Piketty on Marx

In his new book, Piketty has a rather lucid interpretation of Marx’s hypothesized “tendency of the rate of profit to fall” that also helps illuminate his hypothesis that capital’s share of income will grow in the next century.

For Marx, the logic of capitalism would either cause the rate of profit to fall endlessly or capital to gobble up an increasing share of national income endlessly, either of which would generate political instability that would unwind the whole system.

Piketty plugs Marx’s somewhat vague prosaic presentation of this theory into the two formulas Piketty relies upon to describe the dynamics of capital.

  • β = s/g
  • α = r*β

The first formula states that, in the long run, the capital/income ratio (β) of a nation’s economy is equal to the savings rate (s) divided by the growth rate (g). By capital/income ratio, Piketty means the total level of national capital divided by the total flow of national income. A nation with $6 of total capital that has an annual national income of $1 therefore has a β of 6 (or 600%). By savings rate, Piketty means the percentage of national income added to the stock of capital each year (each period really). A nation with a national annual income of $100 that saves $12 has an s of 0.12 (or 12%). By growth rate, Piketty means growth in the national income caused both by population growth and per capita productivity growth. A nation with $100 national income one year that has $102 national income the next year, has a g of 0.02 (or 2%).

So the formula is β = s/g. If s = 12, and g = 2, then β is equal to 6. That would be the long-term capital/income ratio, which is to say this is the capital/income ratio a nation would tend towards and eventually stop at.

Piketty then uses a second formula to relate β to capital’s share of the national income. This formula states that capital’s share of the national income (α) is equal to the rate of return on capital (r) multiplied by the capital/income ratio (β). So the formula is α = r*β. If r = 0.05 (5%) and β = 6 (600%), then α is equal to 0.30 (or 30%). That is, capital’s share of the national income would be 30%. Out of every dollar of national income, 30 cents would go to capital.

To repeat:

  • β = s/g
  • α = r*β

Piketty claims that Marx’s view (along with others in the period) is that growth (g) is primarily a function of capital deepening: you get more output because you add more capital. Today, we have the concept of Total Factor Productivity that captures the fact that productivity can grow without or in excess of additional capital inputs.

But without TFP, you may believe that growth in national income would eventually run towards zero. In that zero-growth world, if savings continued to be non-zero (capitalists continued putting aside some of their income to build out more capital), then the capital/income ratio escalates towards infinity. In formula terms, since β = s/g, if g is at 0, and s is above 0, β asymptotically approaches infinity.

If β asymptotically approaches infinity, that then generates problems for the second formula α = r*β. If the capital/income ratio (β) is constantly increasing, then either the rate of return (r) will have to constantly decrease towards zero, or capital’s share of income (α) will have to constantly increase. That’s the only way to make the equation balance.

The case where r decreases to compensate is the “tendency of the rate or profit to fall” scenario. The rate of return on capital trends towards zero and that causes all sorts of political instability because of capitalists tearing each other apart to try to scratch out a return. The case where α increases to compensate is a world where capital slowly gobbles up more and more of the national income until it gobbles up all of it, a scenario which will surely generate worker revolution.

So, if we assume growth or near-zero growth will eventually result after capital deepening has essentially run its course (Piketty’s account of what Marx may have had in mind), capitalism does appear to self-destruct from internal contradictions. It is only the existence of TFP-driven growth elements that allows us to stave off this particular conclusion, something Marx would not have been aware of.

Piketty’s View
Using the concepts from above, Piketty’s own view about the future dynamics of capital becomes easy to explain.

Recall again the two formulas:

  • β = s/g
  • α = r*β

Because population growth, and catch-up growth, and recovering-from-20th-century-shocks growth will subside, the rate of growth (g) will decline, though it wont race towards zero: it will be stable, just lower. If savings (s) hold steady, that then means that the capital/income ratio (β) will increase.

Moving to the second formula (α = r*β), the operative question is how will the rate of return on capital (r) respond. As the amount of capital increases, the marginal productivity of capital will decline, meaning that r will decline. But will r decline enough to offset the increase in the capital/income ratio (β) in such a way as to keep capital’s share of income (α) from climbing? Piketty doesn’t believe so.

Therefore, a decline in growth will cause the capital/income ratio to increase, an increase which will not be totally offset by falling returns on capital. Consequently, capital’s share of total income will increase in the next century.

Piketty on Economists

From “Capital in the Twenty-First Century:”

To put it bluntly, the discipline of economics has yet to get over its childish passion for mathematics and for purely theoretical and often highly ideological speculation, at the expense of historical research and collaboration with the other social sciences. Economists are all too often preoccupied with petty mathematical problems of interest only to themselves. This obsession with mathematics is an easy way of acquiring the appearance of scientificity without having to answer the far more complex questions posed by the world we live in. There is one great advantage of being an academic economist in France: here, economists are not highly respected in the academic and intellectual world or by political and financial elites. Hence they must set aside their contempt for other disciplines and their absurd claim to greater scientific legitimacy, despite the fact that they know almost nothing about anything.

Why Not Socialism?

I have decided to begin a book recommendation series. Occasionally, I will pick a book I enjoyed — either recently or in the past — and link to it via the sidebar, as well as write a post about it. The first book is Why Not Socialism? by G.A. Cohen.

Cohen begins this very short book (really a long essay) by telling a story about a camping trip. During camping trips, he notes, individuals behave in a very socialist manner. Campers share what they bring with one another, and share equally in the fruits of their labor (e.g. fishing). If anyone were to behave differently in such a circumstance, people would think them a jerk. If, for instance, someone decided to charge the others to use their pan or their ball, nobody would find that even remotely acceptable. If someone was really good at fishing and claimed that they should get the best of the caught fish, similar disgust would follow.

After establishing this hypothetical, Cohen proceeds to use it as an expository tool to probe the desirability and viability of socialism on a larger scale. In Cohen’s view, socialism rests upon two normative principles: equality of opportunity and community. To explain the socialist sense of equality of opportunity, Cohen establishes three different types of equal opportunity: 1) bourgeois equality of opportunity, 2) left-liberal equality of opportunity, and 3) socialist equality of opportunity.

Bourgeois equality of opportunity seeks the elimination of formal and informal status restrictions that affect life chances (e.g. caste positions and race). Left-liberal equality of opportunity takes it one step further, and seeks to eliminate all circumstances of birth that affect life chances, whether they derive from birth status or from the conditions of one’s birth position. So for instance, under left-liberal equality of opportunity, an effort is made to provide extra aid to poor children because of the hardships they face.

Socialist equality of opportunity takes it one last step, and seeks to eliminate all unchosen disadvantages that affect life chances. The net result is that differences between individuals merely reflect differences in taste and choice, not inherent differences in ability, differences in birth privileges, or differences in status. This, Cohen argues, is the most preferable and just approach to equal opportunity.

It has its flaws however. For instance, it can allow for massive inequalities that result from option luck, i.e. totally fair and voluntary money gambles. This failure and others motivate Cohen’s second socialist principle: community. Community has two main elements. The first involves individuals positioning themselves such that they can relate to one another and their experiences. This necessarily prohibits massive amounts of inequality as such inequality would create gulfs in lived experiences that will make individuals unable to relate to one another. The second involves communal reciprocity in which individuals give and serve others, not for the purpose of market exchange, but because others need their help. Cohen believes both elements are essential to socialist morality.

After sketching this picture of socialist moral requirements, Cohen then turns to the more interesting question: viability. Cohen focuses heavily on the economic calculation problem. Popularized by Hayek, the economic calculation problem points out that, in addition to its other functions, market pricing is a massive informational tool. Pricing reflects the aggregate preferences of billions of individuals while also accounting for resource scarcity. Socialism, Hayek argues, has no way of doing the kind of calculating work that market prices do.

Although conceding that such a problem is real, Cohen points to a handful of market socialist systems that keep pricing in place while also achieving the kind of distributions and equality that his system prefers. These market socialist systems are not perfect, but they are, to Cohen, a big improvement.

Throughout the book, Cohen’s clarity, simplicity, and intellectual seriousness shines brightly. As in his other writing, Cohen writes with a very earnest desire for the actual achievement of socialism. As such, he takes on challenges and admits his faults, all while laying out the best case he can for the socialist vision he advocated during his later academic life.