Suppose a Family Is Considering Going to a Hockey Game $x$

Essay

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 $x$ from attending the game together, but incurs a cost of $\mathrm{c}$ for driving on the hazardous roads. The family's utility function is given by $u_{g}(x)+u_{l}(c)=\ln (x-3)-\ln (2-c)$ . The family determines that the cost of driving on the icy roads is 1 unit ( $\mathrm{c}=1$ ). 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 $x$ )? (Hint: if they do not go to the game, they receive 0 and pay no costs).