Exam 8: Buying and Selling

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.

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?

Georgina earns 6 dollars an hour. She has no nonlabor income. She has 100 hours a week available for either labor or leisure. Her utility function is U(c, r) = cr³, where c is dollars worth of goods and r is hours of leisure. How many hours per week will she work?

Henri is paid $9 an hour for the first 40 hours per week that he works. He can also work as many hours overtime as he wishes to. He is paid $15 an hour for every hour that he works beyond 40 hours a week. Leisure is a normal good for Henri and he is currently working some overtime. If his hourly wage for the first 40 hours per week that he works rises to $11 and his wages for overtime remain at $15 per hour, he will choose to work

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

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

Bill receives half of his income in wages and half of his income in dividends. Bill would be indifferent between a 50% increase in his wage rate and a 50% increase in his dividend income.

Will is paid $10 an hour for the first 40 hours per week that he works. He can also work as many hours overtime as he wishes to. He is paid $15 an hour for every hour that he works beyond 40 hours a week. Leisure is a normal good for Will and he is currently working some overtime. If his hourly wage for the first 40 hours per week that he works rises to $12 and his wages for overtime remain at $15 per hour, he will choose to work

Jack earns 5 dollars per hour. He has 100 hours per week which he can use for either labor or leisure. The government institutes a plan in which each worker receives a $100 grant from the government but has to pay 50% of his or her labor income in taxes. If Jack's utility function is U(c, r) = cr, where c is dollars worth of consumption of goods and r is hours of leisure per week, how many hours per week will Jack choose to work?

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 5 dollars of nonlabor income per day and gets a wage rate of 11 dollars per hour when he works, his budget equation, expressing combinations of consumption and leisure that he can afford to have, can be written as

A farmer gets 20 eggs and 10 tomatoes every week from her chickens and her tomato plants. She has no other source of income. She has convex, downward-sloping indifference curves. The current market prices are $2 per egg and $3 per tomato. At these prices she chooses the same bundle that she is endowed with (20 eggs and 10 tomatoes).

Tomoko receives a lump sum child support payment of $200 per week. She has 80 hours a week to divide between labor and leisure. She earns $5 an hour. The first $100 per week of her labor income is untaxed, but all labor income that she earns above $100 is taxed at the rate 50%. If we graph her budget line with leisure on the horizontal axis and consumption on the vertical axis, her budget line has

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 Abishag owns 16 quinces and 15 kumquats and if the price of kumquats is 4 times the price of quinces, how many kumquats can she afford if she buys as many kumquats as she can?

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 19 dollars of nonlabor income per day and gets a wage rate of 15 dollars per hour when he works, his budget equation, expressing combinations of consumption and leisure that he can afford to have, can be written as