Imagine the following signaling game:
The productivity of a given worker is drawn by nature. It can be High or Low, with p=0.5 for each. The worker, upon observing her productivity level, can decide whether to get a college degree or not. Finally, there is a firm who does not observe the workers type, but only her level of education. This firm must decide whether to hire (or not) the worker. If the firm does not hire the worker, both get a payoff of 0. If the firm hires the worker, its payoff is given by the difference between her productivity and the wage that is paid. Regarding the employee, her payoff is given by the difference between the wage she receives and the education costs. Assume that, for a high productivity worker, the productivity is 4 and the cost of a college degree is 2. For a low productivity worker, the productivity is 2, and the cost of a college degree is 4 (bear in mind that both types have an educational cost of 0 when they decide to not pursue a degree). Finally, assume that the firm pays a wage of 1 to non-educated workers, and a wage of w to educated ones. Which of the following statements is/are TRUE :

Question

Imagine the following signaling game: 
 The productivity of a given worker is drawn by nature. It can be High or Low, with p=0.5 for each. The worker, upon observing her productivity level, can decide whether to get a college degree or not. Finally, there is a firm who does not observe the workers type, but only her level of education. This firm must decide whether to hire (or not) the worker. If the firm does not hire the worker, both get a payoff of 0. If the firm hires the worker, its payoff is given by the difference between her productivity and the wage that is paid. Regarding the employee, her payoff is given by the difference between the wage she receives and the education costs. Assume that, for a high productivity worker, the productivity is 4 and the cost of a college degree is 2. For a low productivity worker, the productivity is 2, and the cost of a college degree is 4 (bear in mind that both types have an educational cost of 0 when they decide to not pursue a degree). Finally, assume that the firm pays a wage of 1 to non-educated workers, and a wage of w to educated ones. Which of the following statements is/are  TRUE :

Accepted Answer

The only possible Pooling Equilibrium requires both types of worker not to pursue a college degree

Answer

The minimum wage (w) that the firm should offer to an educated worker so that there is an equilibrium where her level of education sends an informative signal about her productivity is 2

Answer

The maximum wage (w) that the firm should offer to an educated worker so that there is an equilibrium where her level of education sends an informative signal about her productivity is 4

Answer

The only possible Pooling Equilibrium requires both types of worker to pursue a college degree

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Imagine the following signaling game: The productivity of a given worker is dr...

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