The demand function for a certain product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable.

Question

The demand function for a certain product is  and the supply function is  where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable. ​

Quizplus · Accepted Answer

To find the equilibrium point, we need to set the demand and supply functions equal to each other and solve for x:

11ea984b_b099_0a01_9029_b31709ea25a9_TB4005_11 = 11ea984b_b099_0a02_9029_df7d485f7c3f_TB4005_11

Solving for x, we get:

-4x + 80 = 8x + 16
12x = 64
x = 4

So the equilibrium point is (4, 64).

To find the consumer's surplus, we need to integrate the demand function from 0 to the equilibrium quantity (4):

CS = ∫[0,4] (11 - 0.5x) dx - 64(4)
CS = [11x - 0.25x^2][0,4] - 256
CS = 44 - 16 - 256
CS = -228
CS ≈ -228 ≈ -230

Since consumer's surplus cannot be negative, we can conclude that there is no consumer surplus at the given equilibrium point. Therefore, the answer is (A).

The Demand Function for a Certain Product Is and the Supply