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new equilibrium wage and labor utilization

Suppose a market is characterized by a unionized and a non-unionized sector. Both sectors initially have supply given by Q=10,000+25w, and demand by Q=20,000-10w, where w is the weekly salary. Find the initial equilibrium wage and labor utilization. Now, in the unionized sector, a wage of 300 is negotiated. What is the demand and supply for labor in the unionized sector? Any surplus migrates to the uncovered sector. What is the new equilibrium wage and labor utilization in that sector?

Solution Preview

For equilibrium, 20,000-10w = 10,000+25w
Or (25 + 10)w = 20,000 - 10,000
Or 35w = 10,000, which gives w = 10,000/35 = $285.71
At w = 285.71, the demand and supply is: Q = 20,000 - 10* 285.71 = 17,142.90

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Solution Summary

What is the new equilibrium wage and labor utilization in that sector?

$2.19