this is based off of Anthony and Brigg's Mathematics 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?