Exam 8: Buying and Selling

Dr. Johnson receives a lump sum payment of $100 per week. Suppose that the first $100 per week of labor income is untaxed but all labor income above $100 is taxed at a rate of 40%.

Holly consumes x and y. The price of x is 4 and the price of y is 4. Holly's only source of income is her endowment of 6 units of x and 6 units of y which she can buy or sell at the going prices. She plans to consume 7 units of x and 5 units of y. If the prices change to $7 for x and $7 for y,

Suppose a consumer is initially endowed with a positive amount of two goods, sells some of one to get more of the other, and has no other sources of income. If the price of one good falls, his new budget line is everywhere above his old budget line.

If a rational utility maximizer is a net demander of a good and if an increase in its price causes him to buy more of it, then it must be an inferior good.

Holly consumes commodities x and y and her utility function is U(x, y) = xy⁵. Good x costs $2 per unit and good y costs $1 per unit. If she is endowed with 7 units of x and 4 units of y, how many units of good y will she consume?

If Abishag owns 18 quinces and 5 kumquats and if the price of kumquats is 6 times the price of quinces, how many kumquats can she afford if she buys as many kumquats as she can?

Nick insists on consuming 3 times as much of y as he consumes of x (so he always has y = 3x). He will consume these goods in no other ratio. The price of x is 2 times the price of y. Nick has an endowment of 20 x's and 75 y's which he can trade at the going prices. He has no other source of income. What is Nick's gross demand for x?

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%.

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

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.

Dudley's utility function for goods and leisure is U(G, L) = G - (20 - L)(20 - L), where G is consumption of goods and L is the number of hours of leisure per day. Goods cost $1 per unit. a. If Dudley had an income from nonlabor sources of $25 per day and could work as much as he chose to but would get zero wages, how much would he work? b. Sketch Dudley's indifference curves on a graph with leisure on the horizontal axis and income on the vertical axis. If Dudley's nonlabor income were $25 a day and he could work as much as he wished for $10 an hour, how many hours a day would he choose to work?

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?

Is it ever possible that if someone is a net seller of a good, and the price of the good he sells falls, the consumer could wind up better off than he was before by switching from being a seller to being a buyer? Draw a graph to justify your answer.

Susan's utility function is U(x, y) = (x + y)R², where x and y are the quantities of goods X and Y that she consumes and R is the number of hours of leisure that she has per day. Good X costs 4 dollars per unit and good Y costs 2 dollars per unit. Her wage rate is 8 dollars per hour and she has 15 hours per day to allocate between labor and leisure. She will

Heather and Myrtle have the same tastes. Heather is paid $10 an hour and chooses to work 9 hours a day. Myrtle is paid $9 an hour for the first 8 hours she works and $18 an hour for any time she works beyond 8 hours a day.

If a person is a net supplier of a normal good and its price increases while all other prices stay the same, then his demand for the good must decrease.

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

Lucetta changes light bulbs. She is paid $10 an hour. She can work as many hours as she wishes. Lucetta works only 6 hours a day. But she says she loves her job and is happier working at this job than she would be if she made the same income without working at all. Though this may sound strange, Lucetta is perfectly rational. Draw a graph showing leisure on the horizontal axis and income on the vertical axis. Draw a budget line and some indifference curves for Lucetta that are consistent with Lucetta's words and actions. Explain in words what happens.

Quincy consumes only uglifruits and bananas. His only source of income is an initial endowment of 30 units of uglifruits and 10 units of bananas. Quincy insists on consuming uglifruits and bananas in fixed proportions, 1 unit of uglifruits per 1 unit of bananas. He initially faces a price of $20 per unit for each fruit. The price of uglifruits rose to $40 per unit while the price of bananas stayed unchanged. After the price change, he would

If leisure is a normal good, then an increase in nonlabor income will reduce labor supply.