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The circular flow diagram, whether in its limited form in macroeconomics, or broader form in ecological economics, depicts a duality of flows – physical resources in one direction with financial transactions in the opposite. Biophysical models of the economy can be constructed based on the physical flows and their associated stocks. In previous work, I demonstrated how the accumulation of wealth – measured by the capital stock – can be established using a biophysical model. With capital, energy use, and the distribution of labour determined by biophysical economics, here I investigate the range of potential distributions of wealth – profits versus wages – that follow in the political economy. The analysis is conducted using a four-sector model of Great Britain's economy from 1760 to 1913, including agriculture, coal mining, construction & materials, and production of goods and services. Energy price is a key variable in the model, influencing the distribution of income between different sectors. Taking the price of coal at historically observed values, the distribution of total factor income per worker is plotted as a trade-off between annual wages and profits per worker for example years of 1761, 1817, and 1871. The plots reveal how possible alternative distributions of income might be achieved under different political-economic regimes, subject to the same biophysical constraints. Conclusions are framed in the context of the grand challenges faced by ecological economists of developing environmentally sustainable economies with a just and equitable sharing of resources. [Display omitted] • The paper frames the challenge of wealth distribution subject to biophysical constraints. • Prices, wages, and profits are added to a biophysical model of the Industrial Revolution. • The distribution of total factor income per worker is posed as a trade-off between wages and profits per worker. • Changes in energy price are shown to impact the distribution of income between and within sectors. • The influence of the political economy on the biophysical economy is also discussed. [ABSTRACT FROM AUTHOR]