Exam 10:Intertemporal Choice-Part A

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Roger's utility function is U =min{1,a2}min{b1,b2},where a1 and a2 are the number of piano lessons he consumes this year and next and b1 and b2 are the number of ice skating lessons he consumes this year and next.The price of piano lessons is $10 each and the price of ice skating lessons is $4 each.The prices won't change,but the interest rate is 7%.If Roger consumes 20 piano lessons this year,how many ice-skating lessons will he consume next year?

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Will Wisp will live for exactly two periods.His utility function is U(c1,c2)=c1c2,where c1 is consumption in period 1 and c2 is consumption in period 2.He will have no income in period 2.His income in period 1 is $80,000.If the interest rate rises from 10 to 12%:

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In an isolated peasant village,the only crop is corn.Good harvests alternate with bad harvests.This year the harvest will be 1,000 bushels.Next year it will be 150 bushels.There is no trade with the outside world.Corn can be stored,but rats will eat 25% of what is stored in a year.The villagers have the Cobb-Douglas utility function U(c1,c2)=c1c2,where c1 is consumption this year and c2 is consumption next year. a.Draw a budget line for the village with this year's consumption on the horizontal axis and next year's consumption on the vertical axis.On your graph show the quantities at which the budget line intercepts the vertical and horizontal axes. b.How much will the villagers consume this year? c.How much will the rats eat? d.How much will the villagers consume next year?

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The nominal interest rate is 5% and the inflation rate is 6%.A rational consumer

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In an isolated mountain village,the harvest this year is 6,000 bushels of grain and the harvest next year will be 900 bushels.The villagers all have utility functions U(c1,c2)=c1c2,where c1 is consumption this year and c2 is consumption next year.Rats eat 40% of any grain that is stored for a year.How much grain could the villagers consume next year if they consume 1,000 bushels of grain this year?

(Multiple Choice)
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Harvey Habit has a utility function U(c1,c2)=min{c1,c2},where c1 and c2 are his consumption in periods 1 and 2 respectively.Harvey earns $189 in period 1 and he will earn $63 in period 2.Harvey can borrow or lend at an interest rate of 10%.There is no inflation.

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Patience has a utility function U(c1,c2)=c1/21 +0.83c1/22,where c1 is her consumption in period 1 and c2 is her consumption in period 2.Her income in period 1 is twice as large as her income in period 2.At what interest rate will she choose to consume the same amount in period 1 as in period 2?

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Ymir Larson farms near Niffleheim,Minnesota.He works 80 hours a week.He can either grow rutabagas or raise pigs.Every hour that he spends growing rutabagas gives him $2 of income this year.Every hour that he spends raising pigs this year will add $4 to his income next year.In fact,next year's weekly income will be 100+ 4H dollars where H is the number of hours he spends raising pigs this year.Ymir's utility function is U(c1,c2)=min{c1,c2},where c1 and c2 are his consumption expenditures this year and next year.Ymir doesn't believe in banks and will neither lend money nor borrow money. a.Draw Ymir's budget line for current and future consumption,labeling key points on it. b.How many hours a week will he choose to spend raising pigs? c.How much money will he spend per week on consumption in each year?

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Peregrine consumes ($700,$880)and earns ($600,$990).If the interest rate is 0.10,the present value of his endowment is

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Suppose that a person can borrow and lend at an interest rate of 10%.But there is a 5% rate of inflation and the person has to pay an income tax of 30% on all interest income.If the person borrows money,he can deduct interest as an expense.Where current consumption is on the horizontal axis and future consumption is on the vertical axis,the budget line will

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If the nominal interest rate is 5% and if prices fall by 3% per year,then the real rate of interest is approximately 8%.

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Luella has to pay an interest rate of 50% to borrow.She only gets an interest rate of 5% if she lends.She is currently endowed with $1,000 in period 1 and $1,050 in period 2.She considers two alternative investment projects.She can only choose one of them.For project A she would have to pay $500 in period 1 and would be paid back $630 in period 2.For project B,she would be paid $500 in period 1 and would have to pay back $525 in period 2. a.Diagram her budget set if she chooses project A.Also show her budget if she chooses project B. b.If she neither borrows nor lends,which project has the higher present value at the interest rate 50%? Which has the higher present value at an interest rate of 5%? c.Draw indifference curves such that she should choose A. d.With different preferences might she choose B?

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I am always indifferent between a unit of consumption today and tomorrow and the interest rate is 5%.

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If current and future consumption are both normal goods,an increase in the interest rate will necessarily

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Harvey Habit has a utility function U(c1,c2)=min{c1,c2},where c1 and c2 are his consumption in periods 1 and 2 respectively.Harvey earns $147 in period 1 and he will earn $63 in period 2.Harvey can borrow or lend at an interest rate of 10%.There is no inflation.

(Multiple Choice)
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Patience has a utility function U(c1,c2)=c1/21 +0.80c1/22,where c1 is her consumption in period 1 and c2 is her consumption in period 2.Her income in period 1 is twice as large as her income in period 2.At what interest rate will she choose to consume the same amount in period 1 as in period 2?

(Multiple Choice)
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In an isolated mountain village,the harvest this year is 3,000 bushels of grain and the harvest next year will be 1,100 bushels.The villagers all have utility functions U(c1,c2)=c1c2,where c1 is consumption this year and c2 is consumption next year.Rats eat 10% of any grain that is stored for a year.How much grain could the villagers consume next year if they consume 1,000 bushels of grain this year?

(Multiple Choice)
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Mandy has an income of $800 in period 1 and will have an income of $500 in period 2.Her utility function is U(c1,c2)=c0.801c0.202,where c1 is her consumption in period 1 and c2 is her consumption in period 2.The interest rate is .25.If she unexpectedly won a lottery which pays its prize in period 2 so that her income in period 2 would be $1,000 and her income in period 1 would remain $800,then her consumption in period 1 would

(Multiple Choice)
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Molly has income $200 in period 1 and income $920 in period 2.Her utility function is ca1c1 - a2,where a = 0.80 and the interest rate is 0.15.If her income in period 1 doubled and her income in period 2 stayed the same,her consumption in period 1 would

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If the real rate of interest is 8% and the nominal rate of interest is 28%,then the rate of inflation must be about

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