Question

The demand price for a certain brand of CDs is modeled by the function D(q) = −0.01q2 − 0.2q + 12, where p is the wholesale unit price in dollars and q is the quantity demanded each week, measured in thousands of discs. The supply price for the CDs is given by the function S(q) = 0.01q2 + 0.6q − 3, where price is the wholesale unit price in dollars and q stands for the number of CDs that will be made available in the market by the supplier, measured in thousands. (a) Determine market equilibrium quantity (in thousands of discs) and price (in dollars). (Round your answers to two decimal places.) market equilibrium quantity Incorrect: Your answer is incorrect. thousand discs market equilibrium price $ Incorrect: Your answer is incorrect. (b) Determine the consumers' surplus in thousands of dollars. (Round your answer to three decimal places.) $ thousand (c) Interpret the consumers' surplus in the context of this problem. (Round your answer to the nearest dollar.) $ is the total Correct: Your answer is correct. . (d) Determine the producer's surplus in thousands of dollars. (Round your answer to three decimal places.) $ thousand (e) Interpret the producer's surplus in the context of this problem. (Round your answer to the nearest dollar.) $ is the total Correct: Your answer is correct. .

Answer 1

a) D(q) = −0.01q2 − 0.2q + 12

S(q) = 0.01q2 + 0.6q − 3

In equillibrium the supply and demand is equal so equating both equations

0.01q2 + 0.6q − 3=−0.01q2 − 0.2q + 12

0.02q2+0.8q-15=0

Solving the quadratic equation, the solutions are 13.912 and -53.912

the negative solution is discarded as quantity cannot be negative.

so it is 13912 discs.

7.28 $ is the price which is obtained by putting the value of q in any of the equation.

b)

So maximum price is 12 by putting 0 demand. thus surplus is 12-7.28 = 4.72

c)

d) similiarly producer surplus = 7-(-3) {using supply equation and 0 quantity}

=10

couldnt interpret because of the vagueness of what to be done in the interpretation