Given Demand Equation, Calculate Consumer Surplus

Question

Given the demand equation P=60-1/2q^2

 

Calculate the consumer surplus when q*=6 at the equilibrium price.

 

a-144

b-252

c-60

d-70

e-324

Answer 1

If Demand equation is p=60-(1/2)q^2,  which I assumed,

Consumer surplus is the area enclosed by q= 0, q=6, p=60-(1/2)q^2, and  p _q=6 = 42Therefore, Integral (from 0 to 6) (60-(1/2)q^2 - 42)dq = (18q - (1/2)q^3/3)|form 0 to 6) = 108 - 36 = 72