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**preview**shows half of the first page. to view the full**1 pages of the document.**8.4 Challenging Integral Applications

Economics & Biology Applications

Question #3 (Medium): Producer Surplus Given a Supply Curve

Strategy

Consumer Surplus is how much consumer (ie. buyer) saves when the demand curve lies above the

selling price. So it is given by

, where is the

number sold. On the other hand from the merchant’s perspective, they gain when the supply curve lies

below the selling price. Thus, the Producer Surplus is given by

Sample Question

If the supply function is modeled by the equation , find the producer surplus when the

selling price is .

Solution

Producer surplus is given by

. is the number sold at the selling price , given the price

function . First the number sold needs to be determined based on the information given. Selling at

, the number sold is: ;

; , however since it is

number sold, only positive works, thus . Then the producer surplus is:

Therefore, given the supply curve of when the item is selling at the producer

surplus is .

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