Exam 8: Buying and Selling

Aristotle earns 5 dollars per hour. He has 110 hours per week available for either labor or leisure. In the old days he paid no taxes and received nothing from the government. Now he gets a $200 payment per week from the government but he must pay half of his labor income in taxes. (His before-tax wages are the same as they were before, and he has no other source of income than wages and payments from the government.) He notices that with the government payment and his taxes, he can exactly afford the combination of leisure and consumption goods that he used to choose. How many hours per week did he work in the old days?

Harvey's net demands for goods 1 and 2 are (2, -3) and his endowment is (6, 5). a. What are his gross demands? b. Draw a diagram illustrating his budget line, his endowment, and his consumption. (Put good 1 on the horizontal axis.) c. Draw a dotted line to show what his budget line would be if the price of good 1 doubled and the price of good 2 stayed the same.

Jackie's net demands for x and y are (6, -6) and her gross demands are (15, 15). What is her initial endowment of x?

Marsha Mellow is very flexible. She consumes x and y. She says, "Give me x or give me y, I don't care. I can't tell the difference between them." She is currently endowed with 8 units of x and 17 units of y. The price of x is 3 times the price of y. Marsha can trade x and y at the going prices but has no other source of income. How many units of y will Marsha consume?

Milton consumes two commodities in a perfect market system. The price of x is $4 and the price of y is $1. His utility function is U(x, y) = xy. He is endowed with 76 units of good x and no y. Find his consumption of good y.

Mario consumes eggplants and tomatoes in the ratio of 1 bushel of eggplants per 1 bushel of tomatoes. His garden yields 30 bushels of eggplants and 10 bushels of tomatoes. He initially faced prices of $25 per bushel for each vegetable, but the price of eggplants rose to $100 per bushel, while the price of tomatoes stayed unchanged. After the price change, he would

If a person has no nonlabor income, a decrease in wages causes the budget line between leisure and other goods to shift downward in a parallel fashion.

If a consumer is a buyer of some goods and a seller of others, then a change in prices will generate an extra income effect in the Slutsky equation due to the revaluation of the consumer's endowment.

May's utility function is , where C is dollars spent on goods other than housecleaning, D is the number of hours per day that somebody spends cleaning her house, H is the number of hours per day May spends cleaning her house, and J is the number of hours per day May spends working at her job. All May's income comes from her job. She can work as many hours a day as she wishes at a wage of $7 an hour. a. If she cannot hire anyone to do her housecleaning, how many hours will she spend on the job and how many hours will she spend housecleaning? b. If she can hire a housecleaner at $5 an hour, how many hours will she work on her job, how many hours of housecleaning will she hire, and how many hours will she clean house?

Yolanda receives a lump sum child support payment of $150 per week. She has 80 hours a week to divide between labor and leisure. She earns $5 an hour. The first $150 per week of her labor income is untaxed, but all labor income that she earns above $150 is taxed at the rate 30%. If we graph her budget line with leisure on the horizontal axis and consumption on the vertical axis, her budget line has

Ollie South has an endowment of 10 guns and 10 pounds of butter. He can buy or sell butter at $1 a pound. But the world market for guns is more complicated: he can buy guns for $5 each, but he can sell guns for only $2. If we graph his budget line with guns on the horizontal axis and butter on the vertical axis, then Ollie's budget line is a straight line

There are no taxes on the first $500 that Debra earns per week, but on income above $500 per week, she must pay a 60% tax. Debra's job pays $10 per hour. Her utility function is U(c, r) = rc², where r is hours of leisure and c is dollars worth of consumption. She has 100 hours to divide between work and leisure. How many hours per week will she choose to work?

Gladys Goodhands is an insurance agent. She must choose one and only one of two possible alternative jobs. She can either work for a large national insurance company for which she must work exactly 40 hours a week and will receive a salary of S dollars per week, or she can work as an independent insurance agent, in which case she can work exactly as many hours per week as she wishes and will earn w dollars for every hour that she works. Gladys satisfies the weak axiom of revealed preference and she cares only about how much money she makes and about how much leisure time she has.

Is it ever possible that an increase in the price of a good for which a person is a net seller can make him worse off? Use a diagram to illustrate your answer.

Yoram insists on consuming 4 times as much of y as he consumes of x (so he always has y = 4x). He will consume these goods in no other ratio. The price of x is 3 times the price of y. Yoram has an endowment of 20 x's and 45 y's which he can trade at the going prices. He has no other source of income. What is Yoram's gross demand for x?

Les is allowed to work only 8 hours a day at his main job, although he would like to work more hours. He takes a second job. He can work as many hours as he wishes at the second job, but at a lower wage. If leisure is a normal good, then an increase in the wage rate for his first job will reduce the number of hours he chooses to work at his second job.

Dudley has a utility function U(C, R) = C - (12 - R)², where R is leisure and C is consumption per day. He has 16 hours per day to divide between work and leisure. If Dudley has a nonlabor income of $20 per day and is paid a wage of $0 per hour, how many hours of leisure will he choose per day?

Fanny consumes x and y. The price of x is $9 and the price of y is $9. Fanny's only source of income is her endowment of 12 units of x and 12 units of y which she can buy or sell at the going prices. She plans to consume 13 units of x and 11 units of y. If the prices change to $12 for x and $12 for y,

Ernie's wage rate is $10 an hour. He has no earnings other than his labor income. His utility function is U(C, L) = CR², where C is the amount of money he spends on consumption, and R is the number of hours a day he spends not working. a. Write an equation that describes Ernie's budget constraint. b. How many hours does Ernie choose to work per day? c. How much money does he spend on consumption per day?

Wendy and Mac work in fast-food restaurants. Wendy is paid $4 an hour for the first 40 hours a week that she works and $6 an hour for every hour beyond 40 hours per week. Mac gets $5 an hour no matter how many hours he works. Each has 110 hours per week to allocate between work and leisure. Each has a utility function U = cr, where c is expenditure per week on consumption and r is hours of leisure per week. Each can choose the number of hours to work. If Wendy works W hours and Mac works M hours, then