Suppose the market demand function in a certain market where Q is measured in thousands of units is Q^d = 20 - 2.5P,and the market supply function is Q^s = 2.5P - 7.5.How much deadweight loss would there be in this market if the quantity bought and sold was 6,000 units? A) $0.03 B) $25 C) $500 D) $2,500

Question

Quizplus · Accepted Answer

To find the deadweight loss, we first need to find the equilibrium price and quantity. This is where the market demand and supply curves intersect:

20 - 2.5P = 2.5P - 7.5
5P = 27.5
P = 5.5

Now we can find the equilibrium quantity:

QS1U1P1 = QS1U1P1s
20 - 2.5P = 2.5P - 7.5
Q = 6,000

At this quantity and price, the consumer surplus is:

CS = (0.5)*(20 - 5.5)*(6,000) = $57,750

And the producer surplus is:

PS = (0.5)*(5.5 - 2.5)*(6,000) = $9,000

The total surplus is the sum of the consumer and producer surplus:

TS = CS + PS = $66,750

Now suppose a price floor of $6 is imposed. This means that a price of $6 will be enforced, regardless of the market equilibrium. At a price of $6, the quantity demanded is:

20 - 2.5(6) = 5

And the quantity supplied is:

2.5(6) - 7.5 = 9

So there is a surplus of 4 units. The deadweight loss is the loss of surplus due to the price floor. In this case, the loss of consumer surplus is:

CS2 = (0.5)*(20 - 6)*(6) = $84

And the loss of producer surplus is:

PS2 = (0.5)*(6 - 2.5)*(6) = $13.5

The total deadweight loss is the sum of these two losses:

DWL = CS2 + PS2 = $97.5

Therefore, the answer is B) $25.

Suppose the Market Demand Function in a Certain Market Where