Chapter 16 - Capital

Question 1

Financial capital (Definition)

Answer 1

Money or other paper asset that functions like money

Question 2

Real capital (Definition)

Answer 2

physical capital.

productive equipment that generates a flow of services

Question 3

general equation for C(2)

- consumption in the future

Answer 3

C2 = Present value of lifetime income - i(C1)

Question 4

Real vs Nominal equation

Answer 4

i= (n-q)/ 1+ q

n = nominal 
q = inflation rate 

i= n-q if inflation rate is v small

Question 5

Marginal rate of time (MRTP)

Answer 5

∆c2/∆c1

definition = the number of units of consumption in the future of a consumer would exchange for 1 unit of consumption in the present

if > 1 then positive time preference and consumes more in the future (patient)

if < 2 then negative and consumes more today (impatient)

Question 6

Milton Friedman’s primary determinant of current consumption

Answer 6

Primary determinant of current consumption is =

Permanent income

Permanent income = PV of lifetime income

Question 7

Effect of a fall in IR on consumers who are:

1) saver
2) borrower

Answer 7

Saver

• future consumption decreases!
• current consumption (? ambiguous)

Borrower

• future consumption (? ambiguous)
• current consumption increases!

Question 8

Demand for REAL capital
- constant rental rate

(MRP)

Answer 8

MRP(k) = MP * MP(k) = r

Value of marginal product of capital
VMP(k) = P* MP(k)

Question 9

Bond (definition)

Answer 9

A contract in which the borrower agrees to pay the bondholder a stream of money

Question 10

Perpetuity (type of bond or also known as Consol)

Answer 10

A bond that pays out a fixed amount each year forever

example: endowments
- face value doesn’t matter

Pc = X /I (derived through PV equation)

Question 11

Technological obsolescence (Definition)

Answer 11

a good loses value (not due to depreciation) but due to improvements in technology, making substitute products more attractive

Question 12

Retail price of a unit of real capital

Answer 12

r = i + m + depreciation

I = IR 
m = maintenance cost

Question 13

PV equation

Answer 13

R-M/(1+i) + R-M/(1+i)^2 … R-M/(1+i)^n + S/(1+i)^n

Firm should buy machine if Pv > Pk
Pk = price of machine (physical capital)

Question 14

Interest rate determination

Answer 14

Demand:
1) Firm - how much capital it has and how much it would like to have

2) Consumers - borrow finance for house or other goods
3) Government - funding

Supply:
1) Consumer savings

2) International lenders (growing importance)
- upward sloping supply curve

Question 15

Risk Premium (definition)

Answer 15

a payment differential necessary to compensate the supplier of a good or service for having to bear risk

Question 16

Trade-off between safety and expected return

Answer 16

Cautious investors invest in safer stocks (with lower returns)

Less cautious investors give up safety for a higher expected return

Question 17

Economic rent (definition)

Answer 17

Difference between what a factor of production is paid and the MIN necessary to indue it to remain in its current use

Question 18

Exhaustible resources

Answer 18

Cannot be replenished by people.
owner of stock must decide: how much to sell of current stock and how much to keep for sale in the future

For market equilibrium:
- Price must be increasing at precisely the rate of interest

Pt = Po (I + i)^t ——> price after t years

Stock exhaustion path: plotting the quantity of a good remaining at each moment
- downward sloping curve

if ∆Pt > i then no one would sell (& if MB to someone using the resource today > Pt then they will bid up current price)

if ∆ Pt < i then everyone would sell (& if MB to someone of last unit of resource today is < Pt thy will not purchase and current price must fall)

Example: Solar and oil

• lowering price of solar = price path of oil shifts downwards
• more demand for oil and oil being depleted earlier

Question 19

Deriving Perpetuity bond equation

Use PV

Answer 19

PV = X/(1 + i) + X/(1+i)^2 + X/(1+i)^3

y = 1/1+I + 1/(1+i)^2 (multiply both sides by 1+i)

y(1+i) = 1 + 1/(1+i) + 1/(1+i)^2

RHS is function of Y
y = 1/ i

PV = X/i

If P > PV then no one would buy
If P < PV then P would bid up till the point P = PV

Question 20

Annual Return for Stock (equation)

Answer 20

R = (P1 - Po + d)/Po 
   = (∆P + d)/ Po 
Po - initial price
P1 - end price 
d - dividends

Question 21

Risk Averse investors

Answer 21

Rm > Rf

Rm = expected return on stock market

Rf = Return on risk free asset

Question 22

Expected Value of Portfolio

Rp

Answer 22

Rp = Rf + (Rm - Rf)/σm (σp)

• tradeoff between expected payout and risk
• since Rf, Rm and σm are constants

Intercept = Rf

Slope = (Rm-Rf)/σm

• price of the risk
• the increase in return needed to offset the higher risk
• difference in return from risk free and risky assets and variance on return of risky assets

Question 23

Question of finding effective yield

Answer 23

effective yield is the interest rate for which PV = P

so set P = PV and find IR

Question 24

What happens to price in the LR if IR was lower than the effective yield (P=PV) of the bond

Answer 24

If IR < Effective yield then purchasing would be a good investment

• as PV > IR
• Firms would realise this and bid up price till PV = P

Alternatively more firms can enter market & increase competition
- this would result in lower price of product sold by firm and decrease return generated

• essentially excess profits will be eroded through competition

Question 25

Calculating Float

Answer 25

Dell question from tutorial.

APR = annual percentage rate

• e.g. making suppliers wait 37 days to get paid when paid by consumers immediately
• Annual IR = 4%
• as 37 days is around 1/10
• 1/10 * 4% = 0.4%

they retain 0.4% of spending

Question 26

Expected value

Answer 26

Each of possible outcomes * probability of outcome occurring

Question 27

Variance of random variable

• tells us about the spread of possible values of the variable
• an indicator of risk!

Answer 27

𝑉𝑎𝑟(𝑋) = 𝐸[(𝑋−𝐸(𝑋))^2]

• calculate expected value to use equation
• take that away from return and square
• multiple it by the probability for each outcome

Question 28

What is the expected return of a portfolio?

Answer 28

xr(a) + (1-x) r(b)

Question 29

What is the variance of the return of the portfolio?

Answer 29

Calculate all possible outcomes and their probabilities and then find the expectations

Question 30

Capital (flow or stock)?

Answer 30

Capital is measured as a stock

durable and can be used several periods in a row!

Question 31

Budget Constraint for investors

Answer 31

Always upward sloping.

Cannot be downward sloping as it would mean one of the assets have lower return and higher risk, this wouldn’t happen given assumption of risk averse investors

Question 32

Budget Constraint if p = -1

• direction of asset movement
• change in original graph

Answer 32

Assets would move in different directions, as p = -1.

E.g. with p = 1, linear combination of assets and would move together, both fall during recession and both increase during boom

decreased return in one asset will be offset by an increased return on the other.
- now graph = 2 straight lines from point B, joined at y axis where risk is equal to 0

when 0 < p < 1, BC will be within the triangle
Closer P is to = 1, closer BC will be to p = 1
and same for p = -1

Question 33

Rf?
Rm?
rf?
b?

Answer 33

Rf = Return on risk free assets

Rm = expected return on stock markets

rf = realise return on stock market

b = proportion invested in stock market

Risk averse investors therefore Rm > Rf

Question 34

Budget Constraint

Answer 34

𝑐1+𝑐2/(1+r) ≤𝑤1+𝑤2(1+r)

total consumption cannot exceed present value of total income

• increase in IR makes BC steeper