Question

Suppose the discrimination coefficient at a firm increases as the firm employs more Black workers. In particular, the discrimination coefficient is δ=0.01⋅βˉ​, where βˉ​ is the number of Black workers hired by the firm, so that the firm acts as if they face wages of w​ for white workers and wᵦ​(1+0.01βˉ​) for Black workers. Assume that the firm must employ exactly 200 workers.

If the firm ends up hiring both Black and white workers, then it will continue to do so until ww​=wb​(1+0.01βˉ​). Solve for the equilibrium number of Black workers as a function of the white-Black wage ratio.

Answer 1

To find the equilibrium number of Black workers, set the white wage equal to the Black wage and solve for the variable representing the number of Black workers hired by the firm.

Step-by-step explanation:

This question is asking to solve for the equilibrium number of Black workers as a function of the white-Black wage ratio. In this case, the discrimination coefficient is defined as δ=0.01⋅βˉ​, where βˉ​ is the number of Black workers hired by the firm. The firm acts as if they face wages of w​ for white workers and wᵦ​(1+0.01βˉ​) for Black workers. To find the equilibrium number of Black workers, we need to set the white wage (w​) equal to the Black wage (wᵦ​(1+0.01βˉ​)).

Therefore, we have the equation ww​=wb​(1+0.01βˉ​), where ww​ represents the white wage, wb​ represents the Black wage, and βˉ​ represents the number of Black workers hired by the firm. Solving for βˉ​, we have βˉ​=100(wᵦ​-w​)/wᵦ​. This equation gives us the equilibrium number of Black workers as a function of the white-Black wage ratio.