Which curve is rectangular hyperbola in pure monopoly?

Question

Accepted Answer

The correct option is 3:
The Average Revenue (AR) curve, also known as the demand curve for the monopoly firm, can be a rectangular hyperbola only under a very specific theoretical condition: when the Price Elasticity of Demand (PED) is equal to unity (e = 1) at all points on the curve. In a pure monopoly, Average Revenue (AR) is equal to Total Revenue (TR) divided by Quantity (Q), or P x Q / Q, which simply means AR = Price (P). If the total revenue remains constant regardless of the quantity sold, then the AR curve will trace a rectangular hyperbola. Since a rectangular hyperbola is defined by the property that the product of the x and y coordinates (P x Q = TR) is constant, this implies that Total Revenue (TR) is constant at all output levels. Although in most realistic monopoly scenarios, the AR curve is a downward-sloping straight line, the rectangular hyperbola shape is used conceptually to illustrate the special case of unit elastic demand throughout the entire curve.

The incorrect option is 1:
Average Cost (AC) typically exhibits a U-shape, reflecting the law of variable proportions and the initial benefits and eventual diminishing returns to scale. AC decreases initially due to economies of scale and then rises due to diseconomies, so it is never a rectangular hyperbola.

The incorrect option is 2:
Marginal Cost (MC) represents the change in total cost resulting from producing one extra unit. Like AC, the MC curve is generally U-shaped, often intersecting the AC curve at its minimum point. There is no economic principle in monopoly that would cause MC to be a rectangular hyperbola.

The incorrect option is 4:
Marginal Revenue (MR) is the change in total revenue from selling one more unit. In a monopoly, the MR curve always lies below the AR curve and decreases faster. Since TR must be increasing up to the point of profit maximization (where MR is positive), the MR curve cannot be a rectangular hyperbola, as that would imply a continuously constant TR.