Most people prefer the first lottery in Question 1 but the second lottery in question 2.

Expert Solution

Allais Paradox.

Question 1: ($1,1) or ($1,0.89; $5,0.10; $0,0.01)

Question 2: ($1,0.11;$0,0.89) or ($5,0.10;$0,0.90)

Most of the people prefer first lottery in question 1 but the second lottery in question 2.

Suppose we strictly prefer ($1,1) to ($1,0.89;$5,0.10;$0,0.01)

Value functions v(x) ={ x^0.1 if x>=0

2x if x<0

V(1)> 0.89 v(1)+ 0.10 v(5) + 0.01 v(0)…………………………..(i)

Now suppose we strictly prefer ($5,0.10;$0,0.90) to ($1,0.11; $0,0.89)

0.10 v(5) + 0.90 v(0)> 0.11 v(1) + 0.89 v(0)

=> 0.10 v(5) + 0.01 v(0) > 0.11 v(1)

=> 0.89 v(1) + 0.10 v(5) + 0.01 v(0) > v(1)………………………….(ii)

(i) and (ii) opposed to each other.

If you are EU, then you cannot choose the first lottery in question 1 but the second lottery in question 2.

This explains the Allais Paradox.

Junaid answered 2 years ago

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Most people prefer the first lottery in Question 1 but the second lottery in question 2.

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