As you know, couples usually decide how many children they want to have (x1). since family resources are limited, there is a tradeoff between the quantity of children in a family and consumption of "other goods" (x2). assume a family budget of m, a "price" per children of pi, and a price of other goods" of p2. assume also that parental preferences are described by u(x1x2) = xı x2. assume perfect divisibility of children. a. find the demand functions for x and x2 in terms of m, pi and p2. b. assume m= 14 and pi = p2 = 1. what is the optimal bundle? c. now assume the price of children increases to pı = 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. e. what would be the optimal bundle if the couple had an income of 14 + am and faced the original prices (pı = p2 = 1)? f. focusing on x1, express the income and substitution effects in terms of your answers to parts b, c and e. g. draw a graph with the three bundles and the corresponding indifference curves and budget lines. carefully label the income and substitution effects.