We analyze the equilibrium spread when the transaction size of informed traders is elastic in the value of private information (α). We show that the pooling equilibrium is likely to be inefficient when trade size is sensitive to α and the inefficient equilibrium can occur before the market breaks down. The pooling equilibrium spread does not monotonically increase with α, although it increases with the elasticity of informed trades to α. The upper bound of the elasticity of informed trades for the market to remain open for the active specialist is higher than the corresponding value for the passive specialist when the specialist has enough leverage over brokers.
Kee H., Chung, and Jiang Jing. "Information-Based Trading And The Bid-Ask Spread." International Review Of Applied Financial Issues & Economics 2.2 (2010): 341-358.