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.
A) Equilibrium point: (4, 64); Consumer's surplus: 43 million dollars
B) Equilibrium point: (10, 64); Consumer's surplus: 123 million dollars
C) Equilibrium point: (8, 64); Consumer's surplus: 203 million dollars
D) Equilibrium point: (4, 8); Consumer's surplus: 187 million dollars
E) Equilibrium point: (10, 8); Consumer's surplus: 107 million dollars

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. ​
A) Equilibrium point: (4, 64); Consumer's surplus: 43 million dollars 
B) Equilibrium point: (10, 64); Consumer's surplus: 123 million dollars 
C) Equilibrium point: (8, 64); Consumer's surplus: 203 million dollars 
D) Equilibrium point: (4, 8); Consumer's surplus: 187 million dollars 
E) Equilibrium point: (10, 8); Consumer's surplus: 107 million dollars

Quizplus · Accepted Answer

To find the equilibrium point, we need to set the demand equal to the supply and solve for x: 
11ea984b_b058_08b8_9029_6b010b3ed2c6_TB4005_11 = 11ea984b_b058_08b9_9029_43b79ea62264_TB4005_11 
64 - 2x = 4 + 3x  
Solving for x, we get x = 4. Thus, the equilibrium point is (4, 64).
To find the consumer's surplus at this point, we need to integrate the demand function from 0 to the equilibrium quantity (4) and subtract from it the price paid (which is 64): 
CS = ∫0^4 (64 - 2x) dx - 64 
CS = [64x - x^2]0^4 - 64 
CS = 256 - 16 - 64 = 176 
Rounding to the nearest million, we get a consumer's surplus of 43 million dollars, which matches option A.

The Demand Function for a Certain Product Is and the Supply