Give a numerical example to show that a monopolist's marginal revenue can be upward-sloping over part of its range. Hint: The price on the demand curve is the producer's average revenue
Certainly! Let's consider a hypothetical example to illustrate the concept.
Suppose we have a monopolist selling widgets in a market. This monopolist has the ability to set the price of the widgets it sells. Let's assume that the monopolist's demand curve, which represents the relationship between the price of the widget and the quantity demanded, is given by the equation P = 100 - Q, where P is the price in dollars and Q is the quantity in units.
To find the monopolist's marginal revenue, we need to calculate the change in total revenue resulting from selling one additional unit of output. Since the monopolist can influence the price, selling one more unit not only increases revenue from the sale of that unit but also affects the revenue generated from the other units sold.
To calculate the monopolist's marginal revenue at a particular quantity, we need to first find the corresponding price on the demand curve. Since the monopolist can sell any quantity at that price, the revenue from selling that additional unit would be equal to the price itself.
Let's calculate the monopolist's marginal revenue at a quantity of 50 units. According to the demand curve equation, P = 100 - 50 = 50 dollars. Therefore, selling one more widget at this quantity would generate an additional revenue of 50 dollars.
Now, let's calculate the monopolist's marginal revenue at a quantity of 40 units. The price on the demand curve would be P = 100 - 40 = 60 dollars. Selling one more widget at this quantity would lead to an additional revenue of 60 dollars.
Comparing the marginal revenue at 50 units (MR = 50 dollars) with the marginal revenue at 40 units (MR = 60 dollars), we can observe that the marginal revenue is increasing as we move from 40 units to 50 units. This demonstrates that the monopolist's marginal revenue is upward-sloping over this range.
In conclusion, by analyzing the relationship between quantity, price, and marginal revenue, we can see how a monopolist's marginal revenue can be upward-sloping over part of its range.