ANS: Sam\'s utility function is Ux, y)-2rty, where x is the number of x\'s he co

Question

ANS: Sam's utility function is Ux, y)-2rty, where x is the number of x's he consumes per week and y is the number of y's he consumes per week. Sam has $200 a week to spend. The price of x is $4. Sam currently doesn't consume any y. Sam has received an invitation to join a club devoted to the consumption of y. If he joins the club, Sam can get a discount on the purchase of y. If he belonged to the club, he could buy y for $1 a unit. How much is the most Sam would be willing to pay to join this club? a. Nothing b. $100 a week c. $50 a week d. $40 a week e. None of the above.

Explanation / Answer

Consider the given problem, here the utility function is given by, “U=2*X + Y”, has “$200” to spend on these 2 goods” and “Px=4”, so if the consumer want to consume only “X”, then optimum quantity of “X” is “200/4=50”. So, the utility is “U=2*50=100”.

Now, if the person join the club then the person have to pay “$1” per unit of “Y”, => to get the initial level of utility (100) by consuming only “Y”, required “100” units of Y. So, the cost of “100” unit of “Y” is “100*1=$100”. So, the person is willing to pay maximum “$200 - $100 = $100”.

So, the amount to join is < 100 then the consumer will be able to get more utility compared to the previous utility level, So, maximum the consumer can pay $100 per week. So, "b" be the correct answer.

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