In a perfectly competitive market, a firm's demand curve is perfectly elastic.
As mentioned above, the perfect competition model, if interpreted as applying also to short-period or very-short-period behaviour, is approximated only by markets of homogeneous products produced and purchased by very many sellers and buyers, usually organized markets for agricultural products or raw materials. In real-world markets, assumptions such as perfect information cannot be verified and are only approximated in organized double-auction markets where most agents wait and observe the behaviour of prices before deciding to exchange (but in the long-period interpretation perfect information is not necessary, the analysis only aims at determining the average around which market prices gravitate, and for gravitation to operate one does not need perfect information).
In the absence of externalities and public goods, perfectly competitive equilibria are Pareto-efficient, i.e. no improvement in the utility of a consumer is possible without a worsening of the utility of some other consumer. This is called the First Theorem of Welfare Economics. The basic reason is that no productive factor with a non-zero marginal product is left unutilized, and the units of each factor are so allocated as to yield the same indirect marginal utility in all uses, a basic efficiency condition (if this indirect marginal utility were higher in one use than in other ones, a Pareto improvement could be achieved by transferring a small amount of the factor to the use where it yields a higher marginal utility).
A simple proof assuming differentiable utility functions and production functions is the following. Let wj be the 'price' (the rental) of a certain factor j, let MPj1 and MPj2 be its marginal product in the production of goods 1 and 2, and let p1 and p2 be these goods' prices. In equilibrium these prices must equal the respective marginal costs MC1 and MC2; remember that marginal cost equals factor 'price' divided by factor marginal productivity (because increasing the production of good by one very small unit through an increase of the employment of factor j requires increasing the factor employment by 1/MPji and thus increasing the cost by wj/MPji, and through the condition of cost minimization that marginal products must be proportional to factor 'prices' it can be shown that the cost increase is the same if the output increase is obtained by optimally varying all factors). Optimal factor employment by a price-taking firm requires equality of factor rental and factor marginal revenue product, wj=piMPji, so we obtain p1=MC1=wj/MPj1, p2=MCj2=wj/MPj2.
Now choose any consumer purchasing both goods, and measure his utility in such units that in equilibrium his marginal utility of money (the increase in utility due to the last unit of money spent on each good), MU1/p1=MU2/p2, is 1. Then p1=MU1, p2=MU2. The indirect marginal utility of the factor is the increase in the utility of our consumer achieved by an increase in the employment of the factor by one (very small) unit; this increase in utility through allocating the small increase in factor utilization to good 1 is MPj1MU1=MPj1p1=wj, and through allocating it to good 2 it is MPj2MU2=MPj2p2=wj again. With our choice of units the marginal utility of the amount of the factor consumed directly by the optimizing consumer is again w, so the amount supplied of the factor too satisfies the condition of optimal allocation.
Monopoly violates this optimal allocation condition, because in a monopolized industry market price is above marginal cost, and this means that factors are underutilized in the monopolized industry, they have a higher indirect marginal utility than in their uses in competitive industries. Of course this theorem is considered irrelevant by economists who do not believe that general equilibrium theory correctly predicts the functioning of market economies; but it is given great importance by neoclassical economists and it is the theoretical reason given by them for combating monopolies and for antitrust legislation.
Read more about this topic: Atomistic Market
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