The market for Soda was represented by the following demand

The market for Soda was represented by the following demand and supply: Qd= -100P + 1150 and Qs= 400P +100. After the FDA required additional information on calories on labels, the cost to the Bottling Co. increased and the Supply shifted to Qs= 400P + 150 a. What is the Pre-Regulation equilibrium quantity and price? b. What is the Post-Regulation Equilibrium price and quantity? c. What is the pre and post regulation producer surplus? d. Based on the change in producer surplus, do you think the supplier would have volunteered to provide label on calories information without it being required? Explain.

Solution

(a)

Pre-regulation Scenario -

Demand is as follows -

Q = -100P + 1,150

Supply is as follows -

Q = 400P + 100

In equilibrium,

Demand = Supply

-100P + 1,150 = 400P + 100

500P = 1,050

P = 1,050/500

P = 2.1

Q = -100P + 1,150 = (-100 * 2.1) + 1,150 = -210 + 1,150 = 940

Thus,

The pre-regulation equilibrium quantity is 940 cans.

The pre-regulation equilibrium price is $2.1 per can.

(b)

Post-regulation Scenario -

Demand is as follows -

Q = -100P + 1,150

Supply is as follows -

Q = 400P + 150

In equilibrium,

Demand = Supply

-100P + 1,150 = 400P + 150

500P = 1,000

P = 1,000/500

P = 2

Q = -100P + 1,150 = (-100 * 2) + 1,150 = -200 + 1,150 = 950

Thus,

The post-regulation equilibrium quantity is 950 cans.

The post-regulation equilibrium price is $2 per can.

(c)

Pre-regulation scenario -

Calculate the Producer Surplus -

PS = 1/2 * (Equilibrium price - 0) * Equilibrium quantity = 1/2 * (2.1 - 0) * 940 = $987

The pre-regulation producer surplus is $987.

Post-regulation scenario -

Calculate the Producer Surplus -

PS = 1/2 * (Equilibrium price - 0) * Equilibrium quantity = 1/2 * (2 - 0) * 950 = $950

The post-regulation producer surplus is $950.

(d)

As answer in part (c) indicates that producer surplus have decreased after the regulation was imposed by the FDA.

Decrease in producer surplus indicates adverse impact on soda suppliers.

So, the soda suppliers would not have volunteered to provide label on calories information without it being required.