For this question, please only answer part c. A health club offers two different plans for its visitors. Under plan A, no membership is required and each visit costs $10. Under plan B, an annual fee of $200 is paid to become a member and each visit costs only $4. It also sells beverages at a unit price of $10. a). Let v denote the visits to the health club and b the amount of beverages a customer buys there and pv and pb be their respective prices. Note that pv differs for each plan. Assuming that the potential customers have an annual income of $1000, draw the budget constraints under the two plans on the same graph. [Place v on the horizontal axis and b on the vertical axis.] Label all relevant intercepts and slopes. b). Visits to the health club -v- and beverage consumption -b- can be considered as being perfect complements. Let the preferences of a customer be given by: U(v, b) = { min v, (5/2)b } What plan would such a customer choose if he is maximizing his utility? Determine the optimal consumption levels v* and b* c). A different customer has the following preferences Z(v, b) = min {4v, b}. In other words, this customer tends to drink more in each visit than the customer in part (b). What plan would this customer choose? Again, determine the optimal consumption levels v**and b**.
For this question, please only answer part c.
A health club offers two different plans for its visitors. Under plan A, no membership is required and each visit costs $10. Under plan B, an annual fee of $200 is paid to become a member and each visit costs only $4. It also sells beverages at a unit price of $10.
a). Let v denote the visits to the health club and b the amount of beverages a customer buys there and pv and pb be their respective prices. Note that pv differs for each plan. Assuming that the potential customers have an annual income of $1000, draw the budget constraints under the two plans on the same graph. [Place v on the horizontal axis and b on the vertical axis.] Label all relevant intercepts and slopes.
b). Visits to the health club -v- and beverage consumption -b- can be considered as being perfect complements. Let the preferences of a customer be given by: U(v, b) = { min v, (5/2)b }
What plan would such a customer choose if he is maximizing his utility? Determine the optimal consumption levels v* and b*
c). A different customer has the following preferences Z(v, b) = min {4v, b}.
In other words, this customer tends to drink more in each visit than the customer in part (b). What plan would this customer choose? Again, determine the optimal consumption levels v**and b**.
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