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 number of children.(Ignore the fact that children only come 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 number of children and lifetime consumption.