Fiscal Cooperation between Europe and America

Abstract

The model of unemployment, inflation, and the structural deficit can be characterized by a system of six equations:

$$ u_{1} = A_{1}- G_{1} + 0.5G_{2} $$

(1)

$$ u_{2} = A_{2}- G_{2} + 0.G_{1} $$

(2)

$$ \pi_{1} = B_{1}+G_{1}-0.5G_{2} $$

(3)

$$ \pi_{2} = B_{2}+G_{2}-0.5G_{1} $$

(4)

$$ s_{1}=G_{1}- T_{1} $$

(5)

$$ s_{2}=G_{2}- T_{2} $$

(6)

The policy makers are the European government and the American government. The targets of fiscal cooperation are zero unemployment and a zero structural deficit in each of the regions. The instruments of fiscal cooperation are European government purchases and American government purchases. There are four targets but only two instruments, so what is needed is a loss function. We assume that the European government and the American government agree on a common loss function:

$${\rm L} = {\rm u^2_1} + {\rm u^2_2} + {\rm s^2_1} + {\rm u^2_2}$$

(6)

L is the loss caused by unemployment and the structural deficit in each of the regions. We assume equal weights in the loss function. The specific target of fiscal cooperation is to minimize the loss, given the unemployment functions and the structural deficit functions.