Find the consumer's surplus for the following demand function at the given point.
-Find the consumers' surplus at a price level of for the price-demand equation
A) $4050
B) $720
C) $405
D) $29,250

Question

Find the consumer's surplus for the following demand function at the given point.
-Find the consumers' surplus at a price level of  for the price-demand equation 
A) $4050 
B) $720 
C) $405 
D) $29,250

Quizplus · Accepted Answer

To find the consumer surplus, we need to integrate the demand function from the point of zero quantity demanded to the point at which the consumer is willing to pay (in this case, a price level of 11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11).

The demand function given is: 11ebb6d7_489d_6316_b437_4fb4a87bfedd_TB8593_11

Integrating this from q=0 to q=11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11:
∫(0 to 11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11) (80 - 5p) dp

= 80(11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11) - (5/2)(11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11)^2

= $405

Therefore, the consumer surplus is $405. To find the consumer's surplus at a price level of 11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11, we need to first find the quantity demanded at that price level.

Substituting the price level into the demand equation:

11ebb6d7_489d_6315_b437_4fb4a87bfedd_TB8593_11

Qd = 4000 - 50P 
Qd = 4000 - 50(11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11)
Qd = 4000 - 550 
Qd = 3450

So, at a price level of 11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11, the quantity demanded is 3450.

Next, we need to find the maximum amount a consumer is willing to pay for that quantity. To do this, we need to find the demand equation in terms of quantity:

Qd = 4000 - 50P 
P = 80 - 0.02Q

Now we can find the maximum amount a consumer is willing to pay (also known as the reservation price) for a quantity of 3450:

P = 80 - 0.02(3450) 
P = 80 - 69 
P = 11

So, the maximum amount a consumer is willing to pay for the quantity demanded at a price level of 11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11 is 11.

Consumer surplus is the difference between what a consumer is willing to pay (reservation price) and what they actually pay (market price):

CS = Reservation Price - Market Price 
CS = 11 - 11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11
CS = 11 - 11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11
CS = 405

Therefore, the consumer's surplus at a price level of 11ebb6d7_489d_6315_b437_9b7c777e4ca3_TB8593_11 is $405.

Find the Consumer's Surplus for the Following Demand Function at the Given