Question

Given:

QD = 132 – 8P

QS = 6 + 4P

(i) Find the equilibrium P and Q.

(ii) How does a per unit tax t affect outcomes?

(iii) What is the equilibrium P and Q if unit tax t = 4.5? 

Answer 1

(i) Equilibrium values

QD = QS

132 – 8P = 6 +4P

12P = 126

P = 10.5

Knowing P, find Q

Q = 6 +4P

= 6 + 4(10.5) = 48

Equilibrium values: P = 10.5 and Q=48

(ii)After adding tax

QD = 132 – 8P

QS = 6 + 4(P – t)

QD = QS

132 – 8P = 6 +4(P – t)

12P = 126 +4t

P = 10.5 +1/3 t

Knowing P, find Q

Q = 6 +4[P-t]

= 6 + 4[(10.5+1/3 t) – t]

= 48 - 8/3 t  

Imposing t increases consumer P by 1/3t, supplier pays 2/3t, and decreases Q by 8/3t

(iii)If per unit t = 4.5

P = 10.5 +1 /3(4.5) = 12

Q = 48 - 8 /3(4.5) = 36

Consumer P: £12 (pre-tax eq. p + 1/3t)

Supplier P: £7.5 (pre-tax eq. p – 2/3t) 

Imposing a tax increases the price a buyer pays by less than the tax. Similarly, the price the seller obtains falls, but by less than the tax.