In neoclassical macroeconomic models that assume perfect competition, there can in the long run be no such thing as profit — defined as revenue left over after all costs have been subtracted.
Clearly, in the real world where many businesses have lived and died profitably there is no such thing as perfect competition, and therefore the neoclassical models that treat profit as a short-run anomaly are working from an unrealistic assumption.
My definition of profit is that profit is what happens when a business’s input transactions are priced less than its output transactions. That is, the sum of the cost of a business’s inputs from those it buys is transacted for a lower price than the sum of those it sells its goods and services to. Because transactions are assumed to be voluntary — and when they are not voluntary, any residual gain is theft, not profit — and businesses are assumed to try to negotiate the best price in both inputs and outputs, any profit is due to those who purchase the business’s output valuing the output higher than those who sold the business its inputs. That an output or input transactor would accept a profit-creating price could be for any number of perceived reasons: convenience, or expertise, or prestige, or necessity, or even outright trickery. Their decision to accept the price is subject to their own subjective valuation, and it is the difference between prices that creates the profit.
Marx and Lenin represented this idea as surplus value; that businesses make a profit by extracting uncompensated labour value out of their workers. But why not the other transactors? In my view, profit is derived from the sum of the business’s transactions with all of its transactors: consumers, supplies, labour (etc). Workers (etc) cannot extract a greater share of the firm’s revenue than they can negotiate, and at various points in history (including the present day) the working class seems to have had little real leverage for negotiation.
In my view, any model that attempts to represent real world markets should begin from the historical fact of profit and loss, and the historical fact of a disequilibrium between input transactions and output transactions.