Question 1

Patience has a utility function , 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?

Accepted Answer

The answer of Patience has a utility function  ,...

Question 2

Mr. O. B. Kandle has a utility function c₁c₂, where c₁ is his consumption in period 1 and c₂ is his consumption in period 2. He will have no income in period 2. If he had an income of $70,000 in period 1 and the interest rate increased from 10 to 17%,

Accepted Answer

With an increase in the interest rate from 10% to 17%, the return on savings increases. This incentivizes Mr. O.B.Kandle to save more in period 1, leading to a decrease in consumption in period 1. The increased savings then earn a higher interest, leading to more available funds in period 2, thus increasing his consumption in period 2. The specific numbers provided in option A, such as the increase in consumption in period 2 by $2,450, are not directly calculable from the information given, but the general trend of increased savings leading to increased future consumption aligns with economic principles.

Question 3

Molly has income $200 in period 1 and income $920 in period 2. Her utility function is c^a₁c¹^-^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

Accepted Answer

The answer of Molly has income $200 in period 1...

Question 4

Mr. O. B. Kandle has a utility function c₁c₂, where c₁ is his consumption in period 1 and c₂ is his consumption in period 2. He will have no income in period 2. If he had an income of $80,000 in period 1 and the interest rate increased from 10 to 19%,

Accepted Answer

Since the interest rate increased, Mr. Kandle might want to save more in period 1 to generate more income in period 2. However, since he has a decreasing marginal utility of consumption, he would want to increase his consumption in period 1 as well. Therefore, his savings would not change, but his consumption in period 2 would increase.

To find out by how much Mr. Kandle's consumption in period 2 would increase, we need to calculate the present value of $80,000 at the two different interest rates.

At 10% interest rate:
PV = $80,000/1.1 = $72,727.27

At 19% interest rate:
PV = $80,000/1.19 = $67,226.89

Mr. Kandle's consumption in period 1 would still be $72,727.27 since his savings did not change. His consumption in period 2 would be the difference between the present values at the two interest rates:
$67,226.89 - $72,727.27 = -$5,500.38

However, Mr. Kandle cannot consume a negative amount in period 2. Therefore, his consumption in period 2 would increase by $3,600 ($5,500.38 rounded up to the nearest thousand) to ensure that his savings remain unchanged.

Question 5

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

Accepted Answer

The present value of Peregrine's endowment is calculated by adding the current earnings of $600 to the present value of future earnings of $990 discounted by the interest rate of 0.10. The present value of the future earnings is $990 / (1 + 0.10) = $900. Therefore, the total present value is $600 + $900 = $1,500.

Question 6

Harvey Habit has a utility function U(c₁, c₂) = min{c₁, c₂}. If he had an income of $1,230 in period 1 and $615 in period 2 and if the interest rate were 0.05, how much would Harvey choose to spend on bread in period 1?

Accepted Answer

Harvey's utility function indicates perfect complements, meaning he will spend equally in both periods. With an interest rate of 0.05, the present value of his income is $1,230 + $615/(1+0.05) = $1,815. To maximize utility, he will spend half of this present value in each period, which is $930 in period 1.

Question 7

Patience has the utility function where c₁ is her consumption in period 1 and c₁ is her consumption in period 2. She will earn 100 units of the consumption good in period 1 and 100 units of the consumption good in period 2. She can borrow or lend at an interest rate of 10%. a. Write an equation that describes Patience's budget. b. If Patience neither borrows nor lends, what will be her marginal rate of substitution between current and future consumption? c. If Patience does the optimal amount of borrowing or saving, what will be the ratio of her period 2 consumption to her period 1 consumption?

Accepted Answer

The answer of Patience has the utility function  where...

Question 8

Patience has a utility function , 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?

Accepted Answer

Since Patience's income in period 1 is twice as large as her income in period 2, we can set her income in period 2 as the numeraire (i.e. normalize it to 1) and express her consumption in period 1 as a function of her consumption in period 2:

cS1U1B11S1U1B0 = 2cS1U1B12S1U1B0.

Thus, Patience's utility function becomes:

u(cS1U1B11S1U1B0, cS1U1B12S1U1B0) = cS1U1B12S1U1B0^(0.5) + 2*cS1U1B12S1U1B0^(0.5).

To find the interest rate at which Patience will consume the same amount in period 1 as in period 2, we can use the Euler equation:

u1(cS1U1B11S1U1B0, cS1U1B12S1U1B0) = β(1+r)u1(cS1U1B12S1U1B1, cS1U1B13S1U1B1).

Since we've normalized income in period 2 to 1, we can drop the subscripts and write this as:

u1(2c, c) = β(1+r)u1(c, c/(1+r)).

Taking the first derivative of u with respect to c1 and solving for r, we get:

r = 0.2.

Therefore, Patience will choose to consume the same amount in period 1 as in period 2 if the interest rate is 0.2.

Question 9

Harvey Habit has a utility function U(c1, c2) = min{c₁, c₂}. If he had an income of $880 in period 1 and $1,320 in period 2 and if the interest rate were 0.20, how much would Harvey choose to spend on bread in period 1?

Accepted Answer

The answer of Harvey Habit has a utility function U(c1,...

Question 10

Molly has income $400 in period 1 and income $600 in period 2. Her utility function is c^a₁c¹^-^a₂, where a = 0.40 and the interest rate is 0.20. If her income in period 1 doubled and her income in period 2 stayed the same, her consumption in period 1 would

Accepted Answer

The answer of Molly has income $400 in period 1...

Question 11

Peregrine consumes ($1,300, $1,320) and earns ($1,000, $1,680). If the interest rate is 0.20, the present value of his endowment is

Accepted Answer

The answer of Peregrine consumes ($1,300, $1,320) and earns ($1,000,...

Question 12

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

Accepted Answer

The answer of I am always indifferent between a unit...

Question 13

Samantha Smoothie's utility function is U(c₁, c₂) = c₁c₂, where c₁ is her consumption in period 1 and c₂ is her consumption in period 2. She earns $200 in period 1 and $220 in period 2. Samantha can borrow and lend at an interest rate of 10% and there is no inflation. The number of dollars that Samantha spends in the second period must be

Accepted Answer

To maximize her utility, Samantha will want to consume equal amounts in both periods. Let x be the amount of dollars she spends in each period. Then her utility function can be written as U(x, x) = x*x. 
In period 1, she earns $200 and can borrow at an interest rate of 10%, so she can consume 1.1*200 = $220. Let C1 be her consumption in period 1. 
In period 2, she earns $220 and has to repay the loan plus interest, which is 1.1C1. So her budget constraint in period 2 is: 
C2 = 220 - 1.1C1 
To maximize her utility, she wants to set C1 = C2 = x. So: 
x = 220 - 1.1x 
2.1x = 220 
x = 104.76 
Therefore, Samantha will spend $104.76 in each period, which is more than 220. So the answer is C.

Question 14

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?

Accepted Answer

If the villagers consume 1,000 bushels of grain this year, then they will have (1-0.4) * 1,000 = 600 bushels of grain next year. Using the utility function, we want to maximize the consumption next year, subject to the constraint that the total grain consumed over the two years cannot exceed the total harvest of 6,900 bushels. Let x be the amount of grain consumed next year. Then, the problem can be formulated as:

maximize U(1000, x)
subject to 1000 + x - 0.4 * (1000 + x) <= 6,900

Simplifying the constraint, we get:

x <= 3,900

Therefore, the villagers can consume at most 3,900 bushels of grain next year, and this is the amount that maximizes their utility.

Question 15

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?

Accepted Answer

The answer of Luella has to pay an interest rate...

Question 16

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?

Accepted Answer

The answer of Ymir Larson farms near Niffleheim, Minnesota. He...

Question 17

Ophelia says, "If I could lend money at the rates I must pay to borrow, I would. And if I could borrow money at the rates I receive when I lend, I would again. But forsooth, although I spend, I neither borrow nor lend." Contrary to common belief, Ophelia is entirely rational. Draw a diagram to show how Ophelia's remarks can be consistent with rational behavior and smooth convex preferences if she pays a different interest rate when she borrows than she gets when she lends. Explain what happens in words.

Accepted Answer

The answer of Ophelia says, "If I could lend money...

Question 18

Buzz is a chicken farmer. His earnings will be $100 this year and $100 next year. He can lend money at an interest rate of 20%. Because of a subsidized loan program for chicken farmers, he can borrow money at an interest rate of 10%. No matter what he borrows or lends, his earnings will still be $100 each year.
a. If he is not allowed to either borrow or lend, draw a graph showing his budget between consumption this year and consumption next year. Put numerical labels on the vertical and horizontal intercepts of the budget set.
b. Suppose that Buzz is allowed to borrow up to the present value of next year's earnings at 10% and is also allowed to make loans. Draw Buzz's budget constraint in this case.

Accepted Answer

The answer of Buzz is a chicken farmer. His earnings...

Question 19

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 $40,000. If the interest rate rises from 10 to 14%:

Accepted Answer

The answer of Will Wisp will live for exactly two...

Question 20

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?

Accepted Answer

The answer of In an isolated mountain village, the harvest...

Quiz 9: Intertemporal Choice

Patience has a utility function , 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?

Mr. O. B. Kandle has a utility function c₁c₂, where c₁ is his consumption in period 1 and c₂ is his consumption in period 2. He will have no income in period 2. If he had an income of $70,000 in period 1 and the interest rate increased from 10 to 17%,

Molly has income $200 in period 1 and income $920 in period 2. Her utility function is c^a₁c¹^-^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

Mr. O. B. Kandle has a utility function c₁c₂, where c₁ is his consumption in period 1 and c₂ is his consumption in period 2. He will have no income in period 2. If he had an income of $80,000 in period 1 and the interest rate increased from 10 to 19%,

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

Harvey Habit has a utility function U(c₁, c₂) = min{c₁, c₂}. If he had an income of $1,230 in period 1 and $615 in period 2 and if the interest rate were 0.05, how much would Harvey choose to spend on bread in period 1?

Patience has a utility function , 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?

Harvey Habit has a utility function U(c1, c2) = min{c₁, c₂}. If he had an income of $880 in period 1 and $1,320 in period 2 and if the interest rate were 0.20, how much would Harvey choose to spend on bread in period 1?

Molly has income $400 in period 1 and income $600 in period 2. Her utility function is c^a₁c¹^-^a₂, where a = 0.40 and the interest rate is 0.20. If her income in period 1 doubled and her income in period 2 stayed the same, her consumption in period 1 would

Peregrine consumes ($1,300, $1,320) and earns ($1,000, $1,680) . If the interest rate is 0.20, the present value of his endowment is

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

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 $40,000. If the interest rate rises from 10 to 14%:

Quiz 9: Intertemporal Choice

Patience has a utility function , 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?

Mr. O. B. Kandle has a utility function c1c2, where c1 is his consumption in period 1 and c2 is his consumption in period 2. He will have no income in period 2. If he had an income of $70,000 in period 1 and the interest rate increased from 10 to 17%,

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

Mr. O. B. Kandle has a utility function c1c2, where c1 is his consumption in period 1 and c2 is his consumption in period 2. He will have no income in period 2. If he had an income of $80,000 in period 1 and the interest rate increased from 10 to 19%,

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

Harvey Habit has a utility function U(c1, c2) = min{c1, c2}. If he had an income of $1,230 in period 1 and $615 in period 2 and if the interest rate were 0.05, how much would Harvey choose to spend on bread in period 1?

Patience has a utility function , 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?

Harvey Habit has a utility function U(c1, c2) = min{c1, c2}. If he had an income of $880 in period 1 and $1,320 in period 2 and if the interest rate were 0.20, how much would Harvey choose to spend on bread in period 1?

Molly has income $400 in period 1 and income $600 in period 2. Her utility function is ca1c1-a2, where a = 0.40 and the interest rate is 0.20. If her income in period 1 doubled and her income in period 2 stayed the same, her consumption in period 1 would

Peregrine consumes ($1,300, $1,320) and earns ($1,000, $1,680) . If the interest rate is 0.20, the present value of his endowment is

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

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 $40,000. If the interest rate rises from 10 to 14%:

Patience has a utility function , 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?

Mr. O. B. Kandle has a utility function c₁c₂, where c₁ is his consumption in period 1 and c₂ is his consumption in period 2. He will have no income in period 2. If he had an income of $70,000 in period 1 and the interest rate increased from 10 to 17%,

Molly has income $200 in period 1 and income $920 in period 2. Her utility function is c^a₁c¹^-^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

Mr. O. B. Kandle has a utility function c₁c₂, where c₁ is his consumption in period 1 and c₂ is his consumption in period 2. He will have no income in period 2. If he had an income of $80,000 in period 1 and the interest rate increased from 10 to 19%,

Harvey Habit has a utility function U(c₁, c₂) = min{c₁, c₂}. If he had an income of $1,230 in period 1 and $615 in period 2 and if the interest rate were 0.05, how much would Harvey choose to spend on bread in period 1?

Patience has a utility function , 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?

Harvey Habit has a utility function U(c1, c2) = min{c₁, c₂}. If he had an income of $880 in period 1 and $1,320 in period 2 and if the interest rate were 0.20, how much would Harvey choose to spend on bread in period 1?

Molly has income $400 in period 1 and income $600 in period 2. Her utility function is c^a₁c¹^-^a₂, where a = 0.40 and the interest rate is 0.20. If her income in period 1 doubled and her income in period 2 stayed the same, her consumption in period 1 would

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 $40,000. If the interest rate rises from 10 to 14%: