1. Consider a job market signaling model. A single worker can be one of two types 1 = 0L < 0H = 3 with Pr (0H) = 1/3. The worker can acquire education e, and e is observable but has no effect on productivity. c (e, 0) is cost to the worker of acquiring e units of education when he has type 0. Assume c (e, 0) = e/0. Two firms compete for the worker. If either firm employs the worker at w, it gets - w. Timeline: Stage 1. Nature chooses the worker's types. Stage 2. Worker chooses e. Stage 3. Firms simultaneously make wage offers. Stage 4. Worker then accepts the highest wage and produces. If indifferent, he chooses each firm with equal probability. (a) Separating equilibrium Find a separating equilibrium in which high type's education level is neither the minimum level for separating equilibria nor the maximum, and describe the equilibrium precisely. Explain why the separating equilibrium in which high type's education level is the minimum Pareto dominates the equilibrium above. (b) Pooling equilibrium Find a pooling equilibrium in which both types' education level is neither zero nor the maximum level for pooling equilibria, and describe the equilibrium pre- cisely. If the government bans education (no education at all), is there any Pareto improvement?