Suppose that there are three types of firms (High/Medium/Low), which are all equity financed with 1 billion shares outstanding. High/Medium/Low quality firms are worth $10 billion, $9 billion, and $8 billion, respectively. While each firms insiders (e.g., the management team) know the type of firm, outside investors do not know such information. These firms consider seasoned equity offerings to raise additional capital for their new investment opportunities.

a. Under this information asymmetry, which firm would provide a seasoned equity offering, and what price (per share) would uninformed outsiders pay for the equity offering in equilibrium? Provide your answer with reasoning.

b. To signal the quality of the firm to outside investors, each firms managers consider changing their equity holdings in the firm. Would they increase or decrease their equity holdings? If so, why?