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Suppose a Family Is Considering Going to a Hockey Game xx

Question 16

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Suppose a family is considering going to a hockey game, but the roads are covered in ice. The tickets were a gift and the family gets a value of xx from attending the game together, but incurs a cost of c\mathrm{c} for driving on the hazardous roads. The family's utility function is given by ug(x)+ul(c)=ln(x3)ln(2c)u_{g}(x)+u_{l}(c)=\ln (x-3)-\ln (2-c) . The family determines that the cost of driving on the icy roads is 1 unit ( c=1\mathrm{c}=1 ). What is the minimum value they must obtain from the attending the game in order for them to decide to go (what must be the value of xx )? (Hint: if they do not go to the game, they receive 0 and pay no costs).

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