Week 2 A closer look at the representative agent model 2 Flashcards

1
Q

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

A

In the next period (ie in the future)

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2
Q

What is the capital transition equation?

A

K’= aI + (1 − δ)K

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3
Q

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

A

An investment-specific technology shock

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4
Q

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

A

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

The firm takes K, w and r as given.

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5
Q

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

A

Means in the next period

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6
Q

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

A
  • 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
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7
Q

What does intertemporal choice mean?

A

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.

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8
Q

What is the discount rate?

A

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.

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9
Q

What does a change in “a” effect?

A

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

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10
Q

What is the first order condition for K?

A

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

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11
Q

So therefore what does MPK’ =?

A

MPK’= (1+r)/a - (1-δ)/a’

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12
Q

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

A

MPK’ must fall.

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13
Q

How does a firm lower its MPK’?

A

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

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14
Q

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

A

Y = zK^αN^1−α

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15
Q

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

A

It means that there are constant returns to scale.

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16
Q

What does labour supply being inelastic mean?

A

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

17
Q

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

A

MPK’

18
Q

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

A

MPK = αzk^α-1N^α-1

19
Q

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

A

y=x^1/2

20
Q

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

A

Alpha should be a decimal

21
Q

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

A

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

22
Q

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

A

Higher N’= Higher MPK’

23
Q

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

A

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

24
Q

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

A

The discount factor

25
Q

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

A

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

26
Q

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

A

The smaller β is, the higher the

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

27
Q

What Is Ricardian Equivalence?

A

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.

28
Q

What does R do in a General Equilibrium model?

A

R adjusts to ensure equilibrium

29
Q

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?

A

1/1+β[y1 +y2/R]

30
Q

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

A

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

31
Q

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

A

They smooth their consumption

32
Q

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

A

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

33
Q

Is this a 1 or 2 period model?

u(c, l) = ln(c) + ln(1 − n)

A

1 period

34
Q

How do we know when we have found a solution?

A

Endogenous variable= LHS

Exogenous variables = RHS

35
Q

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

How do we write the MPK and MPN?

A

MPK= βY/K

MPN=αY/N

36
Q

What happens if Nd rises but Ns stays fixed?

A

Wages rise.