Suppose that the government decides to impose an excise tax of T on each unit of the commodity discussed in Exercise 1.3. What price will the consumers end up paying for each unit of the commodity?

Exercises

Exercise 1.1 Ifx + y = 3 and x – 2y = -3, what are x and y ?

Exercise 1.2 Solve the following simultaneous equations.
2x + y = 9,
x – 3y = 1.

Exercise 1.3 Suppose the market for a commodity is governed by supply and demand sets defined as follows. The supply set S is the set of pairs (q,p) for which q – 6p = -12 and the demand set D is the set of pairs (q,p) for which q + 2p = 40. Sketch Sand D and determine the equilibrium set E = S n D, the supply and demand functions qS, qD, and the inverse supply and demand functions pS, pD.

Exercise 1.4 Suppose that the government decides to impose an excise tax of T on each unit of the commodity discussed in Exercise 1.3. What price will the consumers end up paying for each unit of the commodity?

Exercise 1.5 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.

Exercise 1.6 The supply and demand functions for a commodity are If an excise tax of T is imposed, what are the selling price and quantity sold, in equilibrium?