Firm j uses labor L to produce output in amount Q according to the production function: Q=AL where A>1 is a parameter reflecting the manager's talent and (0,1) is a parameter reflecting a manager's ability to oversee workers (her "span of control"). The firm's output has a price 1 and workers receive a wage w. 1. What is unit cost? 1 2. Write down the firm's profit as a function of its choice of L and solve for the L that maximizes profit. What is its profit ? What happens to employment and profit when A increases and when w increases. 3. Solve for the value of A, called A, at which the manager's profit is the same as the wage. The economy has a unit continuum of people who can be either managers or workers. Each person has an A that represents her ability as a manager. The distribution of A in the economy is: F(a)=Pr[Aa]=1a where >0 is a parameter. People with A>A become managers, earning their profit from Question 2 , and people with A1 is a parameter reflecting the manager's talent and (0,1) is a parameter reflecting a manager's ability to oversee workers (her "span of control"). The firm's output has a price 1 and workers receive a wage w. 1. What is unit cost? 1 2. Write down the firm's profit as a function of its choice of L and solve for the L that maximizes profit. What is its profit ? What happens to employment and profit when A increases and when w increases. 3. Solve for the value of A, called A, at which the manager's profit is the same as the wage. The economy has a unit continuum of people who can be either managers or workers. Each person has an A that represents her ability as a manager. The distribution of A in the economy is: F(a)=Pr[Aa]=1a where >0 is a parameter. People with A>A become managers, earning their profit from Question 2 , and people with A