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 set the demand equal to the supply:

11ea984b_b0e8_893a_9029_89fd133f14f1_TB4005_12 = 11ea984b_b0e8_b04b_9029_1d4bf9a417d9_TB4005_12

Simplifying:

120 - 0.5p = 40 + 0.3p

0.8p = 80

p = 100

Substituting p back into either equation to solve for x:

x = 4

So the equilibrium point is (4, 100).

To find the consumer's surplus, we need to find the area between the demand curve and the equilibrium price, from x=0 to x=4:

CS = 0.5(64-100)(4) = 18

Rounding to the nearest million, the consumer's surplus is 18 million dollars, which is closest to answer choice A.

The Demand Function for a Certain Product Is and the Supply