4.2 Revenue of a Firm

Why firms set the market price for their products
•In a perfectly competitive market, a firm believes that it can sell as many units of the good as it wants by setting a price less than or equal to the market price.
•Hence, there is no reason to set a price lower than the market price.
•The firm should thus desire to sell some amount of the good, the price that it sets is exactly equal to the market price.
Total Revenue
•A firm earns revenue by selling the good that it produces in the market.
     •Let the market price of a unit of the good be p.
     •Let q be the quantity of the good produced, and therefore sold
•Then, total revenue (TR) of the firm is defined as the market price of the good (p) multiplied by the firm’s output (q).
•Hence, TR = p × q
Total revenue curve of a firm
•The total revenue curve of a firm shows the relationship between the total revenue that the firm earns and the output level of the firm.   
Three observations of revenue curve 
1. When the output is zero, the total revenue of the firm is also zero. Therefore, the TR curve passes through point O.
2. The total revenue increases as the output goes up. Total revenue ‘TR = p × q’ is a straight line because p is constant.
3. The slope of the straight line is Aq1/Oq1 = p.
Average revenue ( AR )
•The average revenue ( AR ) of a firm is defined as total revenue per unit of output.
     Hence AR = TR/q
     = p q/q
     = p
•Hence, for a price-taking firm, average revenue equals the market price.
Price Line
•If we plot the average revenue for market price for different values of a firm’s output, we obtain a horizontal straight line that cuts the y-axis at a height equal to p.
•This horizontal straight line is called the price line.
•The price line shows the relationship between the market price and a firm’s output level.
•The vertical height of the price line is equal to the market price, p.
Elasticity of demand Curve
•Price Line is also the firm’s Average Revenue (AR) curve under perfect competition
•The price line also depicts the demand curve facing a firm.
•Here the demand curve is perfectly elastic.
•This means that a firm can sell as many units of the good as it wants to sell at price p. However, if it increase the price, the demand reduces to zero.
Marginal Revenue (MR)
•The marginal revenue (MR) of a firm is defined as the increase in total revenue for a unit increase in the firm’s output.
•Marginal revenue is the same as the price.
•Given the market price p,
     MR = (pq2 –pq1)/ (q2 –q1)
     = [p (q2 –q1)]/ (q2 –q1)]
     = p
•Thus, for the perfectly competitive firm, MR=AR=p
•Hence, for a price-taking firm, marginal revenue equals the market price.
Explanation of Marginal Revenue
•When a firm increases its output by one unit, this extra unit is sold at the market price.
•Hence, the firm’s increase in total revenue from the one-unit output expansion, i.e. MR is precisely the market price.

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