Week 2 A closer look at the representative agent model 2

Question 1

If you invested today, in which period will you accrue the benefits?

Answer 1

In the next period (ie in the future)

Question 2

What is the capital transition equation?

Answer 2

K’= aI + (1 − δ)K

Question 3

In the capital transition equation what does “a” represent?

Answer 3

An investment-specific technology shock

Question 4

Suppose that the capital transition equation is given by K’= aI + (1 − δ)K, how would you write the value of the firm?

Answer 4

V = zF(K, N) − wN − I +[(z’F(K’, N’) − w’N’-I’)/1+r]+…

The firm takes K, w and r as given.

Question 5

What does having a prime after a letter mean (eg K’)?

Answer 5

Means in the next period

Question 6

What does everything stand for in this equation: K’= aI + (1 − δ)K

Answer 6

• K’ = Capital stock in the next period
• a = An investment-specific technology shock
• I = investment
• δ = The depreciation rate as a %
• K = Capital stock in the current period, which is fixed

Question 7

What does intertemporal choice mean?

Answer 7

Intertemporal choice is the process by which people make decisions about what and how much to do at various points in time, when choices at one time influence the possibilities available at other points in time.

Question 8

What is the discount rate?

Answer 8

The discount rate is the interest rate charged to commercial banks and other financial institutions for short-term loans they take from the Federal Reserve Bank.
The discount rate refers to the interest rate used in discounted cash flow (DCF) analysis to determine the present value of future cash flows.

Question 9

What does a change in “a” effect?

Answer 9

The trade off between investing today and investing in the present.

Question 10

What is the first order condition for K?

Answer 10

dV/dK’=0= [−1/a+MPK’ + (1 − δ)/a’]/1 + r

Question 11

So therefore what does MPK’ =?

Answer 11

MPK’= (1+r)/a - (1-δ)/a’

Question 12

So if “a” increases, what must happen to MPK’?

Answer 12

MPK’ must fall.

Question 13

How does a firm lower its MPK’?

Answer 13

It invests more now, then due to diminishing returns MPK’ falls. (ie increase K’)

Question 14

If a firm’s production function is Cobb-Douglas, what does it look like?

Answer 14

Y = zK^αN^1−α

Question 15

What does it mean if the exponentials add up to 1 in a Cobb-Douglas?

Answer 15

It means that there are constant returns to scale.

Question 16

What does labour supply being inelastic mean?

Answer 16

Whatever happens to the wage, the households decision whether to supply labour or not will not change.

Question 17

When we have z’F(K’,N’) and we do dV/dK, what do we end up with?

Answer 17

MPK’

Question 18

If we differentiate the Cobb-Douglas production function- Y = zK^αN^1−α with respect to capital what do we get?

Answer 18

MPK = αzk^α-1N^α-1

Question 19

If y^2 = x, what does y= in terms of x?

Answer 19

y=x^1/2

Question 20

In Cobb-Douglas, is α usually going to be a decimal or percentage?

Answer 20

Alpha should be a decimal

Question 21

If we get something with the power 1/α-1, what should we do?

Answer 21

Turn it into 1/1-α and flip the number of which its a power to.

Question 22

What is the effect of higher N’ on the MPK’?

Answer 22

Higher N’= Higher MPK’

Question 23

Assume that the agent’s utility function is
u(c1, c2) = ln c1 + βln c2
How would you assume the labour supply?

Answer 23

As there’s no leisure in the utility function, assume the labour supply to be perfectly inelastic.

Question 24

Assume that the agent’s utility function is
u(c1, c2) = ln c1 + βln c2
What is β<1 often called?

Answer 24

The discount factor

Question 25

Assume that the agent’s utility function is
u(c1, c2) = ln c1 + βln c2
Why is β<1?

Answer 25

As you value more consumption in the present than in the future.

Question 26

Assume that the agent’s utility function is
u(c1, c2) = ln c1 + βln c2
Why is the meaning of a smaller β?

Answer 26

The smaller β is, the higher the

weight the consumer assigns to present consumption relative to future consumption.

Question 27

What Is Ricardian Equivalence?

Answer 27

Ricardian equivalence is an economic theory that says that financing government spending out of current taxes or future taxes (and current deficits) will have equivalent effects on the overall economy.

Question 28

What does R do in a General Equilibrium model?

Answer 28

R adjusts to ensure equilibrium

Question 29

Assume that the agent’s utility function is
u(c1, c2) = ln c1 + βln c2
Now assume the same utility as above, but BC is (endowment)
c1 +c2/R= y1 +y2/R
What is lifetime income?

Answer 29

1/1+β[y1 +y2/R]

Question 30

Do agents know if there future income is going to rise?

Answer 30

Yes, otherwise there would be no point in the exercise.

Question 31

How do people react when they know their income is going to rise?

Answer 31

They smooth their consumption

Question 32

Why can’t overall consumption change when everyone has the desire to increase their consumption?

Answer 32

As interest rates will go up to such an extent that we are left where we started

Question 33

Is this a 1 or 2 period model?

u(c, l) = ln(c) + ln(1 − n)

Answer 33

1 period

Question 34

How do we know when we have found a solution?

Answer 34

Endogenous variable= LHS

Exogenous variables = RHS

Question 35

Say there’s a CD function written like Y=AK^βN^α

How do we write the MPK and MPN?

Answer 35

MPK= βY/K

MPN=αY/N

Question 36

What happens if Nd rises but Ns stays fixed?

Answer 36

Wages rise.