Consider the following version of the Spence's job-market signalling model. There are two types of workers...

 

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Consider the following version of the Spence's job-market signalling model. There are two types of workers in the market: low ability workers (L-workers) and high ability workers (H-workers). The group of low ability workers makes up 80% of the work force, the group of low ability workers makes up the remaining 20%. Any firm in the market is willing to pay a wage of 50 to an L-worker and a wage of 100 to an H-worker. However no firm can directly observe which group a job applicant belongs to (i.e., ability is private information of workers).< H a. Assume that workers do not have a credible way for signalling their ability to firms, and find the wage both types will receive in this case. [20%]< b. Assume now that workers try to use education as a signal of ability. Specifically, the education attainment consists of a university degree which does not affect the productivity (ability) of any worker. To achieve a degree, an L-worker must bear a total cost C₁= 60, whilst an H-worker can achieve the degree at the lower cost CH = 55< Denote with wd and wo the wages firms would offer to a job candidate with and without a university degree, respectively. The utility of the two types of workers, with and without a degree, are provided in the table below: (i) (ii) Degree H-workers UH (Wd, CH) = Wd-CH UL (WA, CL) = Wd-CL No-degree UH (W₂) = W₂ UL (W₁) =W₁ L- workers Does there exist a separating equilibrium where H-workers achieve a university degree and use it as a signal of high ability, while the L-workers do not go to university. Explain your answer clearly [30%] If your answer to part (i) is NO, then state which constraint is violated. Assuming the firm's willingness to pay each type of worker remaining the same, propose what should change for that constraint to hold. [10%] C. Assuming all other things equal, find out the maximum cost of acquiring the degree for an H- worker such that a separating equilibrium exists? [40%] Consider the following version of the Spence's job-market signalling model. There are two types of workers in the market: low ability workers (L-workers) and high ability workers (H-workers). The group of low ability workers makes up 80% of the work force, the group of low ability workers makes up the remaining 20%. Any firm in the market is willing to pay a wage of 50 to an L-worker and a wage of 100 to an H-worker. However no firm can directly observe which group a job applicant belongs to (i.e., ability is private information of workers).< H a. Assume that workers do not have a credible way for signalling their ability to firms, and find the wage both types will receive in this case. [20%]< b. Assume now that workers try to use education as a signal of ability. Specifically, the education attainment consists of a university degree which does not affect the productivity (ability) of any worker. To achieve a degree, an L-worker must bear a total cost C₁= 60, whilst an H-worker can achieve the degree at the lower cost CH = 55< Denote with wd and wo the wages firms would offer to a job candidate with and without a university degree, respectively. The utility of the two types of workers, with and without a degree, are provided in the table below: (i) (ii) Degree H-workers UH (Wd, CH) = Wd-CH UL (WA, CL) = Wd-CL No-degree UH (W₂) = W₂ UL (W₁) =W₁ L- workers Does there exist a separating equilibrium where H-workers achieve a university degree and use it as a signal of high ability, while the L-workers do not go to university. Explain your answer clearly [30%] If your answer to part (i) is NO, then state which constraint is violated. Assuming the firm's willingness to pay each type of worker remaining the same, propose what should change for that constraint to hold. [10%] C. Assuming all other things equal, find out the maximum cost of acquiring the degree for an H- worker such that a separating equilibrium exists? [40%]

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a In the absence of a credible way for workers to signal their ability to firms both low and high ability workers will receive a wage of 50 b There do... View the full answer