Answer to Question #232643 in Microeconomics for WAQUAS

Question

Suppose the following demand and supply function:

Q^d = 750 – 25P

Q^s = -300 + 20 P

       i.           Find equilibrium price and quantity

Find consumer and producer surplus

Answer 1

Equilibrium price and quantity

• At equilibrium, Qd = Qs
• But,
• Q^d = 750 – 25P
• and
• Q^s = -300 + 20 P
• Hence,
• 750 – 25P = -300 + 20 P
• – 25P – 20P = -300-750
• -45P = -1050
• P = $23.3333
• Equilibrium Price = $23.33
• Q^d = 750 – 25 (23.33)
• Q = 166.6675 units
• Equilibrium Quantity = 166.67 Units

Consumer and producer surplus

To determine consumer and producer surplus, we will first sketch the demand and supply curves.

Find prices when Qd and Qd equals zero

• When Qd = 0
• Qd = 750 – 25P
• 0 = 750 – 25P
• -25P = -750
• P = 30
• When Qs = 0
• Qs = -300 + 20 P
• 0 = -300 + 20 P
• 20P = 300
• P = 15

Using the above figures, sketch demand and supply diagram curves.

In the figure above, consumer surplus is exhibited by region shaded purple while producer surplus is shown by area shaded blue.

Consumer surplus

• Area = 1/2 * base * height
• But,
• Base = 166.67
• Height = 30 – 23.33 = 6.67
• Hence,
• Area = 1/2 * 166.67 * 6.67 = $555.84

Producer surplus

• Area = 1/2 * base * height
• But,
• Base = 166.67
• Height = 23.33 – 15 = 8.33
• Hence,
• Area = 1/2 * 166.67 * 8.33 = $694.18