Introduction The table shows the demand schedule of a monopolist, presenting a clear relationship between price and quantity demanded. This simple yet powerful tool allows the monopolist to forecast revenue, evaluate market power, and ultimately determine the profit‑maximizing output level. By examining the numbers in the table, we can see how changes in price influence consumer behavior, how total revenue varies across different price points, and why the monopolist must consider marginal revenue when making production decisions. Understanding this demand schedule is essential for anyone studying monopoly theory, pricing strategy, or welfare economics, as it forms the foundation for analyzing market outcomes and policy implications.
Understanding the Demand Schedule
A demand schedule lists the quantities of a product that consumers are willing to purchase at various prices, holding all other factors constant (ceteris paribus). For a monopolist, the schedule is especially important because the firm faces the entire market demand curve, unlike firms in perfect competition that face a horizontal price line.
Key points to notice in the table:
- Inverse relationship: As price falls, quantity demanded rises, reflecting the law of demand.
- Linear pattern: The example table assumes a constant slope, which simplifies calculations but is not required in real markets.
- Price elasticity: The steepness of the schedule indicates how responsive quantity is to price changes. A steep schedule suggests inelastic demand, while a flatter schedule points to elasticity.
Italic terms such as ceteris paribus and elastic help convey the nuances of consumer behavior without breaking the flow of the explanation That alone is useful..
Steps to Analyze the Demand Schedule
To extract the maximum insight from the table, follow these systematic steps:
- List price‑quantity pairs – Write down each price level and its corresponding quantity, as shown in the table.
- Calculate total revenue (TR) – Multiply price by quantity for each pair (TR = P × Q). This yields a new column that shows how revenue changes with price.
- Derive marginal revenue (MR) – Compute the change in total revenue when quantity changes by one unit (ΔTR/ΔQ). Because the demand curve is downward sloping, MR will be negative and will fall faster than price.
- Identify marginal cost (MC) – Assume the monopolist’s cost structure is given (e.g., constant MC = $4). If costs vary with output, calculate the appropriate MC for each quantity level.
- Set MR = MC – The profit‑maximizing condition for a monopolist is that marginal revenue equals marginal cost. Locate the quantity where this equality holds.
- Determine the optimal price – Plug the optimal quantity back into the original demand schedule to find the price that maximizes profit.
These steps are illustrated with a simple numerical example using the table below:
| Price | Quantity | Total Revenue (TR) | Marginal Revenue (MR) |
|---|---|---|---|
| $10 | 100 | $1,000 | — |
| $9 | 150 | $1,350 | $350 |
| $8 | 200 | $1,600 | $250 |
| $7 | 250 | $1,750 | $150 |
| $6 | 300 | $1,800 | $50 |
| $5 | 350 | $1,750 | –$50 |
| $4 | 400 | $1,600 | –$150 |
| $3 | 450 | $1,350 | –$250 |
| $2 | 500 | $1,000 | –$350 |
| $1 | 550 | $550 | –$450 |
In this illustration, MR equals MC (assuming MC = $50) at a quantity of 300 units, implying a profit‑maximizing price of $6 Simple, but easy to overlook..
Scientific Explanation
The relationship between marginal revenue and price stems from the law of diminishing marginal returns. As the monopolist sells additional units, each extra unit must be sold at a lower price to attract more buyers, which reduces the revenue gained from previously sold units. As a result, the MR curve is steeper than the demand curve Worth keeping that in mind..
Mathematically, if the demand function is Q = a – bP, the inverse demand is P = (a – Q)/b. Total revenue is *TR = P × Q = (aQ – Q²
