Perfect competition 

A market is said to be in perfect competition when firms are price takers, i.e., when they take the price, which is unique, as given. Firms assume that the market price is independent of its own level of production. In other words, their individual decisions have no effect on the price of the product. In fact, the price results from the combined actions of all firms and all consumers. It is the result of the maximization of profits by producers and the maximization of preferences over budget sets by consumers.  

The concept of perfect competition is founded on the work of Augustin Cournot in 1838 in his Mathematical Principles of the Theory of Wealth. Cournot work sought to answer the question on how firms’ revenues are affected by the level of production. Defining profits as the difference between revenues and costs and assuming that the price is independent of the level of output, Cournot concluded that profits attained its maximum value when the price equalizes the marginal cost of production and the number of firms competing in the market is sufficiently large. Another relevant condition, first studied by William Stanley Jevons, is that all traders (suppliers and consumers) have perfect knowledge of the market, i.e., each trader knows the price offered by every other trader. Nonetheless, it was not until 1881 when Francis Edgeworth provided the first attempt to systematically and rigorously defined the concept of perfect competition in his work Mathematical Psychics. Edgeworth’s work compelled both Cournot’s and Jevons’ conditions to conjecture that a unique competitive price would emerge when the number of traders became large. 

The supply decision of a perfect competitive firm 

Since a perfect competitive firm takes decisions independent to the other firms, its maximization problem becomes: 

[Equation] 

The firm maximizes its profits, equal to revenues ([Equation]) – costs c(.). Assuming a well-defined cost function c., it is sufficient to derivate with respect to y and set the derivate equal to zero to find the level of production y that maximizes profits (this might not be the case depending on the form the cost function). The result is then that 

p = MC(y) 

Thus, a competitive firm will choose a level of output where the marginal cost is equal to the marginal revenue which, in this case, equals the price. Therefore, regardless of the price, the firm will choose the level of output where the price equals the marginal cost. In other words, the marginal cost of a competitive firm is also its supply curve.  

Adapted from Durlauf & Blume (2016), Belleflamme & Peitz​ (2015)​, and Varian ​(2014)​.