Let u(x, y) be a utility function, where x is the consumption of a private good and y the

consumption of a public good. u is continuously differentiable, increasing, strictly quasi concave

and satisfies the Inada conditions (lim u

x (x, y) if x 0, y > 0, lim u

y (x, y) if

y 0, x > 0).

Consider the maximum problem

max{u(x, y) | x + y W} (1)

where the non negativity constraints, being unnecessary, are omitted. Let (xe(W), ye(W)) be the

solution to (1) as a function of the income W. We assume that both the private and the public goods

are normal goods for the preferences represented by u: xe(W) and ye(W) are increasing functions of

W. Since ye(W) is increasing, it is invertible and we denote by the inverse function (for your own

sake interpret the relation W = (y)). Note that (y) y > 0.

Consider now an economy with a private good and a public good, and I agents with the same

preferences represented by the utility function u satisfying the assumptions introduced above. The

production of public good exhibits constant returns, one unit of private good producing one unit

of public good. Agents differ by their incomes. Let wi denote the income of agent i. We want to

show that in a voluntary contribution equilibrium of such an economy there is a level of income w

such that all agents with income lower than w do not contribute, and agents with income above w

contribute wi w.

(a) Let

(xi)

I

i=1,(zi)

I

i=1, y

be a voluntary contribution equilibrium of the economy described

above, where zi denote the contribution of agent i (zi = i xi), and y =

P

i

zi

. Let

Zi =

P

j6=i

zj be the contribution of the agents other than agent i. Show that

- if zi > 0, then y = ye

wi + Zi

;

- if zi = 0, then y ye

wi + Zi

;

[Hint: show that you can express the maximum problem of agent i choosing his optimal contribution

to the public good under the form of problem (1) with one additional inequality constraint on y.]

(b) Let w = (y) y. Deduce from (a) that

(i) If wi w, then it must be that Zi = y and zi = 0.

(ii) If wi > w, then it must be that Zi < y and zi > 0.

(iii) Deduce from (ii) that if wi > w, zi = wi w.

(c) Let us apply the previous result to an economy with two types of agents, the rich and the

poor. All agents have the same utility function

u(xi

, y) = ln(xi) + ln(y), 0 < < 1.

There are n1 "poor" agents with income w1, and n2 "rich" agents with income w2, where

w1 <

n2

1+n2

w2. Show that the voluntary contribution equilibrium cannot be such that all

agents contribute (use (b)(iii) and proceed by contradiction). Calculate the equilibrium with

voluntary contributions.

Explain why international trade is essential for the Irish economy.

(ii) Has Ireland, in recent years, tended to have a surplus or a deficit on the Balance of

Payments Current Account? Outline the economic consequences of this situation.

(30 marks)

(b) State and explain how imports into the Euro-zone would be affected by each of the

following developments:

(i) the US dollar rises in value against the euro;

(ii) employment within the Euro-zone increases.

(20 marks)

(c) Ireland has attracted many multinational companies to establish operations in recent years.

There has also been a recent trend for some of these companies to relocate to eastern Europe

or Asia.

(i) Outline reasons why these multinational companies locate in Ireland.

(ii) Outline possible reasons for the current relocation to other regions.