We assume C1 1 u(Ct,Lt)= t ln(1Lt) with > 0 and > 0. The household can choose values of labour input between 0 and 1. In this model, we can interpret the labour input as the fraction of the household's time that she spends at work. Therefore, 1 Lt is the fraction of her time that she spends on "leisure" (i.e., anything else besides work). 1. How does utility depend on leisure? What role does the parameter play? 2. Write down the Bellman equation of the consumer's dynamic programming problem. Hint: You can apply our result from the lecture: apart from the utility function, nothing has changed. 3. Write down the first-order conditions for the optimal choices of consumption Ct and labour Lt. 4. Combine the two first-order condition to get a relationship between labour Lt, wages wt and consumption Ct. 5. All else equal, how does labour supply react to an increase in wages? How does labour supply react to an increase in consumption