Consider the Spence model of education studied in class with the high-skilled pr

Question

Consider the Spence model of education studied in class with the high-skilled productivity equal to wH = 2 and the low-skilled productivity equal to wL = 1 but with the two following variations: The cost of attending university (which we represented with number of years studied y) is now equal to cL(y) = y^2 for low-skilled workers and cH(y) = y^2/2 for high-skilled workers; and productivity increases by attending university: the productivity of a low-skilled worker is 1+ (y/4) if he gets a university degree, while the productivity of a high-skilled worker is 2 + (y/4) if he gets a university degree.

(a) Find separating perfect bayesian equilibrium that satisfies the following conditions:

(i) for out of equilibrium beliefs assume, like in class, that for y < yH belief is that worker is of low type, and for y > yH she is of high type;

(ii) yH makes low types just indifferent between imitating high types and not.

(b) Argue that separating equilibria other than the one you found in (a) do not satisfy the Intuitive Criterion.

Explanation / Answer

For a separating equlibrium:

for low skilled:

High skilled worker:

The optimal y therefore must be obtained at y=2

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