Suppose that low-ability workers have productivity of TL, while high-ability workers have productivity of H, where...

 

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Suppose that low-ability workers have productivity of TL, while high-ability workers have productivity of H, where тн > TL· Firms can not tell low-ability workers from high-ability workers ex ante, but can observe a worker's education level e. Firms know that half of all workers are low-ability, and half are high-ability. Any worker can acquire as much education as she wishes, but getting e units of edu- cation costs a low ability worker ce², where c> 1, and costs a high-ability worker e². Assume the labor market is competitive, so that a worker earns her expected productivity. 1. Suppose TH 15, TL 1, and c = 3. Does there exist a pooling equilibrium in which both high-and low-ability workers get 1 unit of education? If so, describe a wage function and the belief system that support this equilibrium outcome. If not, explain why. = = 2. Suppose H 15, TL = 1, and c = 3. Does there exist a pooling equilibrium in which both high- and low-ability workers get 2 units of education? If so, describe a wage function and a belief system that support this equilibrium outcome. If not, explain why. 3. Supposе TH= 15, TL = 1, and c = 3. Does there exist a separating equilibrium in which high-ability worker gets 3 units of education? If so, describe a wage function and a belief system that support this equilibrium outcome. If not, explain why. 4. For general rí, TL, and c, solve for the least-cost separating equilibrium. How does the level of education obtained by the high types vary in c in this equilibrium? What is the intuition? 5. Suppose c < 1 instead. Does there exist a separating equilibrium? If yes, find the least-cost separating equilibrium. If not, explain why. Suppose that low-ability workers have productivity of TL, while high-ability workers have productivity of H, where тн > TL· Firms can not tell low-ability workers from high-ability workers ex ante, but can observe a worker's education level e. Firms know that half of all workers are low-ability, and half are high-ability. Any worker can acquire as much education as she wishes, but getting e units of edu- cation costs a low ability worker ce², where c> 1, and costs a high-ability worker e². Assume the labor market is competitive, so that a worker earns her expected productivity. 1. Suppose TH 15, TL 1, and c = 3. Does there exist a pooling equilibrium in which both high-and low-ability workers get 1 unit of education? If so, describe a wage function and the belief system that support this equilibrium outcome. If not, explain why. = = 2. Suppose H 15, TL = 1, and c = 3. Does there exist a pooling equilibrium in which both high- and low-ability workers get 2 units of education? If so, describe a wage function and a belief system that support this equilibrium outcome. If not, explain why. 3. Supposе TH= 15, TL = 1, and c = 3. Does there exist a separating equilibrium in which high-ability worker gets 3 units of education? If so, describe a wage function and a belief system that support this equilibrium outcome. If not, explain why. 4. For general rí, TL, and c, solve for the least-cost separating equilibrium. How does the level of education obtained by the high types vary in c in this equilibrium? What is the intuition? 5. Suppose c < 1 instead. Does there exist a separating equilibrium? If yes, find the least-cost separating equilibrium. If not, explain why.

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