$2.$ Determine the equilibrium price of a December S&P $500$ call, given the S&P $500$ put is trading at $50.$ Assume the spot SP $500$ index is at $2,500,$ the risk free rate is $5\mathrm{.}00\%,$ dividend per index share on the S&P $500$ are $$125$ at the December expiration and one year.

$3.$ Explain what arbitrageurs would do if the price of an American S&P $500$ futures call with an exercise price of $2,100$ were priced at $45$ when the underlying futures price was trading at $2,150.$ What impact would their actions have in the futures option market on the call's price?