larger wage increases, especially if growth is strong and unemployment is low. But given the proper bargaining institutions, high growth need not mean high inflation. Also, recall that post-Keynesians support buffer stock programs to keep prices on raw materials steady, since they do not face constant average costs. In short, “inflation is far from being inevitable; it is the unfortunate result of inefficient institutions”.

6. General Conclusions

Post-Keynesians believe capitalism by itself fosters waste, instability, unemployment, and low aggregate demand. Contrary to mainstream stories, this is not due to regulation, a lack of competition, or price stickiness. In fact, administered prices, norms, and legislation (like capital controls) actually help stabilize the economy. But many post-Keynesians, like Keynes himself, believe capitalism can be efficient if buttressed by a state that provides infrastructure, public services, and helps equalize the income distribution while boosting aggregate demand.

Cutting aggregate demand through austerity is simply no good way to manage an economy, even in the short run. Because of hysteresis, it will have permanent negative effects. “It is time to reverse the priorities of most governments and central banks, by making full employment — instead of inflation — the main priority.”

That being said, post-Keynesians do still care about inflation, they simply have different policies to address it while maintaining full employment. Some support permanent income policies. Some instead favor an employment buffer-stock, also known as a job guarantee. Under such a program, the central government would employ anyone who wants to work, but can’t find a private sector job, at a set wage.