Consider the problem of maximizing LB' (log c, + logd, ) subject to the constraints du = (1-6)d, + e, A,4 = (4, -6, -e, )(1+r) + y.4 4,+1 20 , d, 20 where c is consumption of nondurable goods, dis the stock of durables, a is expenditure on durables, + is the constant interest rate, A are assets and y is income. # is the constant discount factor. What might the constant $ represent? ii) Give an economic interpretation of this problem. iii) Set up the Lagrangian and give the first-order conditions. iv) Assuming the constraints are nonbinding, give a condition linking the marginal utility of durable consumption to the marginal utility of nondurable consumption