Question 4 The equation below is the optimisation problem for an infinite horizon model. Note that n, is hours worked', and not leisure and n is a parameter determining the elasticity of labour supply. L = Est In (C - 47 1=0 + At de [Pekin, "'+ P.(1 - 8) ke - Pekt+1 - Pict] IT (1) Derive the FOCs for ce, my, and ke+1- (2) Derive the optimal choice between consumption and hours worked. (3) What happens to the labour supply when there there is an increase in consumption (assume that the wage stays constant)