Exercise 3. Suppose that Government is currently evaluating a tunnel-building-project from the point of view of society. It has been estimated that this project requires a total investment of 49 million euros, while the opportunity cost of resources employed in the construction of the tunnel is estimated to be 50 million euros for the society. In addition, the construction of the tunnel will cause an environmental damage, which is estimated to be 4 million euros. The calculations by analysts suggest that each passage of the tunnel by a vehicle will cause a cost of 4 euros to the society. The estimated demand for passages of the tunnel is described by demand function: T = 24 2PT , where T denotes the number of passages of the tunnel (in millions) and PT denotes the fee (in euros) charged per passage of the tunnel. (Suppose that this demand curve describes the demand for passages during the lifetime of a tunnel. Suppose also that the social discount rate as well as inflation rate are zero).

Suppose that the Government can not borrow any funds for the construction of the tunnel. The only two possible options for the Government to finance the construction of the tunnel are:

1) alternative 1: to impose an excise tax of 2 euros per unit of good X , or

2) alternative 2: to impose an excise tax of 3.5 euros per unit of good X.

Suppose that the excise tax considered can be established for one year only.

The annual demand in the market for good X is described by the demand function Xd = 80 4Pd, where Xd denotes the quantity of good X demanded (in millions) and Pd denotes the demander price (i.e. the price paid by consumer) per unit of good X (in euros). The annual supply in the market for good X is described by the supply function Xs = 2Ps, where Xs denotes the quantity of good X supplied (in millions) and Ps denotes the supplier price (i.e. the price received by the supplier) per unit of good X (in euros).

Given this information and restrictions imposed, would the construction of the tunnel be justified from the societys point of view? If the Government should implement this tunnel-building-project, then which of the taxes should it apply in order to obtain neccessary funds for the implementation of this project? Justify your answers and provide all the neccesary calculations for proof!