Question

​D(x) is the​ price, in dollars per​ unit, that consumers are willing to pay for x units of an​ item, and​ S(x) is the​ price, in dollars per​ unit, that producers are willing to accept for x units. Find ​(a​) the equilibrium​ point, ​(b​) the consumer surplus at the equilibrium​ point, and ​(c​) the producer surplus at the equilibrium point. D(x)=(x-7)^2, S(x)=x^2+4x+31

Answer 1

Answer:

a. x = 1 b. 36 c. 36

Step-by-step explanation:

a. At the equilibrium point, D(x) = S(x)

(x - 7)² = x² + 4x + 31

Expanding, we ave

x² - 14x + 49 = x² + 4x + 31

collecting like terms

14x + 4x = 49 - 31

18x = 18

x = 18/18 = 1

b. Substituting x = 1 into D(x), we have

D(1) = (1 - 7)² = (-6)² = 36

c. Substituting x = 1 into S(x), we have

S(1) = 1² + 4(1) + 31 = 1 + 4 + 31 = 36