(5.1) Separation theorems

Question 1

2

What 2 decisions do individuals make in an economy with investment?

Answer 1

• Investment decisions - How much to invest today for future returns
• Consumption allocation - How to distribute consumption between present and future

Question 2

2

How does 1st and 2nd separation theorem differ?

Answer 2

• 1st - perfect credit markets (PCM)
• 2nd - imperfect credit markets (IPCM)

Question 3

2

What are perfect credit markets?

Answer 3

• same interest rate for borrowing and saving
• no constraints on borrowing

Question 4

4

What is the 1st separation theorem?

Answer 4

• When credit markets are perfect…
• Individuals can first calculate optimal investments using Net Present Value (NPV)
• Then calculate optimal consumption allocation over time
• The two decisions are independent

Question 5

4

What is the 2nd separation theorem?

Answer 5

• When credit markets are imperfect…
• Investment and consumption decisions are interdependent
• NPV alone is insufficient for investment decisions
• Must consider both decisions simultaneously

Question 6

How do you calculate NPV?

Answer 6

y / (1+r)^n

Question 7

What does the term 1/(1 + r) represent?

Answer 7

‘price’ of one extra unit of consumption in the next time period

Question 8

How do personal preferences (e.g. being thirsty) factor into separation theorem involving PCM?

Answer 8

They don’t

Question 9

Under PCM, what investment will a cosumer choose?

Answer 9

the one with the highest NPV

Question 10

How do we calculate Present Discounted Value (PDV) for income stream y₀, y₁, y₂, …, yₜ, …, yₜ?

Answer 10

y₀ + y₁/(1+r) + y₂/(1+r)² + … + yₜ/(1+r)ᵗ + … + yₜ/(1+r)ᵀ

don’t worry too much on this, just showing it keeps on going

Question 11

How does investment change consumption for a consumer?

Answer 11

Allows consumption to be smoothed

Question 12

photo

What is the PDV of lifetime consumption?

Answer 12

Question 13

5

Why can’t you just compute NPV to find optimal investment in IPCM?

Answer 13

• limited in ability to transfer income from one period to another
• diff investment opps have different implications for diff consumption paths
• optimal investment may not have highest NPV
• because of timing structure of income it generates
• so cannot separate consumption decision from investment decision (interdependent)

Question 14

When asked to find whether there is r between A and B investment opps, what might you need to state?

Answer 14

as r increases, NPV(A) increases/decreases faster/slower than NPV(B)

(Extra: indifferent means NPVs are equal)

Question 15

What might we say about future payoffs from borrowing when the interest rate increases?

Answer 15

it is discounted more heavily

Question 16

3 - do once only

What are some assumptions of PCM?

Answer 16

• Can borrow and lend at same interest rate r
• Only borrowing constraint is that consumer has enough income to repay debt
• Perfect and costless mechanism – ensures no one takes on loans they cannot repay and all debts are repaid