1 The US household In this problem you will study the representative household. Suppose that the utility function is given by U(0,1)=In(c)+yIn(l) where c is consumption, 1 is leisure, and y is a parameter that determines how much the repre- sentative household values consumption versus leisure. Assume that y> 0. Let h be the total time endowment, w the wage and at the dividend payments. 1. Write down the household optimization problem (don't forget taxes and dividends in the bud- get constraint) 2. Write down the feasible at the budget line condition. 3. For the optimal trade-off condition for household decisions, (a) write down the marginal utility of consumption and leisure respectively (b) write down the opportunity cost of leisure (c) write down the optimal trade-off condition