Answer:
To determine the consumer surplus at the market equilibrium point, we first need to find the equilibrium price and quantity.
At equilibrium, the quantity demanded (D(x)) equals the quantity supplied (S(x)). So, we can set the demand and supply functions eq
-4x + 40 = 5x + 4
Combine like terms:
-9x = -36
Divide by -9:
x = 4
Now that we know the equilibrium quantity, we can substitute this value into either the demand or supply function to find the equilibrium price (p). Let's use the demand function:
p = D(x)
p = -4(4) + 40
p = 16 + 40
p = 56
So, the equilibrium price is 56.
To calculate consumer surplus at the market equilibrium point, we need to find the area between the demand curve and the equilibrium price. In this case, the demand function is a straight line with a negative slope (-4x + 40).
To find the consumer surplus, we need to find the area of the triangle formed by the equilibrium price (56), the x-axis (quantity axis), and the demand curve.
The base of the triangle is the equilibrium quantity (x = 4) and the height is the difference between the equilibrium price (56) and the y-intercept of the demand curve (40).
Therefore, the consumer surplus is given by:
Consumer Surplus = (1/2) * base * height
Consumer Surplus = (1/2) * 4 * (56 - 40)
Consumer Surplus = (1/2) * 4 * 16
Consumer Surplus = 8 * 16
Consumer Surplus = 128
So, the consumer surplus at the market equilibrium point is 128.
Please note that the answer options provided in the question do not include 128, so none of the given options are correct.