3. (25) Elsa and Anna are two students each considering whether to pursue a college education before entering the job market. For each worker, an education level of E = 1 indicates that she has completed college and earned a degree, while E = 0) indicates she has not. Elsa can generate VE = 36 worth of output per hour while Anna can only produce VA = 12 per hour. Obtaining a degree is costly, and the students must pay for their educations by taking out student loans that will be repaid during their working years. Elsa is a naturally capable student so the degree costs her the equivalent of CE = 18 per hour in future wages, whereas Anna struggles with her studies and must pay CA = 27 per hour. Note that their education levels do not impact their productivity. Hans is an employer who cannot observe the workers' innate abilities, but can observe their education levels. The labor market is competitive, so that Hans must always offer a wage equal to his reservation price, and thus makes zero profit. (a) (5) Suppose that Hans offers the same wage W to all workers, regardless of whether they attended college or not. What education levels do Elsa and Anna choose? What wage does Hans offer? (b) (5) Now suppose that Hans decides to offer higher wages to workers with college degrees W than to those without W. What education levels must he expect Elsa and Anna to choose in order to justify this? What wages does Hans offer? (c) (5) Show that both Elsa and Anna have an incentive to choose the education levels that match Hans' expectations. (d) (5) Now suppose that the costs of a college education fall, so that now CE = 14 for Elsa and CA = 21 for Anna. What education levels do they choose now, and what wages does Hans offer? 3. (25) Elsa and Anna are two students each considering whether to pursue a college education before entering the job market. For each worker, an education level of E = 1 indicates that she has completed college and earned a degree, while E = 0) indicates she has not. Elsa can generate VE = 36 worth of output per hour while Anna can only produce VA = 12 per hour. Obtaining a degree is costly, and the students must pay for their educations by taking out student loans that will be repaid during their working years. Elsa is a naturally capable student so the degree costs her the equivalent of CE = 18 per hour in future wages, whereas Anna struggles with her studies and must pay CA = 27 per hour. Note that their education levels do not impact their productivity. Hans is an employer who cannot observe the workers' innate abilities, but can observe their education levels. The labor market is competitive, so that Hans must always offer a wage equal to his reservation price, and thus makes zero profit. (a) (5) Suppose that Hans offers the same wage W to all workers, regardless of whether they attended college or not. What education levels do Elsa and Anna choose? What wage does Hans offer? (b) (5) Now suppose that Hans decides to offer higher wages to workers with college degrees W than to those without W. What education levels must he expect Elsa and Anna to choose in order to justify this? What wages does Hans offer? (c) (5) Show that both Elsa and Anna have an incentive to choose the education levels that match Hans' expectations. (d) (5) Now suppose that the costs of a college education fall, so that now CE = 14 for Elsa and CA = 21 for Anna. What education levels do they choose now, and what wages does Hans offer
