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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