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Considering the following economy, there are two possible states a and b in period 1. (a) Describe the payment vector for all Arrow-Debreu securities. Denote that the price vector of these securities is o. (b) Consider a participant with the following endowments: 2 0 Express his endowment as a portfolio of Arrow-Debreu securities. (e) Calculate his financial wealth. Write down his budget set. (d) Suppose the utility function of the participant is as follows: U(Co, Cla, C16) 3(e=c10 +e=) Without considering the non-negative constraints of consumption, write down his opti- mization problem. Find his optimal consumption choice. (e) Discuss how his consumption depends on the Arrow-Debreu security price vector $. (f) Prove that under certain prices, his consumption (under certain periods/states) can be negative. Considering the following economy, there are two possible states a and b in period 1. (a) Describe the payment vector for all Arrow-Debreu securities. Denote that the price vector of these securities is o. (b) Consider a participant with the following endowments: 2 0 Express his endowment as a portfolio of Arrow-Debreu securities. (e) Calculate his financial wealth. Write down his budget set. (d) Suppose the utility function of the participant is as follows: U(Co, Cla, C16) 3(e=c10 +e=) Without considering the non-negative constraints of consumption, write down his opti- mization problem. Find his optimal consumption choice. (e) Discuss how his consumption depends on the Arrow-Debreu security price vector $. (f) Prove that under certain prices, his consumption (under certain periods/states) can be negative

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