Consider a model with asymmetric information (similar to the one covered

in the class) where the sellers produce umbrellas of two qualities: a high-quality

umbrella (good H) and a low-quality umbrella (good L).

The corresponding buyers' valuations (in dollars) are VH = 15 for the good

H, and vI = 10 for the good L. The buyers cannot Bell the quality before

purchasing an umbrella. The productions costs for each seller depend on the

quality of the good, and are cH = 12 for H and c = 11 for L.

Each seller can decide which quality of an umbrella to produce.

1. Explain carefully whether one of the following equilibria exists (in your

explanations, characterize in each case the buyers' beliefs about the quality

of the offered goods):

(a) Only good H is produced in an equilibrium.

(b) Only good L is produced in an equilibrium.

(c) One quarter of sellers produce good H and three quarters of sellers

produce good L.

2.Provide an example of a costly signal that can help sellers of the good H

to distinguish themselves from the sellers of the good L.