Answer to Question #235500 in Microeconomics for Enos

Question

Consider the perfectly competitive market for Diesel. The aggregate demand for gasoline is The aggregate demand for gasoline is

𝑄𝑑 =100−𝑝

While the aggregate supply is 𝑄𝑠 = 3𝑝

a) Work out the equilibrium price and quantity.

b) At the equilibrium level established in part a), calculate the consumer surplus, producer surplus

and total surplus. [7 Marks]

c) It is established that most fuel stations are going out of business To address this problem, the government decides to set a minimum price of 𝑝̅ = 30 . What will be the new equilibrium price and quantity? What will be the new consumer surplus and producer surplus? Who gains and who loses from this regulation? Explain how the total surplus affected? Briefly explain the

intuition

Answer 1

Solution:

a.). At equilibrium: Qd = Qs

100 – p = 3p

100 = 3p + p

100 = 4p

P = 25

Equilibrium price = 25

Substitute in Qd function to get equilibrium quantity:

Qd = 100 – p = 100 – 25 = 75

Equilibrium quantity = 75

 

b.). As per the below graph at equilibrium:

Consumer surplus =$\frac{1}{2}\times (base\times height) = \frac{1}{2}\times (75\times 75) = \frac{1}{2}\times 5625 = 2812.5$

Consumer surplus = 2812.5

 

Producer surplus = $\frac{1}{2}\times (base\times height) = \frac{1}{2}\times (75\times 25) = \frac{1}{2}\times 1875 = 937.5$

Producer surplus = 937.5

 

Total surplus = Consumer surplus + Producer surplus

Total surplus = 2812.5 + 937.5 = 3,750

Total surplus = 3,750

 

c.). When the government sets a minimum price of 30, it will be setting a price floor above the equilibrium price.

The equilibrium price and quantity will not be affected by the price floor but rather the quantity demanded and supplied. The quantity supplied will exceed the quantity demanded, resulting in an excess supply.

 

The new consumer surplus will be as follows with the regards to the below diagram:

New Consumer surplus = $\frac{1}{2}\times (base\times height) = \frac{1}{2}\times (70\times 70) = \frac{1}{2}\times 4900 = 2450$

New Consumer surplus = 2450

New Producer surplus = $\frac{1}{2}\times (70\times 25) + \frac{1}{2}\times (70\times 5) = 875 + 175 = 1050$

New Producer surplus = 1050

 

New Total surplus = Consumer surplus + Producer surplus

New Total surplus = 2450 + 1050 = 3,500

New Total surplus = 3,500

 

Dead Weight Loss (DWL) = 3,750 – 3,500 = 250

 

The producers will gain more from the price floor since the producer surplus increases from the previous figure before the price floor.

 

The total surplus will slightly decrease from the previous figure before the price floor due to the reduction in consumer surplus.