Topic 4- Don't use, read slides

Question 1

What is the national level of desired consumption (C^d)?

Answer 1

The aggregate quantity of goods and services that households optimally choose to consume, given income and other factors that determine households’ economic opportunities

Question 2

Who’s consumption decisions do we analyse?

Answer 2

Individual households

Question 3

How do you calculate the aggregate level of desired consumption?

Answer 3

By adding up the desired consumption of
all households

Question 4

What is desired national saving?

Answer 4

Level of aggregate saving when consumption is at its desired (optimal) level

Question 5

How do you calculate desired national saving?

Answer 5

𝑆^𝑑 = 𝑌 − 𝐶^𝑑 − G

Question 6

What does the d mean in C^d?

Answer 6

Desired (Optimal)

Question 7

What is the lifespan of the representative individual divided into?

Answer 7

The current period and the future preiod

Question 8

What is the budget constraint for the current period?

Answer 8

𝑎^𝑓 = 𝑦 + 𝑎 − c

where:
a^f = assets in the future period
y= current income
c= current consumption
a= assets

Question 9

What is the budget constraint of the future period?

Answer 9

𝑐^𝑓 = 𝑦^𝑓 + (1 + 𝑟)𝑎^f

where:
c^f= future period consumption
y^f= future period income
r= real interest rate

Question 10

What is the equation for when an individual enhances future consumption from saving?

Answer 10

(1 + r) a^f = (1 + r)(s + a)

where rs is return on savings

We say the individual is a saver

Question 11

What is dissaving?

Answer 11

When saving is less than zero

Question 12

When the individual is a borrower, what conditions must be met?

Answer 12

𝑐 > 𝑦 + 𝑎 ⇔ 𝑎^𝑓 < 0

Question 13

How much does the future consumption fall below that period’s income when someone is a borrower?

Answer 13

(1 + 𝑟) x absolute value of a^f

Question 14

What are the conditions for someone to be a lender?

Answer 14

𝑐 < 𝑦 + 𝑎 ⇔ 𝑎^𝑓 > 0

Question 15

If 𝑐 < 𝑦 ⇒ 𝑎^𝑓 > 𝑎, what is the individual?

Answer 15

A saver

Question 16

If 𝑐 > 𝑦 ⇒ 𝑎^𝑓 < a, what is the individual?

Answer 16

A dissaver

Question 17

What is the no borrowing, no lending case represented by? What needs to be noted here?

Answer 17

𝑐 = 𝑦 + 𝑎 ⇔ 𝑎^𝑓 = 0

c^f = y^f

Note: the individual is a dissaver as c - y = a > 0

Question 18

If you consume more in the first period, what happens in the second period?

Answer 18

You can’t consume as much in the second period.
Some of y^f might be required in the current period.

Question 19

What is one dollar of current consumption traded at for future consumption?

Answer 19

1 + r dollars

Question 20

What is the price of one dollar’s worth of extra consumption today?

Answer 20

1 + 𝑟 dollars worth of consumption in the future

Question 21

Combining the two budget constraints, what is the consolidated budget constraint? Outline the steps.

Answer 21

𝑐^𝑓 = 𝑦^𝑓 + (1 + 𝑟)(𝑦 + 𝑎 − 𝑐)

𝑐^𝑓 = 𝑦^𝑓 + (1 + 𝑟)(𝑦 + 𝑎) − (1 + 𝑟) c

c + c^f/(1+r) = y + a + y^f/(1+r)

Question 22

What is the present value of lifetime resources?

Answer 22

y + a + y^f/(1+r) = PVLR = Xbar

Question 23

What is the present value of lifetime consumption?

Answer 23

c + c^f/(1+r) = PVLC

Question 24

What is on the axis for the intertemporal budget constraint?

Answer 24

y-axis c^f
x-axis c

Question 25

What is the vertical intercept of the intertemporal budget constraint?

Answer 25

A(0,c^f): c^f = y^f + (1 + r)(y + a)

Question 26

What is the horizontal intercept of the intertemporal budget constraint?

Answer 26

B(c,0): c = y^f/(1 + r) + y + a

Question 27

What is the slope of thei ntertemporal budget constraint?

Answer 27

dc^f/dc = - (1 + r)

Question 28

What is the constrained optimisation problem for households?

Answer 28

max𝑈 = 𝑢 (𝑐) + 𝛽𝑢(𝑐^𝑓)

Such that 𝑐^𝑓 = 𝑦^𝑓 + (1 + 𝑟)(𝑎 + 𝑦 − 𝑐)

Question 29

What is 𝛽 in the constrained optimisation problem?

Answer 29

𝛽 > 0 is a number reflecting how the individual weighs the current and future consumption.
Alternatively, it is thought to capture the extent to which consumers are patient. If the consumer is very impatient, she places less weight on future utility, thus 𝛽 is lower

Question 30

What does it mean in the constrained optimisation problem if 𝛽 = 1?

Answer 30

The consumer treats utils received today and in the future equally

Question 31

What are the assumptions of the household constrained optimisation problem?

Answer 31

𝑢′(𝑐) > 0 & 𝑢′′(𝑐) < 0

𝑢′(𝑐^𝑓) > 0 & 𝑢′′ (𝑐^𝑓) < 0

Question 32

How do we make the constrained optimisation problem either to solve?

Answer 32

Substitute away future consumption

Question 33

What is the maximisation utility function for households (unconstrained optimisation problem)?

Answer 33

max𝑈 = 𝑢(𝑐) + 𝛽𝑢(𝑦^𝑓 + (1 + 𝑟)(𝑎 + 𝑦 − 𝑐))