The relationship between marginal revenue (MR) and the slope of the revenue function is that marginal revenue is the slope of the total revenue function with respect to quantity. In other words, marginal revenue is the derivative of total revenue with respect to the quantity sold. This means MR measures how much total revenue changes when one additional unit of output is sold
. More specifically:
- If total revenue is represented as a function R(q)R(q)R(q) of quantity qqq, then marginal revenue is MR=dRdqMR=\frac{dR}{dq}MR=dqdR, the slope of the total revenue curve at any point
- For a linear demand curve, the marginal revenue curve has the same intercept but twice the slope (in absolute value) compared to the demand (or average revenue) curve. This means MR falls faster than the demand curve as quantity increases
- In perfect competition, where the firm is a price taker, the total revenue function is linear and its slope (marginal revenue) is constant and equal to the market price, so the MR curve is horizontal
- In imperfect competition or monopoly, the MR curve slopes downward and lies below the demand curve because to sell more units, the firm must lower the price on all units sold, causing MR to decline faster than price
Thus, the marginal revenue at any quantity is the instantaneous rate of change (slope) of the total revenue function at that quantity.
Summary:
- Marginal revenue = slope of total revenue function.
- MR curve is the derivative of the total revenue curve.
- For linear demand: slope of MR = 2 × slope of demand curve.
- Perfect competition: MR = price (constant slope).
- Monopoly/imperfect competition: MR slopes downward, below demand curve.
This relationship is fundamental in economics for determining optimal output and pricing decisions
