Jack is the owner of the only local bar in a small town.He sells whiskey in one-ounce glasses. For simplicity, let’s assume it doesn’t cost Jack anything to run his business. There are two customers, Adam and Burt who are twin brothers. Adam’s demand function is yA = 16 – 2p, and Burt’s demand function is yB = 8 – p (price is measured in dollars and quantity is measured by ounces). Jack knows their demand functions, but the problem is that he cannot tell them apart since they look exactly the same to him. To increase his profits, Jack offers the following two options that his customers can choose from: (1) You can pay $T1 up front and drink as much as you want; or (2) Pay $T2 up front and the price per ounce of whiskey will be $p. 1.a If p = 4, what is the maximal T2 that Jack can charge so that Burt is willing to come to the bar? 1.b What is the maximal T1 that Jack can charge so that Adam will choose the first pricing option? Answer Key that was given. I seems not to understand the process to arrive at the answer. Any help? 3.1. When p = 4, Burt will buy 4 ounces, which he values at $24. Since he already paid $4 × 4 = 16, he is willing to pay up to $8 up front. T2 = 8. 3.2. If Adam chooses option (2), he’ll buy 8 ounces which he values at $48. His total expenditure would be T2 + 4 × 8 = 40, which implies his consumer surplus will be $8. In order for Adam to choose option (1), the highest T1 that Jack can charge is $56 (64 − 8).
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Jack is the owner of the only local bar in a small town.He sells whiskey in one-ounce glasses. For simplicity, let’s assume it doesn’t cost Jack anything to run his business. There are two customers, Adam and Burt who are twin brothers. Adam’s
demand function is yA = 16 – 2p, and Burt’s demand function is yB = 8 – p (price is measured in dollars and quantity is measured by ounces). Jack knows their demand functions, but the problem is that he cannot tell them apart since they look exactly the same to him. To increase his profits, Jack offers the following two options that his customers can choose from:(1) You can pay $T1 up front and drink as much as you want; or (2) Pay $T2 up front and the price per ounce of whiskey will be $p.
1.a If p = 4, what is the maximal T2 that Jack can charge so that Burt is willing to come to the bar?
1.b What is the maximal T1 that Jack can charge so that Adam will choose the first pricing option?
Answer Key that was given. I seems not to understand the process to arrive at the answer. Any help?
- 3.1. When p = 4, Burt will buy 4 ounces, which he values at $24. Since he already
paid $4 × 4 = 16, he is willing to pay up to $8 up front. T2 = 8.
3.2. If Adam chooses option (2), he’ll buy 8 ounces which he values at $48. His
total expenditure would be T2 + 4 × 8 = 40, which implies hisconsumer surplus will
be $8. In order for Adam to choose option (1), the highest T1 that Jack can charge is
$56 (64 − 8).
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