p = 12 − 2q; p = 4

Question

Calculate the consumers' surplus at the indicated unit price p

 for the demand equation. HINT [See Example 1.] (Round your answer to the nearest cent.)

p = 12 − 2q;  p = 4

Answer 1

integrate (12-2q)-4 = 8-2q

= 8q-q^2

evaluate from q=0 to q=4

8(4)-4^2

=32-16

=$16.00 = producer's surplus

or graph the demand curve

and use some simple geometry

the area between it and the price line is a triangle

find the triangle's area

= bh/2

=4(8)/2

= 16