economists have begun to think that decisions by poor families in developping countries to have more or less children are linked to their rational preferences for a range of consumption goods, including chilren as a special good. this question illustrates microeconomic theory of fertility. consider a typical rural family in a developing country Feriland, has an annual income of Y of 2000. each year the household can spend this amount of material goods consumption (gp) and rearing new born babies (cd). if it spends its income on all goods consumption, it gets 400 units of goods. and if it spends it on new babies it gets 5 children. at the present the household is observed to optimally consume 160 units of goods and 3 children.

a)what are the prices of the consumption goods and children?

b)what is the households budget constraint? graph it together with an indifference curve that shows the family's optimium consumption (# of children on horizontal access)

c)assume there are now increased employment opportunities for women such that their opportunity cost of a child rises. thus the price of a child is now 500 per year. derive the families new budget constraint and illustrate it on a graph, including the initial constraint and optimal consumption from part b.

d)assuming the family considers children and material goods as substitutes how will he increased women employment opportunities affects its fertility and child bearing choices. illustrate the new optimal consumption from part b.