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For the rest of this question assume that instead of all golfers being identical,there are two types of golfers, “tragics” and “dilettantes”. There are fifty ofeach type and the demand of a tragic is given byxT (p) = 160  p10 ,while that of a dilettante is given byxD (p) = 80  p10 .Unfortunately for Drumpf, it is not possible to tell beforehand whether agolfer is of either type.(c) (5 points) Explain to Drumpf, what is the most it can set for its(fixed) membership fee if it wishes to attract both types of golfers.(d) (10 points) Explain to Drumpf how it can still have the same aggre-gate demand for rounds of golf but get more from the tragics if it o§ersdi§erent classes of memberships that entitles a golfer to play di§erentamounts of rounds of golf for the di§erent classes. [Hint: consider astandard membership that allows a golfer to play 80 rounds of golf,and a gold membership that at a higher price entitles the golfer toplay as many rounds as they wish. What is the most that a dilettanteis willing to pay for a standard (quantity limited) membership? Andgiven the fee for standard membership, what is the most that a tragicwould be willing to pay to be allowed to play an unlimited number ofrounds of golf?]2

Question

For the rest of this question assume that instead of all golfers being identical,there are two types of golfers, “tragics” and “dilettantes”. There are fifty ofeach type and the demand of a tragic is given byxT (p) = 160  p10 ,while that of a dilettante is given byxD (p) = 80  p10 .Unfortunately for Drumpf, it is not possible to tell beforehand whether agolfer is of either type.(c) (5 points) Explain to Drumpf, what is the most it can set for its(fixed) membership fee if it wishes to attract both types of golfers.(d) (10 points) Explain to Drumpf how it can still have the same aggre-gate demand for rounds of golf but get more from the tragics if it o§ersdi§erent classes of memberships that entitles a golfer to play di§erentamounts of rounds of golf for the di§erent classes. [Hint: consider astandard membership that allows a golfer to play 80 rounds of golf,and a gold membership that at a higher price entitles the golfer toplay as many rounds as they wish. What is the most that a dilettanteis willing to pay for a standard (quantity limited) membership? Andgiven the fee for standard membership, what is the most that a tragicwould be willing to pay to be allowed to play an unlimited number ofrounds of golf?]2

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Solution

(c) The most that Drumpf can set for its fixed membership fee to attract both types of golfers is determined by the maximum price that the golfer with the lower demand (the dilettante) is willing to pay. This is found by setting the demand of the dilettante equal to zero and solving for p:

80 - p/10 = 0 p = 800

So, the most Drumpf can charge for its membership fee is $800.

(d) Drumpf can increase its revenue from the tragics by offering different classes of memberships. For example, it could offer a standard membership that allows a golfer to play 80 rounds of golf, and a gold membership that allows a golfer to play an unlimited number of rounds.

The most a dilettante is willing to pay for a standard membership is found by setting their demand equal to 80 and solving for p:

80 - p/10 = 80 p = 0

So, a dilettante is not willing to pay anything for a standard membership.

Given the fee for a standard membership is $0, the most a tragic would be willing to pay for a gold membership (unlimited rounds) is found by setting their demand equal to zero and solving for p:

160 - p/10 = 0 p = 1600

So, a tragic is willing to pay $1600 for a gold membership. This way, Drumpf can increase its revenue from the tragics without affecting the aggregate demand for rounds of golf.

This problem has been solved

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