Условие:
A perfectly competitive firm is willing to hire a worker. The worker can be either unskilled with the marginal productivity of а1=1 or skilled with the marginal productivity of а2=11, and his preferences over wage (w) look as follows:
𝑢𝑖(𝑤)=𝑤,𝑖∈{1,2}\nEach worker can acquire education e that is measured in years of schooling, must be an integer, and cannot affect his marginal productivity. Also, education is costly:
𝑐1(𝑒)=2𝑒,
𝑐2(𝑒)=𝑒\nThe firm cannot observe 𝑎1 and 𝑎2; however, it knows that the probability of meeting a skilled worker is 0.4.
1) Find the wage rate the firm would offer to each worker's type in the absence of asymmetric information.
2) Suppose there is asymmetric information about workers' skills, and education as a signal is not available.\nCan skilled workers benefit from asymmetric information? Can unskilled workers benefit from asymmetric information?
3) Now, workers can signal their type by acquiring education. The firm believes that all workers with 𝑒≥𝑒∗>0 are definitely skilled and their peers with 𝑒<𝑒∗ are definitely unskilled.\nIs 𝑒∗=2 a credible signal about high skills? Find the smallest value of 𝑒∗ such that unskilled workers never acquire education and skilled workers strictly prefer 𝑒=𝑒∗ to 𝑒=0.
