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Adele is set to go on a massive music tour throughout 2016. She performed 6 concerts at the O2 Arena in London. The arena has a capacity of 20,000 people and tickets were originally sold for $85 per ticket. All 6 concerts were sold out without any scalping (people who sell on tickets to consumers to make a profit) and the maximum a consumer was willing to pay per concert was $117 per ticket (where total tickets sold would = 0 if the ticket price was any more). Assuming a linear demand curve, what was the consumer surplus from one concert only? Answer to the nearest whole number (with no decimal places).

Question

Adele is set to go on a massive music tour throughout 2016. She performed 6 concerts at the O2 Arena in London. The arena has a capacity of 20,000 people and tickets were originally sold for 85perticket.All6concertsweresoldoutwithoutanyscalping(peoplewhosellonticketstoconsumerstomakeaprofit)andthemaximumaconsumerwaswillingtopayperconcertwas85 per ticket. All 6 concerts were sold out without any scalping (people who sell on tickets to consumers to make a profit) and the maximum a consumer was willing to pay per concert was 117 per ticket (where total tickets sold would = 0 if the ticket price was any more). Assuming a linear demand curve, what was the consumer surplus from one concert only? Answer to the nearest whole number (with no decimal places).

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Solution

Consumer surplus is the difference between the maximum price a consumer is willing to pay and the actual price they pay. It can be represented graphically as the area between the demand curve and the price line.

In this case, the maximum price a consumer is willing to pay is 117andtheactualpriceis117 and the actual price is 85. The quantity of tickets sold is 20,000.

Consumer surplus for one concert can be calculated using the formula for the area of a triangle: 1/2 * base * height.

The base of the triangle is the quantity of tickets sold (20,000) and the height is the difference between the maximum price a consumer is willing to pay and the actual price (117117 - 85 = $32).

So, the consumer surplus for one concert is:

1/2 * 20,000 * 32=32 = 320,000.

So, the consumer surplus from one concert is $320,000.

This problem has been solved

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