An investor has a von Neumann-Morgenstern utility function, u(c)=-e^(-αc), where c represents consumption and α > 0. There are two equally probable states of nature, called 1 and 2, and two assets that can be acquired, each of which is attractive in a state of nature as follows: Each unit of asset 1 yields one unit of consumption in state 1 and nothing in state 2. Each unit of asset 2 yields nothing in state 1 and one unit of consumption in state 2. The price of each asset i is denoted by πi, which are normalized to π1 + π2 = 1. The investor has a monetary wealth of w units that must be distributed between the two assets. Denote xi the number of units of asset i that he acquires. Formulate the investor's expected utility maximization problem, subject to your budget constraint. Find the optimal quantities x of each asset i for this investor. How do these amounts of assets vary according to the α parameter? What is the economic interpretation of this relationship?
An investor has a von Neumann-Morgenstern utility function, u(c)=-e^(-αc), where c represents consumption and α > 0. There are two equally probable states of nature, called 1 and 2, and two assets that can be acquired, each of which is attractive in a state of nature as follows: Each unit of asset 1 yields one unit of consumption in state 1 and nothing in state 2. Each unit of asset 2 yields nothing in state 1 and one unit of consumption in state 2. The price of each asset i is denoted by πi, which are normalized to π1 + π2 = 1. The investor has a monetary wealth of w units that must be distributed between the two assets. Denote xi the number of units of asset i that he acquires. Formulate the investor's expected utility maximization problem, subject to your budget constraint. Find the optimal quantities x of each asset i for this investor. How do these amounts of assets vary according to the α parameter? What is the economic interpretation of this relationship?
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