In a monopoly market structure, the relationships between Total Revenue (TR), Average Revenue (AR), and Marginal Revenue (MR) have unique characteristics. Total Revenue (TR) is the total income a firm receives from selling its goods or services, calculated as the price per unit times the number of units sold (TR = P × Q). In a monopoly, the TR curve can be nonlinear, increasing at diminishing rates due to the inelastic portion of the demand curve that the monopolist faces.

Average Revenue (AR) is the revenue earned per unit of output sold, found by dividing total revenue by the quantity sold (AR = TR/Q). The AR curve mirrors the demand curve in all market types, as price equals average revenue.

Marginal Revenue (MR) is the change in revenue that a firm earns by selling one more unit of its product (MR = ΔTR/ΔQ). Here, the MR curve slopes downwards more steeply than the AR (demand) curve. This difference arises because a monopolist must lower the price on all units sold to sell an additional unit, affecting MR more dramatically.

Relationship between AR, TR and MR is

1. When TR is increasing, MR is positive.
2. When TR is at its maximum, MR = 0
3. When TR is decreasing, MR is negative
4. MR = AR only for the first unit sold; afterwards, MR < AR

Understanding the above mentioned relationships between TR, AR, and MR curves is crucial for a monopolist's pricing and output decisions. The fact that MR < AR for a monopolist explains why they typically produce less and charge higher prices compared to firms in competitive markets.