Problem 2. As you know, couples usually decide how many children they want to have (an). Since family resources are limited, there is a tradeoff between the quantity of children in a family and consumption of \"other goods\" (I2). Assume a family budget of m, a \"price\" per children of p 1, and a price of \"other goodS\" ofpz. Assume also that parental preferences are described by u(x1,.72) = 3:132:24. Assume perfect divisibility of children. a. Find the demand mctions for an and x: in terms of m, p1 and p2. b. Assume m = 14 and p1 =p2 = 1. What is the optimal bundle? c. Now assume the price of children increases to 131 = 3. Compute the new optimal bundle. d. What is the (minimum) additional income the couple would need to be able to afford the original optimal bundle (i.e. the one you found in part b)? For simplicity, let's refer to that additional income as Am. Show clearly how you arrive to your results. What would be the optimal bundle if the couple had an income of 14 + Am and faced the new pricesp1= 3 andpz =1? Focusing on in, express the income and substitution effects in terms of your answers to parts b, c and e. Draw a graph with the three bundles and the corresponding indifference curves and budget lines. Carefully label the income and substitution effects. Problem 3. You may remember Philip, the philosopher who was concerned about the time devoted to writing a book (an) and the time of care of his elderly mother (36:). He had 16 hours available and his preferences were represented by the utility function u(x1,x2) = x1+ 4 11102). a. b. 0 Find the \"quantity demanded\" of x1 and x2, i.e. the optimal bundle. Now assume the government provides an in-kind subsidy that is proportional to the time devoted by Philip to the care of her mother. For every two hours devoted by Philip, the government provides one hour of care (assume the authorities send professional nurses as part of this policy). Find the new optimal bundle. . At the new \"prices\" (i.e. in presence of the proportional subsidy), how many hours would we need to \"take away\" from Philip to make the budget line cross the old budget line at the original bundle? Let's call your answer Am. Show clearly how you arrive to your results. What would be Philip's optimal bundle at the new prices and a budget of 16 - Am? . Focus on xi and express the income and substitution effects in terms of your answers to parts a, b and (1. Draw a graph with the three bundles and the corresponding indifference curves and budget lines. Carefully label the income and substitution effects