Consider a potential buyer of a used car. The market price for the used car is $5,000. The used automobile may be in good or poor condition. On average, a proportion p of used automabiles 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 50. The buyer cannot observe the quality of the automobile. However, it can be observed whether the seller has done any cleaning and polishing treatment of the automobile for 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 automaobiles $1,000. As the treatment aims to camouflage the defects of the car, it costs dollars to the seller of poor quality automobiles. In the guestions below, | will ask you about the dollar welfare losses associated with information asymmetry. Suppose that the \"benevolent dictator\" assessing welfare in this economy sums the net gains from exchange, giving a weight of 1 to the buyer's gain, G, of 1p for the benefit of the seller of good quality automobiles,iGz;, and of p for the gain of the seller of poor quality automobiles,(s,,. Its social evaluation function is therefore W= E[Gc] + (1 - p) - E[Gg] + p - E[Gy]. a) Graphically represent the extensive form of the game. b) Suppose that c = $6,000 and p = 0.45. What type of balance (splitter, mixer or hybrid) do we have in this game? Mathematically, what is this balance? c) Mathematically calculate the total welfare loss (in dollars) linked to information asymmetry in this economy? d) Suppose that = $3,000 and p = 0.45. What kind of balance (splitter, mixer, hybrid) do we have in this game? Mathematically, what is this balance? e) Calculate mathematically the total welfare loss (in dollars) linked to information asymmetry in this economy? f) Suppose that = $3,000 and p = 0.75. What kind of balance (splitter, mixer, hybrid) do we have in this game? Mathematically, what is this balance? g) Mathematically calculate the total welfare loss (in dollars) linked to information asymmetry in this economy