#### Market signaling and Educational Signaling Game model

Market signaling:

1) Education as a signal:

Market signaling is a way for sellers of a good or service to convey hidden information about quality to buyers. Let’s think about the model, where a worker’s college educational background serves as a signal of the potential quality of his work. In this model, college education has no direct impact on the worker’s productivity. High-quality workers are more productive because they are more efficient, not because they are well educated.

2) Educational Signaling Game (model):

• 1 worker and 2 prospective employers

• Nature specifies a worker as either high-quality or low-quality with probability 0.5. The worker knows her quality, but employers do not. Low-quality workers produce production q = 6.00 and high-quality workers produce production q = 16.50.

• Workers choose a level of college education. si = 1 (college) and si = 0 (no college).

• The two employers all offer the worker a wage w = (wsi)

• The worker accepts one of the two contracts or rejects both.

• w (1) = 16.50 and w(0) = 6.00

• πW = w − 72(s / q) (worker’s payoff if s/he accepts one w(si))

• πW = 0 (if worker rejects both)

• πE = q − w(employer’s payoff whose contract is accepted. Zero-profit line)

• πE = 0 (for employer whose contract is rejected)

A crucial assumption of the Spence model is that the cost of education, 72(s/q), is greater for low-quality workers (72/6 = 12) than high-quality workers (72/16.50 = 4.36). This means that high-quality workers complete school in less time than low-quality workers, and there have lower opportunity costs of education (single crossing condition or Spence-Mirrless condition).

Competition between employers ensures that firms hire workers as long as the wage equals the value of the worker’s output (wage = VMPL = p ⋅ MPL).

• Hire low-quality worker if w(si) = w(0) = qL = 6.00

• Hire high-quality worker if w(si) = w(1) = qH = 16.50

• π WL = w(0) − 0= 6. 00 − 0= 6. 00 > w(1) −72/6. 00 = 16. 50 −12 = 4. 50

(The low-quality worker is better off not going to college)

• πHW= w(0) − 0= 6. 00 − 0= 6. 00 > w(1)) −72/16.50 = 16.50 - 4. 36 = 12.14

(The high-quality worker is better off going to college)

• The equilibrium for the education game is:

s(low-quality worker) = 0; s(high-quality worker) = 1

and

w(0) = 6.00 ; w(1) = 16.50

• Only high-quality workers get an education, so employers identify the high-quality workers and pay them a wage equal to 16.50. Low-quality workers elect not to get an education, so employers identify the low-quality workers and pay them a wage equal to 6.00.

• In this game, college education seems to be wasteful, because it imposes costs on society but does nothing to increase workers’ productivity. Although this may be a disturbing conclusion, there are reasons to believe that even if a college education is only a signaling device, we are better off with a college education system.

• College facilitates us to match workers with jobs more efficiently. In the absence of college, employers would be unable to differentiate between high-quality and low-quality workers. Without college education signal, low-level position may be filled with high-quality workers and they are underutilized and many of the high-level positions will be under-productive.

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