The law of variable proportions states that when one variable input is increased while other inputs are held fixed, marginal productivity initially increases but eventually decreases. It assumes technology remains constant and one input can vary while others are fixed. Marginal productivity rises until the third worker is added, then falls, reaching zero at the sixth worker and becoming negative at the seventh worker. The law has three stages: increasing returns as marginal exceeds average productivity, diminishing returns as both fall but remain positive, and negative returns as marginal productivity declines below zero.