Answer to Question #233700 in Microeconomics for Teddy

Question

Consider the perfectly competitive market for Diesel. The aggregate demand for gasoline is
The aggregate demand for gasoline is
Q_d=100-p
While the aggregate supply is Q_s= 3p
Work out the equilibrium price and quantity.
At the equilibrium level established in part a), calculate the consumer surplus, producer surplus and total surplus.

Answer 1

Given

$Qd=100-p\\Qs=3P$

At equilibrium Qs=Qd

$100-p=3p\\100=3p+p\\100=4p\\p=25\\Q=3p\\Q=3(25)\\Q=75$

Consumer surplus

$Qd=100-p\\0=100-p\\p=100\\\frac{1}{2}×75×(100-25)\\\frac{1}{2}×75×75\\=2812.5$

Producer surplus

$Qs=3p\\0=3p\\p=0\\\frac{1}{2}×75×(25-0)\\\frac{1}{2}×75×25\\=900$

Total surplus=producer surplus + consumer surplus

$=900+2812.5\\=3712.5$