Week 8: Consumption and Savings

Question 1

Consumption and Savings Model - periods, income, taxes, consumers

Answer 1

2 periods - current and future
income - exogenous
lump sum taxes
consumers can be different

Question 2

Current Period Equation

Answer 2

y-t = c+s

Question 3

When is someone a lender?

Answer 3

savings > 0

Question 4

When is someone a borrower?

Answer 4

savings < 0

Question 5

Bond

Answer 5

A promise to pay in the future with 1 + r consumption good in exchange for 1 unit of consumption of the good today

Question 6

Future period equation

Answer 6

c’ = y’ - t’ + (1+r)s

Question 7

Lifetime Wealth

Answer 7

quantity of resources available to consumer in current consumption goods to spend on consumption goods over lifetime (2 periods)

Question 8

Intertemporal Budget Constraint Definition

Answer 8

constraint faced by a decision maker who is making choices for both the present and future

Question 9

Intertemporal Budget Constraint Equation

Answer 9

c + c’/(1+r) = y- t + (y’-t’/1+r)

C(1) + C(2)/(1+r) = Y(1) + Y(2)/(1+r)

Question 10

Lifetime Wealth Equation

Answer 10

a = y + y’/(1+r) - t - t’/(1+r)

Question 11

Lender and Borrower Diagram - Points X,Y,E

All labels

Answer 11

Question 12

Optimal Choice of Lender Diagram

Answer 12

Question 13

Optimal Choice of Borrower Diagram

Answer 13

Question 14

Marginal Rate of Substitution (MRS)

Answer 14

the amount of a good that a consumer is willing to consume compared to another good, as long as the good is equally as satisfying

Question 15

What happens as a result of an increase in current and future disposable income? (3 things)

Answer 15

1. current and future consumption increases
2. saving increases
3. consumer acts to smooth consumption over time

Question 16

Increase in current disposable income diagram

Answer 16

Question 17

Increase in current disposable income equation

Answer 17

Question 18

Increase in future disposable income diagram

Answer 18

Question 19

Increase in Real Interest Rate for Lender Diagram

Answer 19

Question 20

What happens to future consumption, current consumption and saving when interest rate rises for a lender?

Answer 20

c’ increases
c may increase or decrease
s may increase or decrease

Question 21

What happens to future consumption, current consumption and saving when interest rate rises for a borrower?

Answer 21

c’ may increase or decrease
c decreases
s increases

Question 22

Increase in real interest rate for borrower diagram

Answer 22

Question 23

Government Tax Revenue Equations in Each Period

Answer 23

First period = T =N(t)
Second period = T’ = N(t’)
N = constant population

Question 24

Government Budget Constraint First Period

Answer 24

G = T + B
T = taxes 
B = debt

Question 25

Government Budget Constraint Second Period

Answer 25

G' + (1+r)B = T'

Question 26

Government Intertemporal Budget Constraint

Answer 26

G + G'/(1+r) = T + T'/(1+r)

Question 27

What 3 things happen in competitive equilibrium?

Answer 27

1. Consumers optimally choose current and future consumption given interest rates 2. gov intertemporal budget constraint is satisfied 3. credit market clears

Question 28

Credit Market Equilibrium Diagram

Answer 28

Question 29

Ricardian Equivalence Definition

Answer 29

economic theory that suggests that increasing government deficit spending will fail to stimulate demand as it is intended

Question 30

Endowment Point Definition

Answer 30

The initial allocation of the market

Question 31

Optimal Choice and Ricardian Equivalence Diagram

Answer 31

Diagram:

Question 32

Credit Market Equilibrium and Ricardian Equivalence

Answer 32

Question 33

When is Ricardian Equivalence not satisfied? (4 times)

Answer 33

1. Tax changes are different for different consumers 2. If someone dies in the first period 3. if taxes are not lump sum 4. If the credit market is not perfect , different interest rates for lenders and borrowers

Question 34

How to calculate the intertemporal budget constraint

Answer 34

1. should have 2 budget constraints in the form consumption = incomes - savings 2. combine the two and get intertemporal budget constraint

Question 35

PV of Consumption Equation

Answer 35

PV of consumption = financial wealth + human wealth

Question 36

What is the PV of labour income?

Answer 36

Human wealth

Question 37

Utility Definition

Answer 37

Total satisfaction received from consuming a good or service

Question 38

What does utility depend on?

Answer 38

Consumption today and in the future

Question 39

Utility Equation

Answer 39

Question 40

Diminishing Marginal Utility

Answer 40

the decrease in satisfaction a consumer has from consuming an extra unit of a good or service

Question 41

What does it mean if β < 1 in utility equation?

Answer 41

- future consumption is discounted | - todays consumption is valued more than future consumption

Question 42

What does it mean if β = 1 in utility equation?

Answer 42

current and future consumption is treated equally

Question 43

How do you maximise utility subject to budget constraint?

Answer 43

Question 44

When is utility maximised?

Answer 44

When agents are indifferent between consuming more today or more tomorrow

Question 45

What choices do agents have when maximising utility?

Answer 45

Either: 1. consume today 2. consume 1+r units in the future

Question 46

Euler Equation

Answer 46

Question 47

What does the Euler equation show?

Answer 47

Marginal utility of consuming 1 more unit today = discounted marginal utility of consuming 1+r units in the future

Question 48

Marginal Utility

Answer 48

The added satisfaction a consumer gets from consuming one more unit of a good or service

Question 49

Method to Solve Euler Equation

Answer 49

1. u(c) = log(c) 2. derive u'(c) = 1/c 3. Equation becomes 1/c(t) = β(1+r) 1/c(t+1) 4. rearrange equation becomes c(t+1)/c(t) = β(1+r)

Question 50

What does the Euler equation explain?

Answer 50

explains how interest rates and growth rates are related

Question 51

What does a lower β in euler equation show?

Answer 51

impatient, consumption growth is lower

Question 52

What does a higher β in euler equation show?

Answer 52

patient, consumption growth is faster

Question 53

What do you need to solve for optimal consumption today and in the future?

Answer 53

Euler equation and intertemporal budget constraint

Question 54

Method to solve consumption for today and in the future if β = 1

Answer 54