Consider a labor market. There are equal numbers of two kinds of workers, alphas

Question

Consider a labor market. There are equal numbers of two kinds of workers, alphas and betas. When employed, alphas produce 8 units of output while betas produce 18 units. When unemployed, alphas earn $0 while beta earn $11. Production takes place in perfectly competitive firms who compete to hire workers (based on the expected marginal product of the workers). A worker who produces 1 unit of output would be worth wage $1.

a) Assume employers cannot determine the productivity of individual workers but do know the average productivity of the work force. What will be the wage rate and average income per worker?

b) Now suppose that at a cost of $2, betas can, if they desire, be certified as betas before entering the labor market. The process is error free, so alphas cannot be falsely certified and no beta ever fails the process. If this is common knowledge, and employers are permitted to offer different wages for certified and non-certified workers, what will be the wage rates and the average net income per worker?

c) How would the results in Part (b) change if the cost of certification were $6 rather than $2? Be sure to find all equilibria.

Explanation / Answer

a) The employers will pay workers according to the average productivity of the work force. The average productivity of the workforce is 13 units [= (8 + 18)/2]. Hence, the wage rate and average income per worker will be $13.

b) If the employers recognize the beta, they would know that the productivity of the beta is 18 units and pay then $18 of wage. The net income of beta will be $16 (= $18 - 2) in that case, because $2 is the cost they pay for certification. But since this income is higher than the income betas earn when unemployed, it is rational for all betas to get certification. So the employers will know that employees without certification are alphas and pay them only $8.

Hence, the wage rate and the average income per worker will be $8 for alphas. But for betas, the wage rate will be $18 and the average net income will be $16.

c) The net income of beta will be $12 (= $18 - 6) in this case, because $6 is the cost they pay for certification. But since this income is still higher than the income betas earn when unemployed, it is rational for all betas to get certification.

Hence, the wage rate and the average income per worker will be $8 for alphas. But for betas, the wage rate will be $18 and the average net income will be $12.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.