Find the consumer surplus at the equilibrium point. D(x)=2-4x; x=1
To find the consumer surplus at the equilibrium point, we first need to find the equilibrium quantity (x) by setting the demand function (D(x)) equal to zero:
2 - 4x = 0
Solving for x:
-4x = -2
x = 1/2
So, the equilibrium quantity is x = 1/2.
To find the consumer surplus, we need to find the area between the demand curve and the equilibrium quantity. It is a triangle with base x=1/2 and height D(x=1/2).
Plugging in x = 1/2 into the demand function:
D(x=1/2) = 2 - 4(1/2) = 2 - 2 = 0
So, the height D(x=1/2) is equal to zero.
Thus, the consumer surplus at the equilibrium point is 0.