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Economic behavior > IV) Time & Uncertainty > Flashcards

IV) Time & Uncertainty Flashcards

1
Q

What does a consumer face when there is 2 periods of time, 2 incomes (x), and he cannot borrow nor lend?

A

He faces a trade off consumption between period 1 to period 2.

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2
Q

What is the budget constraint if the consumer chooses to lend money at c1?

A

c2= x2+(x1 - c1)(1+r)

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3
Q

What is the budget constraint if the consumer decides to borrow money?

A

c2= x2- (c1-x1)(1+r)

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4
Q

What will be the future value budget constraint?

A

(1+r)c1+c2 = (1+r)x1+x2

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5
Q

What is the present value budget constraint?

A
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6
Q

Draw the intertemporal budget constraint:

A
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7
Q

What is the effect of a change in the r?

A
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8
Q

Generally, is r different or the same for borrowing and lending?

A

It is different.

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9
Q

What do you compute to choose what is the best investment between 2?

How do you compute it?

A

Net Present Value for the 2 investments.

NPV = r1+r2/(1+r) +…. + rT/(1+r)T-1

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10
Q

According to the NPV, when is investment the best?

A

The higher the NVP, the better the investment.

The revenue can be lower at some periods, but on average, it is greater.

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11
Q

What is a bond?

A

It is characterized by 3 parameters:

  • A coupon (amount paid every period): x
  • A maturity date T
  • A face value (paid at the end of the maturity): F
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12
Q

What si the NPV of a bond?

A

NPV = x/(1+r) + x/(1+r)2 +… + F/(1+r)T

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13
Q

What is a lottery?

How is it represented?

A

List of prizes together with the probabilities of obtaining the prizes.

L = (0, 1000), (0,98, 0,02)

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14
Q

How do you compute the E of a lottery?

A

L = (0, 1000), (0,98, 0,02)

E(L) = 0*0,98 + 1000*0,02

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15
Q

What can we compare choices under uncertainty to?

A

Lotteries.

Consumer doesn’t have preferences over bundles anymore but over lotteries.

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16
Q

What does describe a contingent consumption plan?

A

In each possible contingency, it describes the consumption of the agent.

17
Q

What is an insurance?

How is it composed?

A

Way to modify contingent consumption plans in order to smooth consumption.

It is composed of:

  • a premium which is paid by the consumer, no matter the state.
  • a payment paid by the insurance during the bad state.
18
Q

When are 2 lotteries independent?

A

If and only if L2≻L3 and L’2≻L’3

19
Q

What is the expected utility?

A

Decomposition of the choice into:

  • A probability distribution over outcomes
  • A utility function u(c) over outcomes.

=> Utility is linear in probabilities and risk attitude is captured by the utility function.

L = (c1, c2), (p1, p2)

U(L) = p1u(c1) + p2u(c2)

20
Q

In the expected utility th, of what type are utilities?

A

They are cardinal.

21
Q

What are the classical utility functions?

A
  • Linear quadratic: u(c) = ac - bc2
  • Exponential
    • u(c) = cˠ
    • u(c) = eρx
  • Log: u(c) = ln c
22
Q

How do we determine risk aversion?

A
  • Risk aversion: EU(L) < u(EL)

The utility function of participating the lotery is concave. second derivative negative

  • Risk neutral: EU(L) = u(EL)

Utility function of participating is a line.

  • Risk loving: EU(L) > u(EL)

Utility function of participating is convex. 2nd derivative positive.

23
Q

What is the certainty equivalent?

A

c(L) which solves the equation:

U(c(L)) = EU(L)

For risk averse person, c(L) < EL. c(L) is always lower than the expected value of the lottery.

24
Q

How do you know that an agent is more risk averse than another?

A
  • Risk premium is higher (u(EL)-Eu(L))
  • Certainty equivalent is lower
  • Concave function
  • compute the Arrow Pratt indicator to measure the absolute / relative risk aversion:
25
Q

How do you measure the risk of 2 lotteries?

A

When a risk averse agent chooses ont lottery compared to another, it is less risky.

So it depends…

26
Q

What is a fair insurance?

A

The company doesn’t make positive expected profit.

ɣK = (1-p)K

27
Q

How do you determine the best portfolio choice?

A

r is the return of a bond and σ the σ of the stocks.

MRS increases in x (the fraction of the portfolio invested in the risky asset.

28
Q

Summary 1:

A
29
Q

Summary 2:

A

Economic behavior (6 decks)

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