p = 10 + 2q; p = 16

Question

Calculate the producers' surplus for the supply equation at the indicated unit price p.

 HINT [See Example 2.] (Round your answer to the nearest cent.)

p = 10 + 2q;  p = 16

Answer 1

10+2q =16

2q =16-10=6

q =6/2 =3

3(16) = 48

3(10) = 30

48-30-3(6)/2 = $9 = the producer's surplus

It may help to graph the price line and supply curve

producer's surplus is the area between them

which equals the rectangular area below the price line from q=0 to q=3 minus the area below the supply curve

48-39 = 9

rectangular area = 3(16) =48

area below the supply curve = a rectangular are = 3(10) + a triangular area of 9 = 3(10) + 3(6)/2= 39

48-39 = $9

or use calculus

find the integral of 16-(10+2q)= 6-2q

evaluated from q=0 to q= 3

integral of 6 -2q

= 6q -q^2

from 0 to 3

=18-9

= exactly $9.00