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Consumer Surplus Business Calculus

label Business & Finance
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

If the demand function for a product is 

p = 9/(x + 1)
 and the supply function is 
p = 1 + 0.2x,
 find the consumer's surplus under pure competition.

In this problem, p is in dollars and x is the number of units.

Apr 22nd, 2015

Under pure competition, the market clears. Thus the prices are the same. 1+.2x=9/(x+1); this resolves to a quadratic with solution x=4. Consumer surplus is the integral from 0 to 4 of p-p(4). That is, the price-quantity consumers would be willing to pay but don't need to at the current price. This is integral of (9/(x+1) -9/5) from 0 to 4; int (0 to 4)(9/(x+1) -(9/5)*4. That is 9 (ln(5)-ln1)-4/5)  or 9 (ln5 - 4/5); approximately 7.285 

Apr 22nd, 2015

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Apr 22nd, 2015
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Apr 22nd, 2015
Jun 27th, 2017
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