Hello. Kindly solve these clearly showing each step followed

Consider a three-person coalitional game in which .((O}) = ((1}) = ({2}) = "({3)) = 0, v({1, 2}) = 6, v({1,3}) = v({2,3}) = 2 and v( {1, 2,3}) = 13. (a) Derive the set of equations/inequalities that characterize the core. (b) What is the maximum payoff that Players 1 and 2 can get in any vector that belongs to the core? (c) Compute the Shapley value. Does it belong to the core?Consider a second-hand car market. There are two types of cars, "lemons" and "peaches". A seller values a lemon at $100 and a peach at $200. A buyer values a lemon at $120 and a "peach" at $300. 1. What are the gains-to-trade per car? If the probability of a car being a lemon is , what are the expected gains-to-trade? 2. Suppose that the information is perfect and the the gains-to-trade are split equally between the buyers and the sellers for each type of car. What are the prices and is the allocation pareto-efficient? Suppose that all gains-of- trade are assigned to the buyers. What are the corresponding prices? 3. Suppose that the buyers cannot observe the quality of the car. (a) What is the expected value of a car for a buyer if # of the cars are lemons? What is the maximum price a buyer is willing to pay? (b) If ) of the cars are lemons, does there exist a pooling equilibrium in which both types of cars are sold? What is the minimal fraction of lemons such that an equilibrium does not involve any peaches sold? (c) Suppose that the fraction of lemons in the market is higher than the tireshold obtained in (b). What cars are traded in equilibrium? Is the outcome pareto-efficient? (d) Suppose that the owners of peaches can offer a warranty on the car which the owners of lemons do not offer. What trade pattern emerges in equilibrium?Suppose there are two types of used cars: peaches and lemons. A peach is worth $3000 to a buyer and $1900 to a seller. A lemon, on the other hand, is worth $1000 to a buyer and $500 to a seller. The fraction of used cars that are peaches is 14 and the fraction that are lemons is 1/4. All parties are risk neutral, and when buyers and sellers bargain, the agreed sale price is always the maximum that buyers willing to pay. Assume that buyers cannot tell if a car is a peach or a lemon. Sellers know which type of car they own. (1) What kind of cars will be sold in this market? (ii) Now assume that the fraction of lemons is now 1/2. What kind of cars will be sold in this market?2. The market demand and supply functions for an item are as follows: 9d = 24 - p 4s = 2p. (a) Calculate the equilibrium price and quantity. (b) Suppose the government imposes a per unit tax of Rs 1.50 on sellers. How is the economic burden of the tax distributed across buyers and sellers? Also calculate the deadweight loss of the tax. (c) Consider a general tax rate t per unit, to be paid by the sellers. Find the value of t that maximizes tax revenue for the government. (d) If the government chooses t to maximize the sum of consumers' surplus, producers' surplus and tax revenue, what would be the optimum choice