Answer:
Equilibrium Price P' = 0.2t - 0.24
Equilibrium Quantity Q' = 21.24 -0.2t
Explanation:
Coffee Demand Q = 21 - P .........................
Coffee Supply Q = 3 + 0.25P ......................
Writing equations for the equilibrium price and quantity as a function of a specific tax "t"
New Supply equation:
Q = 3 + 0.25 (P-t)
Q = 3 + 0.25P - 0.25t ...............................
In equilibrium, New Supply is equal to demand
Therefore;
3 + 0.25P - 0.25t = 21 - P
0.25P + P = 0.25t - 3
1.25P = 0.25t - 3
P' = 0.2t - 0.24 .......................................
Substituting P' into demand equation
Q = 21 - [0.2t - 0.24]
Q = 21 - 0.2t + 0.24
Q' = 21.24 -0.2t ........................................
Answer:
The equation for equilibrium price is P = 14.4 + 0.2t and the equation for equilibrium quantity is Q = 6.6 - 0.2t.
The after-tax equilibrium price is $14.58 and the quantity is 6.42 units.
The tax incidence on consumers is 20%.
Explanation:
Qd = 21 - P
Qs = 3 + 0.25P
A tax t is imposed on the producers.
New supply function = Qs = 3 + 0.25(P - t)
The new equilibrium is where Qd = New Qs
21 - P = 3 + 0.25(P - t)
21 - P = 3 + 0.25P - 0.25t
18 + 0.25t = 1.25P
P = (18 + 0.25t) / 1.25
P = 14.4 + 0.2t
Substituting this value of P in Qd function:
Q = 21 - (14.4 + 0.2t)
Q = 6.6 - 0.2t
If t = 0.9, the after-tax equilibrium price and quantity are as follows.
P = 14.4 + 0.2(0.9) = 14.58
Q = 6.6 - 0.2(0.9) = 6.42
The before-tax equilibrium price was:
21 - P = 3 + 0.25P
1.25P = 18
P = 14.4
Tax burden on consumers = After-tax equilibrium price - Before-tax equilibrium price
Tax burden on consumers = 14.58 - 14.4 = 0.18
Tax incidence on consumers
= (Tax / Tax burden on consumers) x 100
= (0.18 / 0.9) x 100
= 20%
