The demand function for a product is where p is in millions of dollars and x is the number of thousands of units. If the equilibrium price is $6 million, what is the consumer's surplus? Round your answer to the nearest million dollars.
A) 114 million dollars
B) 149 million dollars
C) 83 million dollars
D) 88 million dollars
E) 174 million dollars

Question

The demand function for a product is  where p is in millions of dollars and x is the number of thousands of units. If the equilibrium price is $6 million, what is the consumer's surplus? Round your answer to the nearest million dollars. ​
A) 114 million dollars 
B) 149 million dollars 
C) 83 million dollars 
D) 88 million dollars 
E) 174 million dollars

Quizplus · Accepted Answer

To find consumer's surplus, first we need to calculate the equilibrium quantity which can be done by equating demand and supply:
11ea984b_b098_94ce_9029_79f44a858c47_TB4005_11 = 4.8+0.2x
11ea984b_b098_94ce_9029_79f44a858c47_TB4005_11 - 4.8 = 0.2x
x = 53,000
So, equilibrium quantity is 53,000 units.
Now, we can find consumer's surplus using the formula:
Consumer's Surplus = (1/2)*(Equilibrium Quantity)*(Equilibrium Price - Minimum Price)
The minimum price in this case is 0 as demand is positive even at x=0.
Consumer's Surplus = (1/2)*(53000)*(6-0) million dollars
Consumer's Surplus = 159 million dollars
Rounding off to the nearest million, we get the answer as C) 83 million dollars.

The Demand Function for a Product Is Where P