Revenue

In a perfectly competitive market, a single firm is a price taker — it can sell any quantity it wants at the fixed market price $P$. The total revenue (TR) curve in Fig. 4.1 is the simplest possible picture of this idea: it is a straight line through the origin.

The horizontal axis measures the firm’s output level, $q$. The vertical axis measures total revenue, $TR$. Because the firm sells each unit at the same price $P$, total revenue is just price times quantity:

Since $P$ is a constant, this is a linear equation of the form $y = mx$ with slope $m = P$. So the TR curve is a ray from the origin with a constant slope equal to the market price.

The textbook uses the geometry of this line to make the meaning of “slope” concrete. Pick any point $A$ on the TR curve, corresponding to output $q_1$. Draw a vertical line down from $A$ to the horizontal axis — that gives you the point $q_1$ on the output axis. The vertical distance from the origin up to $A$ is the total revenue earned at that output, $TR_1 = P \times q_1$. Now look at the right triangle formed by the origin $O$, the point $q_1$ on the axis, and the point $A$ on the curve. The slope of the TR curve is the ratio of the vertical side to the horizontal side:

But $Aq_1$ is exactly the total revenue $TR_1$, and $Oq_1$ is the output $q_1$. So the slope is $\frac{TR_1}{q_1} = P$. The slope of the TR curve at any point is the market price — and because the line is straight, this slope is the same everywhere.

The physical idea the figure teaches is this: under perfect competition, the firm’s revenue grows in exact proportion to its output. There is no discount for selling more, no premium for selling less — every extra unit adds exactly $P$ rupees to total revenue. That is why the line is straight, not curved. If the market price rises, the line becomes steeper; if it falls, the line becomes flatter. But it always remains a ray from the origin because the firm cannot influence the price.

The figure is a simple two-dimensional graph with the firm’s output (quantity) on the horizontal axis and price (or revenue per unit) on the vertical axis. A single horizontal straight line runs across the entire width of the diagram at a height equal to the market price, $p$. This line is labelled the price line (or sometimes the demand curve facing the firm). The axes are labelled “Output” and “Price”, and the line is marked with the letter $p$ at its left end to indicate its vertical intercept.

The physical idea is straightforward: in a perfectly competitive market, the firm is a price taker. It can sell any amount it chooses at the going market price, but it cannot influence that price by changing its own output. So the relationship between the price the firm receives and the quantity it sells is a constant — a flat line. No matter whether the firm produces 10 units or 10,000, each unit fetches exactly the same price $p$. The price line therefore shows that the firm’s demand curve is perfectly elastic (horizontal) at the market price.

The key formula the textbook develops from this figure is the relationship between total revenue and output. Since each unit sells at price $p$, total revenue is:

$TR = p \times q$ …