Monetary Cooperation between Europe and America: Case B

Abstract

The model of unemployment and inflation can be represented by a system of four equations:

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

(1)

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

(2)

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

(3)

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

(4)

The policy makers are the European central bank and the American central bank. The targets of monetary cooperation are zero inflation and zero unemployment in each of the regions. The instruments of monetary cooperation are European money supply and American money supply. There are four targets but only two instruments, so what is needed is a loss function:

$${\rm L} = \pi_1^2 + \pi^2_2 + {\rm u}^2_1 + {\rm u}^2_2$$

(5)

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