(Signaling and screening) The government is trying to contract the construction of a government building. A contractor can be either a (H)igh or (L)ow quality type. A (H)igh quality contractor builds a high quality building that is worth $30m to the government and it costs $26m to the contractor to construct. On the other hand, a (L)ow quality contractor builds a low quality building that is worth $20m to the government and it costs $16m to the contractor to construct. Assume the contractor knows its type (quality), but the government does not know the contractor's type. The government offers a bid (price) for the construction of the building, and the contractor can accept or reject the offer (when there is no accepted offer, both get 0; it is the outside option for both players, that is). Both players (government and contractor) are risk neutral. (a) What should be the minimum probability that the contractor is the H type, for a pooling equilibrium to exist where both types of contractors accept the bid? (b) If the probability of contractor being H type is %70, what is the possible range of equilibrium government bids (prices) in a pooling equilibrium (that attracts both