(The Allais Paradox) Suppose we are offered a choice between the following two lotteries: L 1 : With
(The Allais Paradox) Suppose we are offered a choice between the following two lotteries:
L_{1}: 
With probability 1, we receive $1 million. 
L_{2}: 
With probability .10, we receive $5 million. 

With probability .89, we receive $1 million. 

With probability .01, we receive $0. 
Which lottery do we prefer? Now consider the following two lotteries:
L_{3}: 
With probability .11, we receive $1 million. 

With probability .89, we receive $0. 
L_{4}: 
With probability .10, we receive $5 million. 

With probability .90, we receive $0. 
Which lottery do we prefer? Suppose (like most people), we prefer L_{1} to L_{2}. Show that L_{3} must have a larger expected utility than L_{4}.
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