Question

Using Supply and Demand to Analyze Markets — End of Chapter Problem

The annual demand for full-spectrum LED light bulbs in Fairbanks, Alaska, is estimated to be ??=20,000−1,000?. The supply is estimated to be ??=−12,000+3,000?.

a. What is the equilibrium price of full‑spectrum LED light bulbs? ____ dollars

b. What is the equilibrium quantity of full‑spectrum LED light bulbs? _____ customers

c. What is consumer surplus? ____ dollars

d. What is producer surplus? _____ dollars

e. What is the total surplus received by both producers and consumers? _____dollars

Answer 1

Equilibrium is achieved where demand and supply both equal.

On a graph, equilibrium is achieved where demand and supply curves intersect each other.

Demand

Q = 20000 - 1000P

Supply

Q = -12000 + 3000P

Equating both demand and supply

20000 - 1000P = -12000 + 3000P

32000 = 4000P

P = 8

Equilibrium price is $8

To find the equilibrium quantity we can use this price in any of the above two equations.

Q = 20000 - 1000P

Q = 20000 - 1000(8)

Q = 12000

Equilibrium quantity is 12000 units

Consumer surplus

In the above graph, the blue region represents the consumer surplus hence the area of this triangle will be equal to consumer surplus.

Area = 1/2 x base x height

Area = 1/2 x 12 x 12000

Area = 72000

Consumer surplus is $72000

Producer surplus

In the above graph, the red region represents the producer surplus hence the area of this triangle will be equal to producer surplus.

Area = 1/2 x base x height

Area = 1/2 x 4 x 12000

Area = 24000

Producer surplus is $24000

Total Surplus

Total Surplus = Consumer Surplus + Producer Surplus

Total Surplus = 72000 + 24000

Total Surplus = 96000

Total surplus is $96000