The inverse market demand and supply functions

Consider a good for which the inverse market demand and supply functions
are given by
PD(q) = 1 − 2q, PS(q) = 3q.
a) Please compute the competitive equilibrium (price and quantity).
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b) What is the consumer surplus? What the producer surplus? Indicate the respective areas in a graph, and
compute their numerical values.
c) Now suppose the government imposes a quantity tax of t = 1/10. Cal- culate the new equilibrium quantity,
the demand price pD, and the supply price pS. Also, solve geometrically for the equilibrium under the
assumption (i) that consumers are in charge of paying the tax to the government, or (i) that firms are in charge.
d) Find out the new consumer surplus and the new producer surplus. How much of the tax burden t per unit is
borne by consumers and producers, respectively? How big is the deadweight loss of the tax?