Use the following equations to calculate aspects of the incidence of a tax on demand: Qd...

Use the following equations to calculate aspects of the incidence of a tax on demand:

Qd = 720 - 205P
Qs = -170 + 150P
Qs (with tax) = -220 + 150P

Find:

Q before tax =
Q after tax =
P before tax =
Pc =
Pp =
Tax rate (t) =
Tax revenue (TR) =
TR (coming from consumer surplus) =
TR (coming from producer surplus) =
Deadweight Loss (DW) =
DW (coming from consumer surplus) =
DW (coming from producer surplus) =

Expert Solution

Before tax, Qd = Qs
So, 720 - 205P = -170 + 150P
So, 150P + 205P = 720 + 170
So, 355P = 890
So, P before tax = 890/355 = 2.51
Q before tax = -170 + 150P = -170 + 150(2.51) = -170 + 376.5 = 206.5

After tax, Qd = Qs (with tax)
So, 720 - 205P = -220 + 150P
So, 150P + 205P = 720 + 220
So, 355P = 940
So, Pc = 940/355 = 2.65
Q after tax = 720 - 205Pc = 720 - 205(2.65) = 720 - 543.25 = 176.75

Qs = -170 + 150P = 176.75
So, 150P = 176.75 + 170 = 346.75
So, Pp = 346.75/150 = 2.31

Tax rate = Pc - Pp = 2.65 - 2.31 = 0.34

Tax revenue (TR) = Tax rate*Q after tax = (0.34)*(176.75) = 60.1

TR (coming from consumer surplus) = (Pc-P)*Q after tax = (2.65-2.51)*(176.75) = (0.14)*(176.75) = 24.75

TR (coming from producer surplus) = (P-Pp)*Q after tax = (2.51-2.31)*(176.75) = (0.2)*(176.75) = 35.35

Deadweight Loss (DW) = (1/2)*(Pc-Pp)*(Q-Q after tax) = (1/2)*(2.65-2.31)*(206.5-176.75) = (1/2)*(0.34)*(29.75) = 5.06

DW (coming from consumer surplus) = (1/2)*(Pc-P)*(Q-Q after tax) = (1/2)*(2.65-2.51)*(206.5-176.75) = (1/2)*(0.14)*(29.75) = 2.08

DW (coming from producer surplus) = 1/2)*(P-Pp)*(Q-Q after tax) = (1/2)*(2.51-2.31)*(206.5-176.75) = (1/2)*(0.2)*(29.75) = 2.98

Rahul Sunny answered 2 years ago

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