Week 2

Question 1

Keyenes model

How much people spend depends on their income. This formula can reprenset by what formula?

State the formula

Answer 1

C = c(Y)

Question 2

What is the formula for the marginal propensity to consume?

Answer 2

c’(Y)

Question 3

c’(Y)<1. What does this assumption mean?

Answer 3

that consumption does not increase 1 for 1 with our
incomes

Question 4

The slope of the consumption function is called the marginal propensity to consume (MPC). The MPC measures the change in consumption that is caused by a unit change in income. For example, if the MPC is 0.7, then a $100 increase in income will lead to

Answer 4

a $70 increase in consumption.

Question 5

What does Y represent

Answer 5

income

Question 6

What relationship does the Euler equation describe?

Answer 6

how households (or
individuals or firms) trade off the present against the future

The interest rate represents the cost of delaying consumption, and the discount factor represents the household’s preference for current consumption over future consumption.

Question 7

What is the Euler equation formula

Answer 7

u′(c1) = β(1 + r)u′(c2)

The interest rate represents the cost of delaying consumption, and the discount factor represents the household’s preference for current consumption over future consumption.

Question 8

Fill in the gap

The Euler equation is the algebraic equivalent of the _____ of
Yolanda’s indifference curve and budget constraint

Answer 8

tangency

Question 9

What does this reflect. Focus of t=1 and t=2. What is the consumer doing

a = y1 − c1 > 0.

Answer 9

t = 2 income is likely to be low (reflecting
retirement).
To be able to consume c2 at t = 2, person saves

Question 10

What does this reflect. Focus of t=1 and t=2. What is the consumer doing

a = y1 − c1 < 0

Answer 10

one could think about Yolanda’s t = 1 earnings being
relatively low during the student years and one might be optimistic
about future earnings such that y2 > y1. anticipating there will be more than enough to pay off debts and
consume in the future

Question 11

Explain the subsitution effect and Income effect

If interest rates increase what happens to consumption

Think about t=1 and t=2

Practice graphing this. Write this out all the affects in order to get this known rather than just saying it

Answer 11

Substition Effect: Increase in r means Yolanda substitutes away from
present towards future and so (ceteris paribus) c1 ↓.

Income Effect: A higher interest rate means that the household will have more money in the future, which can be used to finance future consumption. This leads to an increase in future consumption.

The overall effect of an increase in the interest rate on consumption depends on the relative strength of the substitution effect and the income effect. If the substitution effect is stronger, then the increase in the interest rate will lead to a decrease in consumption. If the income effect is stronger, then the increase in the interest rate will lead to an increase in consumption.

However, the income effect could also be strong in Yolanda’s case. If she is confident that she will be able to repay the loan in the future, then the higher interest rate will not have a significant impact on her disposable income. In this case, the income effect could lead to an increase in her consumption.

Question 12

constant relative risk
aversion (CRRA). Marginal utility is
u′(c) = c−σ. Subbing this into the euler equation we get?

Answer 12

c2 = ([β(1 + r)] ^1/σ)c1

Question 13

Use an equation to help answer the question… “Temporary income”

Explain how a small temporary income change Y menaing that income only changes in t=1 and not expected to change in t=2. How will Yolanda’s consumption in the current period change?

Answer 13

The equation ∂c1/∂y1 = 1/(1 + β) / (σ(1 + r)) / (σ - 1) < 1 shows the sensitivity of current consumption (c1) to current income (y1). This means Yolanda will increase consumption by less than the ↑ in
(temporary) income.

The partial derivative ∂c1/∂y1 measures how much c1 changes in response to a small change in y1.

Question 14

Permanent Rise in income

Now suppose that Yolanda’s salary increases by x amount in both periods. assumption that β(1 + r) = 1,

Answer 14

∂c/∂x = 1. When Yolanda sees an income increase as permanent, Yolanda
increases consumption by the same amount as the increase in
income

Question 15

Government budget question

Lenny’s government budget constraint at t = 1 is given by
B = G1 − τ1, what is B

Answer 15

B is the amount Lenny borrows to fill the gap between
spending and tax revenue.

Question 16

Government budget question

B < 0

Answer 16

→ surplus (saving)

Question 17

At t = 2, Lenny’s government budget is

Answer 17

τ2 = G2 + (1 + r)B
* Debt is paid back with interest.
* We’re assuming the interest rate is the same as Yolanda’s.
* There is no borrowing in the final period.

Question 18

The marginal propensity to save is the response of a household’s
savings to a unit increase in income. It is inversely _______ to
the marginal propensity to consume since a = y1 − c1.

Answer 18

proportional