By analogy with household indifference curves, a short run isoprofit curve for a firm can be defined as the set of all combinations of wage rate and labor hired that yield a positive profit, so that for the short-run profit function f = P.f(L,K') - W.L - R.K' (where P.f(L,K') represents the total value product of labor for fixed capital level K', and (P,W,R) are respectively the output price, wage rate, and capital rental rate, taken as given by the firm) and fixed profit level ?', the slope of a given short-run isoprofit curve is easily shown to equal (dW/dL) where ? is constant = (VMPL - W)/L.
Given this result show how the firm's isoprofit map is positioned with respect to its short-run labor demand curve.