Consider a potential buyer of a used automobile. The market price for the used car is $5,000. The used automobile may be in good or poor condition. On average, a p proportion of used automobiles in this economy are in poor condition. If the automobile is in good condition, the buyer derives utility equivalent to $10,000. If it is in poor condition, he derives utility equivalent to $0. The buyer cannot observe the quality of the automobile. On the other hand, he can observe if the seller has carried out a cleaning and polishing treatment on the automobile for the sale. This treatment has no direct impact on the utility that the buyer derives from the automobile. It only serves to signal the quality of the automobile. This treatment costs the seller of good quality automobiles $1,000.

As the treatment aims to camouflage the defects of the car, it costs the seller of the poor quality car C dollars.

In the questions below, I will ask you about dollar welfare losses related to information asymmetry. Suppose that the "benevolent dictator" assessing welfare in this economy sums the net gains from exchange by giving a weight of 1 to the buyer's gain, G_C, and 1p to the car seller's gain of good quality, G_B , and p to the gain of the seller of poor quality automobiles, G_M. Its social evaluation function is therefore:

W =E[G_C]+(1p)E[G_B]+pE[G_M].

a) Graphically represent the extensive form of the game.

b) Suppose c = $6,000 and p = 0.45. What type of balance (separator, mixing, hybrid) do we have in this game? What is this balance?

c) What is the total welfare loss (in dollars) associated with information asymmetry in this economy?

d) Suppose c = $3,000 and p = 0.45. What type of balance (splitter, mixer, hybrid) do we have in this game? What is this balance?

e) What is the total welfare loss (in dollars) associated with information asymmetry in this economy?

f) Suppose c = $3,000 and p = 0.75. What type of balance (separator, mixing, hybrid) do we have in this game? What is this balance?

g) What is the total welfare loss (in dollars) associated with information asymmetry in this economy?

please give details and do not use A.I. thanks