The wage of a known high-quality worker,w_h,is $10,000.The wage for a known low-quality worker,w_l,is $4,000.The share of the work force that is of high quality,s,is 0.5.For what value of the cost,c,of a college education that serves only as a signal of a high-quality worker does a pooling equilibrium exist? A) c $3,000 B) c

Question

The wage of a known high-quality worker,w_h,is $10,000.The wage for a known low-quality worker,w_l,is $4,000.The share of the work force that is of high quality,s,is 0.5.For what value of the cost,c,of a college education that serves only as a signal of a high-quality worker does a pooling equilibrium exist? A) c > $3,000 B) c < $3,000 C) c < $1,000 D) c = $2,500

Quizplus · Accepted Answer

In a pooling equilibrium, both high-quality and low-quality workers choose the same action, meaning neither type goes to college if it's used solely as a signal. For this to happen, the cost of college, c, must be high enough that high-quality workers prefer not to attend. Since the wage difference between high-quality and low-quality workers is $6,000 ($10,000 - $4,000), the cost of college must be more than half of this difference for neither type to find it beneficial to attend college to signal their quality. Therefore, c must be greater than $3,000 to prevent high-quality workers from attending college solely to signal their quality, maintaining a pooling equilibrium.

The Wage of a Known High-Quality Worker,wh,is $10,000

The Wage of a Known High-Quality Worker,w_h,is $10,000