O que tem me afastado do blog

Tenho postado pouco ultimamente.
Por aqui o semestre vai chegando ao final... trazendo a tradicional alegria.
Selecionei duas partes (de 4) de uma questão da prova de macro do ano passado.
Enfim, tai pra quem quiser brincar. Não achei muito fácil, mas também não é impossível.
Bom disso tudo é que eu descobri (realmente) o que é a curva de oferta de Lucas, tinha uma noção meio estranha dela.
(não sei pq diabos a letra ficou tão pequena no final do post, tentei aumentar mas não funcionou)

b) Assume an economy with many producers of differentiated goods. A representative
producer produces good i according to Qi=Li, where Q denotes the output and L the labor input.
Denote the log of aggregate output by y. Consumption Ci of the representative household
equals real income from the production of good i. Utility of a representative household is given
by:

Ui = Ci − 1/θ L^θ , with θ>0

Assume that individual i can only observe the price Pi of its good i. Let p denote the log of the
price index in the economy which is the average of the logs of all prices pi. Based on this
observation the individual builds rational expectations about the relative price of its good i, i.e.
E[ri|pi], with ri denoting the log of the relative price. Assume further that:

E[ri | pi ] = Vr/(Vr +Vp) [pi - E[p]]

with Vr and Vp denoting the variance of the relative price and
the price level, respectively.
Derive the Lucas supply function (in logs). Discuss your result.

c) Derive the output and the price level in equilibrium as a function of the aggregate demand m
and the expectations on the aggregate demand E[m]. Use the aggregate demand function
y = m − p . Discuss your results. Show that these results can motivate a positively sloped AS
curve. Why can the Phillips-curve relationship implied by the Lucas supply function not be
used by politicians to increase output and thereby employment in an economy?


PS. Inveja das pessoas que já estão de férias