Microeconomics. Provide solutions for the questions mentioned below.

(a) In the following pair of games, check whether the players' preferences over lotteries on the strategy profiles are identical (i.e. row player's preferences on the left to the row player's preferences on the right and column player's preferences on the left to the column player's preferences on the right). L M R. L M R. 2,-2 1,1 -3,7 12.-1 5.0 -3,2 b 1,10 0,4 0,4 b 5.3 3,1 3.1 -2,1 1,7 -1,-5 C -1.0 5.2 1.-2 (b) Under Postulates P1-5 of Savage, let D1, D2. . ... D,, be disjoint non-null events such that Dj~D,~ ~Do, where > and ~ are the at least as likely as and as likely as relations between events, derived from betting preferences as in the class. Given any subsets / and N' of {1, 2, ...,n}, show that UD UD - IN| 2 IN'. iEN iEN'Steel manufacturing in the US requires only one input: labor. Steel is produced by a representative rm under perfect competition according to the production function 1 L = L St ) 2 Throughout this problem assume that the wage in the United States is 1. {1} {4 minuta) Suppose that United States can freely import and expert steel. Foreign supply of steel is supplied with perfect elasticity at a price of 1. How much steel is produced in the US\"? Car manufacturers use steel and labor to make cars. Both steel and labor are variable inputs and cars are produced by a. representative firm under perfect competition according to the production function F[L,S) = \"3+ vi?) {2) {1D minutes} Now suppose the price of steel is p3. Solve for the supply function of US car manufacturers [quantity supplied as a function of the price of cars, is... and the price of steel a)- {3} {3 minutes} Assume the US freely trades steel, where the world price of steel is 1 as before. 1What is the supply curve for cars? {4] {3 minutes] Suppose that the supply of cars from foreign producers is perfectly elastic at p = lll {the world price of cars is Hill}7 and the US demand for cars is Q = lS lP. {a} {4 minutes] Supposing that there is free trade in the car market as well as the steel market, calculate the equilibrium price and quantity of cars consumed {purchased} in the United States. Does the US imp-ort- orerport cars andhow many ow the US import or export?