The main assumptions that imply that individual firms in perfect competition are price takers are: assumption of homogenous products, existence of many sellers non of whom has preferential treatment in the market, and assumption of perfect knowledge in the market.
Homogenous goods - the assumption of the existence of homogenous goods in the market implies that products are perfect substitutes. As a result, demand is perfectly elastic. This means that no firm has market power over its products leading to individual firms being price takers.
Many sellers in the market - each individual firm is very small and hence contributes only a small percentage to the total industry output. This means that no firm has power to influence market supply by altering its output. As a result, individual firms have no power to influence the prevailing market price leading to them becoming price takers.
Perfect knowledge - absence of information assymetries means firms possess perfect knowledge about their competitors, their products, and prices they charge. All firms possess equal information concerning how products are manufactured. This leads to product homogeneity and hence existence of perfect substitutes. More so, buyers also know all the suppliers; the products they sell and their prices since information search costs are zero. As a result, firms face a perfectly elastic demand curve where sales fall to zero if price slightly incresease, and the reduction of price is non profitable as each firm can sell an infinite output at the ongoing market price. Eventually, all firms become price takers.
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