Roger is breeding tropical fish to sell to hobbyists. He feels that his supply curve looks like
y1 = 0.06x2 + 5.06,
where x is the number of fish, in hundreds, sold at y1 dollars each. Articles in his trade newsletters lead him to believe that the demand curve is given by the portion of the quadratic curve
y2 = 0.2x2 - 4.8x + 31.8
that is a decreasing function of x.

(a) Check that the equilibrium quantity is 7. Calculate the producer surplus if Roger sells at y1(7).
(b) What is the consumer surplus?

Any help is greatly appreciated.

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