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Marginal revenue is a critical concept in understanding how firms decide on the quantity of product to sell. It represents the additional income a firm gains from selling one more unit of its product. In perfectly competitive markets, this concept becomes quite straightforward. The market sets the price, and all sellers must accept it. Therefore, for each additional unit sold by a firm, the revenue gained is the same as the market price.
In mathematical terms, marginal revenue is calculated as the change in total revenue divided by the change in quantity. However, in perfect competition, this simplifies to the market price per unit since every unit sold is added at the same price. Thus, whether a firm sells 99 or 100 units, the marginal revenue from the hundredth unit remains the same as the price per unit.
In our exercise, with a market price of $100 per unit, the marginal revenue also is $100 per unit. This understanding helps firms make informed decisions about how to maximize their profits under competitive pressures.

A price-taker, as the name suggests, is a firm that "takes" the price set by the market. This characteristic is a hallmark of perfectly competitive markets. Unlike in monopolies or oligopolies where firms can influence prices, price-takers cannot change the market price by their own actions.
There are several reasons why a firm becomes a price-taker:

• There are many buyers and sellers.
• The products sold by different firms are nearly identical.
• Information about prices is freely available, leading to uniform prices across the board.

Due to these factors, if a firm attempts to set a price higher than the market equilibrium, consumers will simply buy from competitors. This forces firms in a perfectly competitive market to accept the current market price. Being a price-taker means that the firm's individual output decisions do not affect the market price—each unit sold directly reflects the price set by the market conditions.

The market price is the price at which goods are sold in a marketplace. In perfectly competitive markets, this price is determined by the interaction of all buyers and sellers. It's where the supply and demand curves intersect, reflecting both the willingness of consumers to pay and the sellers to accept.
In our exercise, the market price is given as $100. This price also represents the marginal revenue for firms, showing how in perfectly competitive markets, these concepts overlap. This consistency happens because every firm is a price-taker, adhering to the price set by market forces.
The stability of the market price depends on several factors, including consumer preferences, production costs, and the sheer number of market participants. Hence, the market price is a crucial element, dictating the entire economic fabric of a competitive market.
Understanding the nuances of market price helps both firms and consumers navigate decisions effectively—ensuring that production matches consumer demands without excesses or shortages.