Exam 8: Buying and Selling-Part A

Charlie consumes apples and bananas; his utility function is U(a, b)= ab.Charlie's fruit farm yielded 5 apples and 10 bananas.In addition, Charlie has $10 that he was given by a secret admirer.Charlie can buy or sell apples at $2 each and he can buy or sell bananas at $1 each.Charlie will consume

Donald consumes goods x and y.His utility function is U(x, y)=xy³.He is endowed with 10 units of x and 15 units of y.The price of x is $1 and the price of y is $2.Find his net demand for x.

Russ Tickman is a dairy farmer.He consumes milk and other goods.His utility function is given by U(x, y)= y(x + 1), where x is his milk consumption and y is his consumption of other goods.His initial endowment is 19 units of milk per day and no units of other goods.If the price of milk is $2 and the price of other goods is $1, how much milk does he consume?

Dr.Johnson receives a lump sum payment of $150 per week.Suppose that the first $150 per week of labor income is untaxed but all labor income above $150 is taxed at a rate of 10%.

Mr.Cog has 18 hours per day to divide between labor and leisure.His utility function is U(C, R)= CR, where C is dollars per year spent on consumption and R is hours of leisure.If he has a nonlabor income of 40 dollars per day and a wage rate of 8 dollars per hour, he will choose a combination of labor and leisure that allows him to spend

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 14 units of x and 3 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?

Marilyn is a journalist.She is considering two possible jobs.One job is as an editor for a magazine.The other job is writing freelance articles and selling them to whoever will buy them.If she works for the magazine, she must spend 10 hours a day at work and commuting.She will be paid $130 a day net of commuting costs and taxes if she takes this job.If she writes freelance articles, she can work at home and as many hours a day as she pleases.She estimates that she would earn $10 an hour after taxes if she does this.Her utility function is U = (R³)C, where R is the number of hours a day she spends not working or commuting and C is her earnings. a.If Marilyn chooses to freelance, how many hours will she work? b.Calculate her utility in each job and identify which job she will choose.

Donald consumes goods x and y.His utility function is U(x, y)=xy³.He is endowed with 43 units of x and 7 units of y.The price of x is $1 and the price of y is $3.Find his net demand for x.

Peter has an endowment of 3 units of good x and 5 units of good y.He can buy and sell x at a price of $100 and y at a price of $200.He receives an income of $700 as alimony from a former spouse. a.Draw Peter's budget line for x and y.Show his initial endowment of x and y on your diagram. b.Calculate the amount of x that he could afford if he bought only x and the amount of y he could afford if he bought only y. c.Write an equation for Peter's budget.

If a consumer is initially endowed with a positive amount of two goods and sells some of one to get more of the other and if she has no other sources of income, then her budget line will pass through her endowment point.

Diana consumes commodities x and y and her utility function is U(x, y)=xy².Good x costs $2 per unit and good y costs $1 per unit.If she is endowed with 3 units of x and 6 units of y, how many units of good y will she consume?

Mr.Cog has 18 hours per day to divide between labor and leisure.His utility function is U(C, R)= CR, where C is dollars per year spent on consumption and R is hours of leisure.If he has a nonlabor income of 32 dollars per day and a wage rate of 13 dollars per hour, he will choose a combination of labor and leisure that allows him to spend

Jack has a backward-bending labor supply curve.At wages of $5 an hour he chooses to work 50 hours a week.His boss wants him to work more hours per week and offers him $5 an hour for the first 50 hours per week and $7 an hour for every hour beyond 50 hours per week.Because of his backward -bending supply curve, Jack might actually choose to work fewer hours.

George Goodhands is a life insurance agent.He can work 40 hours a week for a large national insurance company and receive a fixed salary of S dollars per week, or he can work independently, for as many or as few hours per week as he likes and earn w dollars per hour.(He cannot take both jobs.)Which of the following responses to an increase in the salary paid by the insurance company would be inconsistent with the weak axiom of revealed preference?

If a utility maximizer is a net seller of something and the price of that good rises while other prices stay constant, her situation might improve so much that she becomes a net buyer.

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 $10 per bushel for each vegetable, but the price of eggplants rose to $30 per bushel, while the price of tomatoes stayed unchanged.After the price change, he would

If a person is a net seller of some good and the price of that good decreases, she might possibly become a net buyer.

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.

Mike Teevee likes to watch television and to eat candy.In fact his utility function is U(x, y)= x²y, where x is the number of hours he spends watching television and y is the number of dollars per week he spends on candy.Mike's mother doesn't like him to watch so much television.She limits his television watching to 36 hours a week and in addition she pays him $1 an hour for every hour that he reduces his television watching below 36 hours a week.If this is Mike's only source of income to buy candy, how many hours of television does he watch per week?

Mr.and Mrs.Brauer owned their own home.There was a real estate boom in their town and the price of houses doubled.Their income and other prices stayed constant.The Brauers complained that "we are being driven from our home; we can't afford to live here any more." a.Draw a diagram that illustrates what happened to the Brauers' budget constraint. b.Could they have been made worse off by the change? Could they have been made better off? Explain why.