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Answer to Question #68212 in Microeconomics for Heisenberg

Question #68212
Consider a couple’s decision about how many children to have. Assume also that over a life time a couple has 325000 hours of time to either work or raise children. The wage is 10 Rand per hour. Raising a child takes 25 000 Hours of time.
i. Draw the budget constraint showing the trade-off between lifetime consumption
and number of children. (Ignore the fact that children come only in whole
numbers) Show indifference curves and an optimal choice for the couple.
ii. Suppose the wages decrease from 10 Rand to 8 Rand 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.
iii. Consider now that the wage is a normal good, answer with a graph
Expert's answer
Assume also that over a life time a couple has 325000 hours of time to either work or raise children. The wage is 10 Rand per hour. Raising a child takes 25 000 Hours of time.
i. The couple can raise maximum of 13 children or earn 3,250,000 Rand. An optimal choice will be near 7 children and 1,500,000 Rand.
ii. If the wages decrease from 10 Rand to 8 Rand per hour, then the couple can raise maximum of 13 children or earn 2,600,000 Rand, so the budget constraint will shift leftward. The higher is the number of children, the lower is lifetime consumption, because less money is earned.
iii. If the wage is a normal good, then the increase in wage will cause the increase in hours worked.

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