Sam’s utility function is U(x1, x2) = 2x1 + x2, where x1 is the number of units

Question

Sam’s utility function is U(x1, x2) = 2x1 + x2, where x1 is the number of units of good 1 he consumes per week and x2 is the number of units of good 2 he consumes per week. Sam has $200 a week to spend. The price of x1 is $4. Sam currently doesn’t consume good 2, as it is way too expensive. Sam has received an invitation to join a club devoted to the consumption of good 2. If he joins the club, Sam can get a discount on the purchase of good 2. If he belonged to the club, he could buy good 2 for $1 a unit. How much is the most Sam would be willing to pay to join this club?

Explanation / Answer

As per the utility function 2 units of x1 and one unit of x2 gives him satisfaction U=2x1 + x2. Price of x1 is 4 that is he can consume maximum of 4 units of x1 when he is not consuming x2. But if he gets discount he would be ready to spend $100 a week on x2. The quantity of x2 gives him utility equalt to around 2 units of x1.

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