In an economic model where the real wage required to motivate workers increases as the level of employment rises, why is an equilibrium with zero unemployment impossible?

The Impossibility of Zero Unemployment

The Inherent Unemployment Equilibrium

In an economic model where a higher real wage is required to motivate workers as employment levels rise, an equilibrium with zero unemployment is impossible because the wage needed to ensure worker effort would become infinitely high.

Evaluating a 'Zero Unemployment' Policy Proposal