Find consumer surplus for demand Q(d) = 1400 - 10P and supply Q(s) = 20P - 400?

Question

Find consumer surplus for demand Q(d) = 1400 - 10P and supply Q(s) = 20P - 400?

Answer 1

Consumer surplus is the upper triangle that the demand curve makes w the equilibrium price and quantity. To find it, you take the difference between the max price and the equilibrium price and multiply it by the  equilibrium quantity and  divide by 2. 

 

Set Qd = 0 and find Max Price=140. 

 

Equilibrium price is found by setting Qs=Qd. 

 

1400-10P=20P-400

30P=1800

P=60. 

 

Subsituting p back into either equation gives Q=800. 

 

CS=.5(140-60)(800)

CS=$32,000