Master Thesis - Humboldt-Universität zu Berlin

4 The Model
Our model consists of two coutries: EU and USA, that may differ in size,
but are otherwise isomorphic, and the rest of the world. Hence, our exposition
below focuses on the EU economy. The model incorporates features
designed to account for the effects of oil and non-oil import shocks by allowing
them to enter both the intermediate goods production and the final
goods production.
4.1 Households
In each country, there is a continuum of households indicated by the index
τ = [0; 1], each one supplying a complete set of differentiated labour.
The instantaneous utility function of each household depends positively on
consumption C t relative to an external habit variable H t and negatively on
labour supply lt τ :
U τ t = 1
1 − σ c
(C τ t − H t ) 1−σc · exp( σ c − 1
1 + σ l
(l τ t ) 1+σ l
) (1)
where σ c determines the intertemporal elasticity of substitution and σ l the
elasticity of work effort with respect to real wage. Habit formation, which
among economists is called ”keeping up with the Joneses” is a constant fraction
of the previous time consumption:
H t = hC t−1 (2)
Each household maximizes an intertemporal utility function with β as discount
factor:
E 0
∞
∑
t=0
β t U τ t (3)
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