Business Applications

Question

Given: (x is number of items)Demand function: Supply function: 

Find the consumers surplus at the equilibrium quantity

Answer 1

Hello Henry,

First, you need to find the equilibrium quantity. You do that by setting the demand function equal to the supply function.

200 - 0.5x = 0.3x ---> 200 = 0.8x ---> x = 200/0.8 = 250

At equilibrium, demand and supply prices are equal. replace x by 250 in either function:

d(250) = 200 - 0.5*250 = 200 - 125 = 75.

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Consumer surplus: if you graph both functions, you will see that the y-axis, the function d(x) and the horizontal line y = 75 will form a right triangle. The consumer surplus will be the area of that triangle.

A = (1/2) * base * height.

The base of that triangle will be 250

The height of that triangle will be 200 - 75 = 125.

All you have to do now is plug those numbers in the formula for area, and that will get you a numerical value for consumer surplus at the equilibrium quantity of 250.

Cheers.