In Chapter 22 we briefly discussed the signaling role of education—i.e. the fact that part of the..

In Chapter 22, we briefly discussed the signaling role of education—i.e. the fact that part of the reason many people get more education is not to learn more but rather to signal high productivity to potential employers (in hopes of getting a higher wage offer). We return to this in part B of this exercise in the context of incomplete information game (built on concepts from Section B of the chapter) but first consider the lack of a role or signaling in a complete information game. Throughout, suppose that there are two types of workers—type 1 workers with low productivity and type 2 workers with high productivity, with a fraction δ of all workers being type 2 and a fraction (1−δ) being type 1. Both types can earn education by expending effort, but it costs type 1 workers e to get education level e > 0 while it costs type 2 workers only e/2. An employer gets profit (2−w) if she hires a type 2worker at wage w and (1−w) if she hires a type 1worker at wage w. (Employers get zero profit if they do not hire a worker). We then assume that the worker decides in stage 1 how much education to get; then, in stage 2, he approaches two competing employers who decide simultaneously how much of a wage w to offer; and finally, in stage 3, he decides which wage offer to accept. A: Suppose first that worker productivity is directly observable by employers; i.e. firms can tell who is a type 1 and who is a type 2 worker by just looking at them. (a) Solving this game backwards, what strategy

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