Question from Past Microeconomics Qualifying ExamEdit
Spring 2001 - Section II, Question one, George Mason University Give complete answers to three of the following four questions (about 25percent each) Write clear concise and legible answers.:
- A parent cares about two goods, children and leisure. Let be the numberr of children and be the number of hours of leisure enjoyed per day. Then the parent's preferences are . (We can ignore the fact that children are inherently discrete and assume that there can be fractional numbers of children). The parent works at a job that pays a fixed wage of per hour. Let be the number of hours worked per day. The parent spends all earnings supporting his children, and each child costs per day.
- a. Write down the parent's optimization problem, clearly indicating objective, choices, and constraints.
- b. Solve for the partent's optimal choices and verbally interpret any first order conditions.
- c. Suppose the government decides to grant a per child subsidy of per day. Use the logic of income and substitution effects to explain what happens to the parent's choices. (Hint: Think about the relationship between and -- A graph might help).
- d. Suppose government imposes a tax tau () on all labor income to pay for the subsidy. Write down
- (i) an equation that must hold for the government's budget to balance, and
- (ii) the parent's new budget constraint. Explain what will happen if the government imposes both the subsidy on children and the income tax.
AnswerEdit
- a.
- b.
- c. A per child subsidy would effectively lower the cost, per child, which would lead to a outward rotation of the budget constraint and a new optimum on a higher utility function. Whether or not more of leisure or children or both is consumed depends on the specific utility function of the parents.
- d.
- (i)
- (ii)
The subsidy lowers as described above the relative cost of children and leads to an increase in effective income. However, the tax lowers the wage per hour, which is equivalent to the cost of leisure (opportunity cost), and therefore lowers the relative price of leisure. Overall the intervention should have no effect and the price ratio of leisure to children should be the same as before the intervention, assuming no transactions cost.
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