Consider a couple's decision about how many children to have. Assume that over a lifetime a couple has 200,000 hours of time to either work or raise children. The wage is $10 per hour. Raising a child takes 20,000 hours of time. a. Draw the budget constraint showing the trade-off between lifetime consumption and the number of children. (Ignore the fact that children come only in whole numbers!) Show indifference curves and an optimum choice. b. Suppose the wage increases to $12 per hour. Show how the budget constraint shifts. Using income and substitution effects, discuss the impact of the change on the number of children and lifetime consumption. c. We observe that, as societies get richer and wages rise, people typically have fewer children. Is this fact consistent with this model? Explain.