Question

Banana Inc. is about to unveil their latest flagship phones, jPhone 11 pro in some few months. After a survey conducted by the company, they realized that the market demand for jPhone 11 pro is characterized by the following equation; P= 4000-0.5Qd. Also, the supply curve for Banana Inc is characterized by the following equation; P=0.5Qs.

a. With the information above, solve for the equilibrium price and quantity.

b. Suppose the government imposes a per unit tax of $100 per unit produced. Determine the new equilibrium price and quantity and illustrate your answer on the diagram. Also calculate the consumer surplus and producer surplus before and after the tax

c. Calculate the dead-weight loss as a result of the tax imposed by the government.

d. Calculate the government tax revenue.  (1 mark)

Answer 1

P= 4000-0.5Qd Demand function

P=0.5Qs Supply function

a.

Equilibrium condition:

Demand = Supply

4000-0.5Q = 0.5Q

4000= Q* Equilibrium quantity

Use Q*= 4000 in supply function:

P*= 0.5(4000)= 2000 Equilibrium price

b.

Suppose the government imposes a per unit tax of $100 per unit produced. This will cause price received by the producer to decrease:

New supply curve: (P-100)= 0.5Qs

P= 0.5Qs+100 New supply curve

Equilibrium condition:

Demand = New Supply

4000-0.5Q = 0.5Q+100

3900= Q** Equilibrium quantity

Use Q*= 3900 in demand function:

P*= 4000-0.5(3900)= 2050 Equilibrium price

Ps= Price seller received= 2050-100= 1950

Before tax:

Consumer surplus= Area (a+b+c+d)= (1/2)(4000-2000)(4000)= 4,000,000

Producer surplus= Area (e+f+g+h+i)= (1/2)(2000-0)(4000)= 4,000,000

Total surplus= 4,000,000+4,000,000= 8,000,000

After tax:

Consumer surplus= Area (a)= (1/2)(4000-2050)(3900)= 3,802,500

Producer surplus= Area (h+i)= (1/2)(1950-0)(3900)= 3,802,500

c.

Deadweight loss is the area which is not earned by anyone in the society after tax.

Here:

Deadweight loss= Area(d+g)= (1/2)(2050-1950)(4000-3900)= 5000

d.

Government tax revenue can be calculated by taken out the product of amount of tax and quantity being traded in the market.

Government revenue= Area(b+c+e+f)= (2050-1950)(3900)= 390000