The Short-Run Supply Curve for an Individual Firm

In the short run, firms face two types of costs: fixed costs (FC), incurred by the firm at any level of output, and variable costs (VC), which vary with the level of output. Added together, FC and VC equal total costs (TC). Marginal costs (MC) are the costs of producing an additional unit, measured by the change in TC divided by the change in output. MC decrease initially, then increase with the level of output in accordance with the law of diminishing returns, which holds that additional output decreases as more of one input is added and other inputs are held constant. Because adding inputs costs money, increasing output becomes increasingly costly.

Say someone wants to open a donut factory. First he needs to purchase a building and all the necessary equipment – the FC. To begin production, he has to buy donut materials, such as sugar, icing, etc., and hire a worker to make the donuts – the VC. Initially, MC are low. The owner already has the building and equipment, and pays a small additional amount for a worker and materials. As production rises, the worker can produce donuts efficiently for 8 hours per day. To further increase production, the owner may decide to hire more workers. At first, two workers work more efficiently together than one worker by himself, because two workers can divide the donut-making process into specialized tasks. Eventually, however, if the owner hires too many workers, they get in each others’ way because they all have to share the same equipment and space. Albeit paid the same as the first two workers, each additional worker produces less efficiently. As a result, the costs of producing additional donuts – the MC – increase.

If one graphed the number of donuts produced and the MC of producing the donuts, with the quantity of donuts on the x-axis and the MC of production on the y-axis, the graph would look like a supply curve – the only difference being that a supply curve would have price (P) instead of MC. The profit-maximizing donut factory owner is only willing to produce donuts at a level of output where P is equal to or greater than MC. Therefore, by substituting P for MC on the graph, one can get a good idea of the donut firm’s supply curve. Regardless of the market structure, all firms maximize profits at the output level where MC equals marginal revenue (MR) – the additional revenue a firm receives from selling an additional unit.

At the donut factory, MC decrease and profits rise after adding the second worker, motivating the owner to hire more workers. On adding too many workers, however, output starts to slow and MC exceed MR; to reverse that trend and maximize profits, the firm cuts back on its donut output by reducing VC, i.e., the number of workers. By definition, average revenue (AR) is the P per unit. In a perfectly competitive market, AR and MR are the same because P is constant – firms are too small and too numerous for any one to affect the market price. Because P is always the same, incremental revenue is equal to per unit revenue. If P = AR and AR = MR, then P = MR. And if firms maximize profits where MR = MC, then in perfectly competitive markets, firms maximize profits where MC = P. As a result, the short-run supply curve for an individual profit-maximizing firm in a perfectly competitive market is exactly the same as the MC curve.

In the short run, profit-maximizing firms still produce when costs exceed revenues, as long as average variable costs (AVC) are lower than P at the profit-maximizing output level. Because firms suffer losses equal to FC if they produce no output, then as long as P is higher than a firm’s minimum AVC, the firm is better off producing because it can cover its VC and use remaining revenues to cover some FC. If P falls below the minimum AVC, however, it is more profitable not to produce, because the firm cannot cover VC at any output level. As a result, the short-run supply curve for an individual profit-maximizing firm in a perfectly competitive market is the increasing part of its short-run MC curve starting above the minimum AVC.