(f) At the equilibrium, the optimal conditions of both parties must be satisfied. Combine the op- timal conditions for the household and the firm and show that the decentralised equilibrium is characterised by the following system of equations !: K Labour supply: NY C? = (1 - Q) At N (9) a-1 Consumption Euler: C," = BE (CH1) "|aAl Ki+1 + 1-6 Ni+1 (10) Resources constraint: Ci + Ki+1 = AK,'N' + (1 -6)K, (11) Stochastic process: In (A,) = p In(A/-1) + 8, where & ~ N(0, oz) ( 12 ) Is the optimal allocation of this decentralised problem Pareto Efficient? Explain. (Hint: what would the social planner's optimal conditions be when faced with the same environment?) (15 marks)