Homework Answers
(a) S(q)= (q+7)2
D(q)= 1000/(q+7)
At equilibrium demand and supply are equal.
(q+7)2 = 1000/(q+7)
(q+7)3 =1000
q+ 7 = 10
q= 3 units (Equilibrium quantity)
P= (q+7)2 = (3+7)2 = $100 (Equilibrium price)
This is shown in the graph B. Hence, option(B) is correct.
(b) Equilibrium is (100, 3) .
(c) Demand curve : P= 1000/q+7
When q=0, P= $142.86.
Consumer surplus is the triangle area above the price and below the demand curve.
CS= (0.5)(142.86-100)(3) = $64.29
(d) Supply curve :P= (q+7)2 = q2 + 14q + 49
When q=0 , P= $ 49
Producers surplus is the triangle area above the supply curve and below the price .
PS = (0.5)(100-49)(3)= $76.5
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