1. Consider a one period exchange economy with complete markets. There are two types of consumers, A and B. There are equal numbers of the two types of consumers. Each consumer maximizes expected utility taking prices as given. Each type A consumer has a logarithmic utility function, while the utility function of each type B consumer las constant relative risk aversion equal to o. There are two states of the world with probability 0.5 cach consumer's endowment of consumption goods is 3, and with probability 0.5 each consumer's endowment of consumption goods is 1. Find the competitive equilibriun allocations and prices for three different values of o: 0.5, 1, and 2. For each case, compute the expected value and standard deviation of each consumer's consumption and compare them to the expectedl value and standard deviation of the consumer's endlowment. 2. Consider a two period exchange economy with two types of consumers, A and B. There are exqual numbers of the two types of consumers. The two types of consumers have identical preferences given by um) + BEwa), where is strictly increasing and strictly coucave. Each consumer is endowed with one consumption good in period 0. In period 1, cach type A consumer is endowed with My consumption goods, and euch type B consumer is endowexl with (1 - 0)y consumption gools. The random variable I can be interpreted as the consumer's share of the aggregate endowment y. Let 8 equal 0.5 + 2 with probability one half and oqual 0.5 z with probability ono-half, where 0