Suppose the cost of obtaining a college degree is identical for high-ability and low-ability workers. What happens to the separating equilibrium in Spence's signaling model?
AThe separating equilibrium is stronger — equal costs mean neither type has an incentive to deviate
BThe separating equilibrium collapses — low-ability workers would mimic high-ability workers since signaling costs no longer deter them
CA pooling equilibrium becomes impossible — only separating equilibria can survive when costs are equal
DEmployers simply offer wages equal to the average ability, and both types attend college
The differential cost condition is the foundation of signaling equilibria. If low-ability workers face the same cost as high-ability workers, the signal is no longer differentially costly — low types would always mimic high types to collect the wage premium. The separating equilibrium dissolves into a pooling equilibrium (or no equilibrium at all), because no signal can credibly distinguish the types. Equal costs destroy the information content of the signal.
Question 2 Multiple Choice
In a pooling equilibrium of a signaling game, what information does the receiver gain from observing the signal?
AThe receiver learns the sender's exact type because the signal uniquely identifies who sends it
BThe receiver gains no new information — the signal is sent by all types, so the posterior equals the prior
CThe receiver infers only that the sender is not the lowest type, since weak types cannot afford any signal
DThe receiver updates beliefs toward high types because signaling is inherently associated with quality
In a pooling equilibrium, every type sends the same signal. Bayes' rule updates the receiver's beliefs using observed signal frequencies, but since all types send the same signal with equal frequency, the posterior is identical to the prior — no updating occurs. The signal transmits zero information about the sender's type. This is why pooling equilibria can feel 'uninformative' compared to separating ones, and why refinements like the Intuitive Criterion often favor separating equilibria.
Question 3 True / False
In a separating equilibrium, the receiver's beliefs after observing each signal are fully pinned down by Bayes' rule, because each signal is sent by exactly one type.
TTrue
FFalse
Answer: True
This is the defining property of separation. If each type sends a distinct signal, observing any on-path signal tells the receiver exactly which type sent it — Bayes' rule assigns probability one to that type. This is why separating equilibria are 'fully revealing': the sender's private information is perfectly communicated through the signal choice, even though the sender may have preferred to conceal it.
Question 4 True / False
A signal credibly separates types as long as it is costly for the sender to send.
TTrue
FFalse
Answer: False
Cost alone is not sufficient — the key condition is *differential* cost. If the signal is costly but equally costly for all types, low types will still mimic high types whenever the benefit (a higher wage or price) exceeds the cost. The signal only separates types when the cost is lower for high types, so that high types find signaling worthwhile but low types find mimicking prohibitively expensive. A uniformly costly signal is merely a barrier, not a credible separator.
Question 5 Short Answer
Why is differential cost — not just cost alone — the essential requirement for a credible separating signal in a signaling game?
Think about your answer, then reveal below.
Model answer: A separating equilibrium requires that low types choose not to mimic high types. If the signal cost is the same for all types, any low type would rationally mimic the high type to collect the higher payoff — the signal conveys no information and the separation collapses. Differential cost creates a self-enforcing wedge: the high type signals because the payoff justifies the cost, and the low type does not signal because the same cost is prohibitively expensive relative to the expected benefit. The signal's credibility comes entirely from this asymmetry in cost, not from the cost level itself.
This is the mechanism behind all real-world credible signals: warranties (costly for low-quality producers who expect many claims), dividends (costly for firms without real cash flow), and retained equity (costly for entrepreneurs who can't afford to hold illiquid assets). In each case, the signal deters mimicry specifically because it is cheap for the genuine type and expensive for an imitator.