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Socrates just placed an order to take a SHORT position in 5 contracts of S\&P 500 E-mini futures for 3750 with an expiration date in 2 months. The contract size is 50 times the index. For these particular futures contracts, the broker requires an initial margin of $4500 per contract with a maintenance margin of $3000 per contract. Socrates chooses to invest only the required amount per contract. a. If by the close of tomorrow, the settle price of the S\&P 500E-mini futures contract is 3700 , what will be the new balance of Socrates' margin account? (5 points) b. At what futures price, would Socrates expect a margin call? (10 points)