In 1963, Paul Samuelson wrote about a colleague who said that he would turm down the...

 

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In 1963, Paul Samuelson wrote about a colleague who said that he would turm down the prospect (-$100,0.5; $200,0.5) but would accept 100 such prospects. In this problem, we will study a simplified version of this statement. Suppose the agent's utility function over gambles is given by: x-wif x2w u(x, w) =-25(w - x) if w> x. where w is the agent's wealth before the gamble and x is the agent's wealth after the gamble. a. (15 points) Show whether this agent would accept the gamble (-S100,0.5; $200,0.5). b. (10 points) Now, suppose the agent has the opportunity to take this gamble twice, She sees the outcome of the first gamble and updates her wealth before the second gamble. Will she take this double gamble? In 1963, Paul Samuelson wrote about a colleague who said that he would turm down the prospect (-$100,0.5; $200,0.5) but would accept 100 such prospects. In this problem, we will study a simplified version of this statement. Suppose the agent's utility function over gambles is given by: x-wif x2w u(x, w) =-25(w - x) if w> x. where w is the agent's wealth before the gamble and x is the agent's wealth after the gamble. a. (15 points) Show whether this agent would accept the gamble (-S100,0.5; $200,0.5). b. (10 points) Now, suppose the agent has the opportunity to take this gamble twice, She sees the outcome of the first gamble and updates her wealth before the second gamble. Will she take this double gamble?

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