Will Is Playing on a Game Show

Essay

Will is playing on a game show. He must choose between two offers. The first offer is a payment of $2000, which he can take for simply being on the show, or he can enter a gamble. In the gamble, he chooses one of two curtains that conceal two items. He makes a draw for curtain one or two, from a hat; he receives the gift behind the curtain picked. He knows that behind one curtain is an automobile valued at $4000 and behind other curtain is a set of encyclopedias valued at $500. If his initial wealth is $1000 and his utility function can be described by U(w)= 1 - 1000/w, then what must be the probability of drawing the car for Will to be indifferent between the two choices?