Economic Help?

Question

I am having a hard time on the following question

You are given the following:

QS = 100 + 3P
QD = 400 - 2P

I know that Equilibirum Price = 60 and Equilibirum Quantity = 280.

Now, suppose that a tax is placed on buyers so that
QD = 400-(2P + T)

If T = 15, solve for the new equilibrium price and quantity. (Note: P is the price received by sellers and P+T is the price paid by buyers.) Compare these answers for equilibrium price and quantity with your first answers.

Answer 1

There is one minor problem with your question, but it would throw you off substantially. The new equation for QD will read QD=400-2(P+T), as the note on the bottom indicates. Then, to find equilibrium, set QS=QD.

100+3P=400-2(P+15)
100+3P=400-2P-30
100+3P=370-2P
5P=270
P=54
Q=262

Thus, sellers now only get 54 instead of 60, while buyers pay 54+15=69. Thus, sellers bear 6 of the tax, while buyers bear the other 9. Quantity reduces by 18.

Answer 2

Assuming your provided equations are correct.

QD= 400 - (2P + T)
QS= 100 + 3P
T= 15

400 - (2P + 15) = 100 + 3P
400 - 2P - 15 = 100 + 3P
285 = 5P
**57 = P**

QD = 400 - (2*57 + 15)
**QD = 271**


So you can see that by imposing this tax the eq. price falls but so does the eq. quantity. You sell less product for a lower price.