Question

This is a 5 part question; (a-e)The question reads: Suppose that a market is described by the following supply & demand equations: Qs=2P & Qd=300-P
a) Solve for the equalibrium price & quantity. (I think I understand this process.)
b)Suppose that a tax of T is placed on buyers so the new demand equation is:
Qd=300-(P+T). Solve for new equalib. What happens to the price received by seller, the price paid by buyers, & qty sold?
c)Tax revenue is T x Q. Use your answer to part (b) to solve for tax revenue as a function of T.
d) Graph the DWL
e) Gov't levies a tax on good of $200/unit. Is this a good policy? Why/Why not? Can you propose a better policy?

Answer 1

a) set Qs=Qd and solve for P.
b) Same, set Qs=Qd and solve for P. Buyer pays P+T, seller gets P. (I get P=100-T/3)
c) Let P^ and Q^ be the equilibrium price and quantity. TR=T*Q^. From supply Q^=2P^. Substitute. TR=T*2P^ = T*2*(100-T/3)= 200T-2T^2/3
d) dwl is dead weight loss, and is represented by the little triangle below demand above supply and to the right of the equilibrium Q.
e) In general, whether a tax is a good policy or not depends on how it compares to the other policy choices. However, this $200 tax is a BAD policy because the government could raise the same amount of money with a lower tax rate. Use calculus on the equation from c) to find the revenue maximizing tax rate. TR' = 200 - 4T/3. You have a maxima at T=150.