Income Concepts - Hicks

Question 1

Hicks’ Definition of income

Answer 1

the amount a person could spend in a period and still remain as well off at the end of the period.

Question 2

Nominal interest in the market formula
(inflation adjusted interest rate)

Answer 2

(1+d) (1+r) = (1+m)

d = inflation rate
r = real required return
m = money or nominal rate (i.e. the inflation compensated interest rate)

Question 3

3 Main implementations of the income definition

Answer 3

Income as interest - The increase in value as discounted future services come nearer

CAPITAL MAINTENANCE (Hicks No 1) - The amount which could be spent in a period without depleting capital

CONSUMPTION MAINTENANCE (Hicks No 2 and No 3) - The amount that could be spent in a period and still permit the spending of the same amount (nominal = No 2, real terms = No 3) in ensuing periods.

Question 4

Income as interest formula

Answer 4

K0(at 0) x i

Kj(at k) = capital at time j, valued on expectations at time k

Question 5

Hicks No1 - Capital maintenance formula

Answer 5

K1(at0) - K0(at0)

Kj(at k) = capital at time j, valued on expectations at time k

Question 6

Hicks No2 - Income maintenance (nominal terms) formula

Answer 6

[(K1(at0)-Y)(1+m^2)-Y]m3

If m2 is the same for ensuing periods e.g. m3, m4 etc., then we can shorten the formula to:
[(K1(at0)-Y)m2

Y = income for period

m = nominal interest rate of period

Question 7

Hicks No3 - Income maintenance (real terms)

Answer 7

[(K1(at0)-Y)(1+r^2)-Y]r3

Y = income for period

r = real interest rate of period

Question 8

Income Ex-Ante, how to do these questions

Answer 8

Ex Ante: Before the event

We calculate Present Value of the cash flows first e.g.

At t0 you buy an asset for £2,000. You expect to receive £1,200 from the asset at t1 and a final £1,080 at t2. At t0 your interest rate expectations are m1 = 10%, m2 = 8%, with 8% continuing in
future periods, but rt = 3% for all time periods.

Calculate t2 at t1 (1,080/1.08) = £1000. Added together we get £1,200 at t1
Discount t1 to present value: £2,200/1.1

Then do all the different formulas from there

Question 9

Income Ex-Post, how to do these questions

Answer 9

Notation slightly differs, replacing K1(at 0) with K1(at 1), but everything is practically the same as ex ante. We redo all our present values again, finding K1(at 1) and K0(at 1)

APART FROM Hicks no1 Capital maintenance, which becomes: K1(at 1) - K0(at 0). Meaning you use the K0 from the ex ante answer, whereas all other ex post formulas will use K0(at 1) when they refer to K0, meaning you use the K0 answer just calculated for ex post.

Question 10

Windfall gains Income concepts formulas:

Answer 10

Income as interest: K0(at 1) - K0(at 0)
Hick’s no1: Not applicable
Hick’s no2 & 3: (K1(at 1) - Y1(at 1)) - (K1(at 0) - Y1(at 0))
While they are same formula, y1 will differ

Question 11

Hicks no2 & 3 example answer

Answer 11

Lets say K1 = £1000 and m2 = 0.1
(K1(at 0) - y)m2
or r2

(1000 - y) x 0.1
100 - 0.1y = y
100/1.1 = y

Question 12

What is Hick’s no’…’ Y2 in t2 £s (t2 purchasing power)

Answer 12

Start with answer you have for Y1.
Use (1+d)(1+r) = 1+m and rearrange to get the inflation rate ‘1+d’
,’, (1+m)/(1+r) = 1+d
Multiply y1 by 1+d to get y2
If you need y3 or y4 etc., do y1 x Inflation rate^2…

Question 13

What will be the ex post incomes for period 1 assuming certainty (or perfect
foresight) i.e. all expectations are achieved in the period and there are no
changes in expectations at the end of the period?

Answer 13

Income ex ante & ex post are the same if there is certainty or perfect foresight