A local gym knows the demand for gym memberships for the typical consumer is given by P = 32 - 3Q, where Q is the number of visits per month. The gym offers two membership plans: Plan 1: $150/month and no fee per visit; Plan 2: $100/month and a $5 per visit. a) Is the $100 monthly fee a reasonable amount to pay? In other words, is $100 less than the maximum a rational consumer would be willing to pay given the $5 per visit fee? (Hint: how many visits would our consumer demand at $5?) b) How many visits per month would make this consumer indifferent between the two plans? Which is more preferred if she is over this number? Under this number? c) Consider a variation of Plan 2: our typical consumer knows for certain exactly how often she will use the gym each month and pays a per visit fee according to the demand curve with a monthly membership price equal to the full associated consumer surplus. Should our consumer go with Plan 1 or Plan 2 if she knows she will use the gym 10 times per month?
A local gym knows the demand for gym memberships for the typical consumer is given by P = 32 - 3Q, where Q is the number of visits per month. The gym offers two membership plans: Plan 1: $150/month and no fee per visit; Plan 2: $100/month and a $5 per visit. a) Is the $100 monthly fee a reasonable amount to pay? In other words, is $100 less than the maximum a rational consumer would be willing to pay given the $5 per visit fee? (Hint: how many visits would our consumer demand at $5?) b) How many visits per month would make this consumer indifferent between the two plans? Which is more preferred if she is over this number? Under this number? c) Consider a variation of Plan 2: our typical consumer knows for certain exactly how often she will use the gym each month and pays a per visit fee according to the demand curve with a monthly membership price equal to the full associated consumer surplus. Should our consumer go with Plan 1 or Plan 2 if she knows she will use the gym 10 times per month?
