The absolute value of the price elasticity of demand at the equilibrium point of a monopolist can vary depending on the specific circumstances and characteristics of the market. However, there are certain general patterns that can be observed.

Demand Elasticity and Equilibrium Point:
Demand elasticity refers to the responsiveness of quantity demanded to changes in price. It is measured by the price elasticity of demand, which is the percentage change in quantity demanded divided by the percentage change in price. In the case of a monopolist, the price elasticity of demand tends to be negative because an increase in price generally leads to a decrease in quantity demanded.

Factors Affecting Demand Elasticity:
1. Substitutability: The availability of close substitutes for a monopolist's product affects the price elasticity of demand. If there are many substitutes, consumers are more likely to switch to alternative products when the price increases, resulting in a higher price elasticity of demand.
2. Necessity vs. Luxury: If a monopolist's product is considered a necessity, consumers are less likely to reduce their demand significantly even when the price increases. On the other hand, if the product is a luxury, consumers may be more responsive to price changes, leading to a higher price elasticity of demand.
3. Time Horizon: In the short run, consumers may have limited options to adjust their consumption patterns, making demand less sensitive to price changes. In the long run, however, consumers have more flexibility, allowing for greater price elasticity of demand.
4. Market Definition: The market in which the monopolist operates also plays a role in determining demand elasticity. A monopolist may face different demand elasticity levels in different regions or market segments.

Equilibrium Point and Elasticity:
At the equilibrium point, a monopolist maximizes its profit by setting the price and quantity combination where marginal revenue equals marginal cost. This occurs when the price elasticity of demand is equal to -1, known as unitary elasticity. At this point, the percentage change in quantity demanded due to a percentage change in price is equal to -1.

Implications of Elasticity at Equilibrium:
- When the absolute value of the price elasticity of demand is less than 1 (inelastic demand), the monopolist has significant market power as consumers are less responsive to price changes. This allows the monopolist to set higher prices and earn higher profits.
- When the absolute value of the price elasticity of demand is greater than 1 (elastic demand), the monopolist faces more price sensitivity among consumers. In order to maximize profits, the monopolist may need to set lower prices, potentially leading to lower profit margins.

Therefore, the absolute value of the price elasticity of demand at the equilibrium point of a monopolist can be influenced by various factors such as the availability of substitutes, the nature of the product, the time horizon, and the market definition.