By bombing Iran and spreading carnage across the Middle East, the US and Israel have put the cost of living crisis back in the headlines. (Has there ever been a more dystopian phrase than ‘cost of living’?) When prices skyrocketed following Russia’s invasion of Ukraine in 2022 we were told it was a one-off; but we now know that this isn’t true. On the contrary, we appear to have entered a period of political instability characterized by high inflation. The standard explanation for inflation is that it occurs when demand for goods exceeds their supply. According to this explanation, the high inflation of recent years was caused by oil supply shocks, first by created by the war in Ukraine and now by the war in Iran. In this blog post I will examine this claim in detail.
To fix ideas, let (A,L) be a Leontief economy where A ≥ 0 is the mxm commodity input matrix and L ≥ 0 is the 1xm labour input row vector. Given scalar profit and wage rates r,w ≥ 0, the equilibrium price vector is the 1xm row vector p* satisfying p* = (1+r)(p*A+wL). Converting this into a recursive equation gives us a model of price dynamics: p’ = (1+r)(pA+wL), where p and p’ denote the price vector at the current and next time step respectively. The solution to this equation is given by: p(t) = c[(1+r)A]t + (1+r)wL[I-(1+r)A], where p(t) is the 1xm price row vector at time step t and c is a constant 1xm row vector whose elements are determined by the initial conditions. We can say that inflation occurs if the sequence {p(t)} does not converge to the equilibrium price vector p*.
According to a standard result from dynamical systems theory, the sequence {p(t)} defined by the equation above converges if and only all of the eigenvalues of the matrix (1+r)A are less than 1. (We say that the 1xm row vector v is an eigenvector of the mxm matrix M with eigenvalue e if vM = ev.) Thus, a necessary and sufficient condition for inflation to occur is that the matrix (1+r)A has at least one eigenvalue which is greater than 1. Note that this condition depends only on the commodity input matrix A and profit rate r, and not on the labour input row vector L or the wage rate w. Thus an increase in wages will increase equilibrium prices but will not result in a runaway increase in prices over time. This is one in the eye for those who wish to blame inflation on increased wages.
We can take the input-output matrix A as fixed as in generally this will change only slowly over time. Therefore, to find the cause of inflation we must examine the profit rate r. Right-multiplying the price equation by an mx1 output vector q gives: p’q = (1+r)(pA+wL)q. Rearranging gives: r = P/(pAq+wLq), where P = p’q-(pA+wL)q is the total profit. In a previous blog post I explained how total profits are determined by the so-called Kalecki profit equation: P = CP+I+N+G-TW, where CP is consumption out of profits, I is investment, N is net exports, G is government spending, and TW is taxes on wages (I have assumed zero saving out of wages, as is customary). This demonstrates that profits are determined by decisions made by capitalists (CP+I+N) and the government (G-TW).
From this we can deduce that inflation can be caused by an increase in consumption out of profits CP, investment I, net exports N, or government spending G; or a decrease in taxes on wages TW. It can also be caused by an decrease in any component of the output vector q or in the average wage w. Thus, not only will an increase in wages not result in inflation; it actually makes inflation less likely! To understand why, note that the equation r = P/(pAq+wLq) demonstrates that there is an inverse relationship between the wage rate r and the profit rate w, so when if the wage rate w goes down then, all else being equal, the profit rate r must go up. This is another one in the eye for those who wish to blame inflation on increased wages.
As I mentioned in the introduction, the increased inflation of recent years is usually blamed on oil supply shocks, first by created by the war in Ukraine and now by the war in Iran. In our framework a supply shock can be modelled as a decrease in the ‘oil’ component of the commodity output vector q. The analysis above shows that a decrease in just one component of this vector will result in an increase in the profit rate r, which in turn can be enough to mean that the largest eigenvalue of the matrix (1+r)A switches from less that to greater than 1. This explains how a supply shock in a single commodity can push the entire global economy into an inflationary spiral. Moreover, the higher the dependency on this single commodity – as specified by the matrix A – the more likely this is to happen.
The analysis above also explains why profits increase during times of crisis: namely, supply shocks automatically result in an increase in the profit rate r. This suggests that it is not (just) capitalist greed that results in increased profits during times of crisis; rather, this is something that is baked into the laws of capitalism itself. We have seen this play out in recent times with the capitalist class benefitting from the financial crisis and the COVID crisis, as well as from the wars in Ukraine and Iran. Of course, the fact that capitalists benefit from crises gives them an incentive to ensure that crises keep occurring. This demonstrates once again that we will never see true peace and stability in our world until we get rid of capitalism.
Groucho Marxism 
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