Question

1000 and the demand function is given by Da)+7 Completeparts a Suppose the supply function for a certain item is given by S()+7 through d below a. Graph the supply and demand curves. Choose the correct graph below ○ A. с. Ов. 10 10 10 10 14 14 14 14 b. Find the point at which supply and demand are in equilibrium. The equilibrium point is (Type an ordered pair. Simplify your answer.) c. Find the consumers' surplus The consumers' surplus is $ (Round to two decimal places as needed.) d. Find the producers' surplus The producers' surplus is S (Round to two decimal places as needed.)

Answer 1

(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