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 5,000 units? A) $0.63 B) $62.50 C) $625 D) $6,250

Question

Quizplus · Accepted Answer

Deadweight loss can be calculated as the difference between the consumer surplus and producer surplus at the equilibrium quantity and price, compared to the maximum possible surplus at the efficient quantity and price.

At the equilibrium quantity of 5,000 units, the equilibrium price can be found by setting the quantity demanded equal to the quantity supplied:

20 - 2.5P = 2.5P - 7.5

5P = 27.5

P = 5.5

So the equilibrium price is $5.50 per unit.

To find the equilibrium quantity, we can plug this price into either the demand or supply function:

Q = 20 - 2.5(5.5) = 6.25

So the equilibrium quantity is 6,250 units (measured in thousands).

The maximum possible surplus at the efficient quantity and price can be found by setting the demand function equal to the supply function:

20 - 2.5P = 2.5P - 7.5

5P = 27.5

P = 5.5

Q = (20 - 2.5(5.5))/5 = 1.5

So the efficient quantity is 1,500 units.

Consumer surplus at the equilibrium quantity and price can be found by integrating the demand function from 0 to 5.5:

CS = ∫(20 - 2.5P)dP from 0 to 5.5

CS = [(20P - 1.25P^2)/2.5] from 0 to 5.5

CS = $55

Producer surplus at the equilibrium quantity and price can be found by integrating the supply function from 0 to 5.5:

PS = ∫(2.5P - 7.5)dP from 0 to 5.5

PS = [(1.25P^2 - 7.5P)/2.5] from 0 to 5.5

PS = $13.75

The maximum possible surplus can be found by multiplying the efficient quantity by the difference between the demand and supply functions at the efficient price:

MPS = (20 - 2.5(5.5) - (2.5(5.5) - 7.5))(1.5)

MPS = $68.75

Therefore, the deadweight loss is $68.75 - ($55 + $13.75) = $0.63 million, or $62.50 when measured in thousands of dollars.

Suppose the Market Demand Function in a Certain Market Where