Swayamsiddha Sarangi

This paper is an attempt to use Input-Output matrices for the US economy for 2012 and discuss some unresolved questions with regards to Brody’s conjecture on convergence and linearity of wage profit curves (one of the components of the Cambridge Capital Controversy). I use data from 2012, Industry by Industry Total Requirements table at 3 levels of aggregation : 15 industries, 71 industries and 405 industries for the findings
in this paper. The observations suggest : 1) Brody’s conjecture about the convergence of subdominant eigenvalues as matrix size increases are not observed when real Input Output data is used, rather the relative size of second eigenvalues increases with increase in the size of the matrix. 2) The distribution of eigenvalues is closely approximated as
an exponential distribution 3) As the size of the matrix increases, more number of zero subdominant eigenvalues are observed, which provides a reason to expect wage profit curves to be linear.