Exam 8: Buying and Selling

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

A person's full income is the amount of income that he or she would have if there were no taxes.

If someone has a Cobb-Douglas utility function and no income from any source other than labor earnings, then an increase in wages will not change the amount that person chooses to work.

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.

Leo thinks leisure and consuming goods are perfect complements. Goods cost $1 per unit. Leo wants to consume 5 units of goods per hour of leisure. Leo can work as much as he wants to at the wage rate of $15 an hour. He has no other source of income. a. How many hours a day will Leo choose to spend at leisure? b. Draw a diagram showing Leo's budget and his choice of goods and leisure. c. Will Leo work more or less if his wage rate increases?

Irene earns 8 dollars an hour. She has no nonlabor income. She has 30 hours a week available for either labor or leisure. Her utility function is U(c, r) = cr², where c is dollars worth of goods and r is hours of leisure. How many hours per week will she work?

Albert consumes only tangerines and bananas. His only source of income is an initial endowment of 30 units of tangerines and 10 units of bananas. Albert insists on consuming tangerines and bananas in fixed proportions, 1 unit of tangerines per 1 unit of bananas. He initially faces a price of $10 per unit for each fruit. The price of tangerines rose to $30 per unit while the price of bananas stayed unchanged. After the price change, he would

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.

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?

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.

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?

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.

If leisure is an inferior good, then an increase in the wage rate will make a person work more.

Wilhelm consumes only apples and bananas. His endowment is 5 units of apples and 10 units of bananas. Both goods are normal goods for Wilhelm. At current prices, Wilhelm is a net seller of apples. If the price of apples rises and the price of bananas stays the same, his demand for apples must decrease.

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 $35 per day and is paid a wage of $6 per hour, how many hours of leisure will he choose per day?

Milton consumes two commodities in a perfect market system. The price of x is $5 and the price of y is $1. His utility function is U(x, y) = xy. He is endowed with 40 units of good x and no y. Find his consumption of good y.

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.

If all goods, including leisure, are normal goods, then an increase in the wage rate will necessarily make people want to work more 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?

Rhoda takes a job with a construction company. She earns $5 an hour for the first 40 hours of each week and then gets "double-time" for overtime. That is, she is paid $10 an hour for every hour beyond 40 hours a week that she works. Rhoda has 70 hours a week available to divide between construction work and leisure. She has no other source of income, and her utility function is U = cr, where c is her income to spend on goods and r is the number of hours of leisure that she has per week. She is allowed to work as many hours as she wants to. How many hours will she work?