this is based off of Anthony and Brigg'sMathematics For Economics And Finance: Methods And Modeling.

it's exercise 1.5 on pg 11.

the question reads, "Find a formula for the amount of money the government obtains from taxing the commodity in the manner described in exercise 1.4. Determine this quantity explicitly when T=0.5."

i'll give you the required equations:

qS = 6p - 12

qD = 40 - 2p

the excise tax = pT = (13/2)+(3/4)T

the answer = 27T - (3/2)T^2

i have no clue how they came up with that answer. i got 27 + (9/2)T.

my process was to substitute the value of pT into qS.

i also tried putting pT-T into qS, which gets me 27 + (3/2)T, close but not exactly the answer.

also, i just followed the example in the book so i don't really have a conceptual understanding of the why, so can someone explain the logic behind inserting pT-T vs pT into qS?