Consider an experiment that lasts 15 periods, where individuals choose to buy or sell an amount of assets amongst each other. Each asset has dividents at the end of each round of either $1 or $3 with a 50% probability of the dividend being either value. The final redemption value equals the sum of the dividends realized at the end of 15 periods. There is no interest paid on the dividends between each round, so the actual final redemption value will depend on the random dividends realized.

a). Calculate the expected value of a single asset at the beginning of the first round, before any dividends have been determined.

b). On average, how fast will the expected value of a single asset decline in each round?

c). What is the highest and lowest amount the final redemption value could be?