Derive all competitive equilibria in the labor market model when 𝑟(𝜃) = 𝜃3 and 𝜃 ∈ {1,2,3} with
Prob(𝜃 = 1) = 1/2, Prob(𝜃 = 2) = Prob(𝜃 = 3) = 1/4, where 𝑟(𝜃) denotes the reservation wage of a worker with productivity 𝜃.