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Lectures in Macroeconomics- Charles W. Upton
Calculating with Our Money Demand Function
Part 3Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
Calculating with Our Money Demand Function-Part 3
Nominal terms
• We can also do the calculation in terms of nominal values.
• A useful exercise.– At the end, a threat
Calculating with Our Money Demand Function-Part 3
Done in Nominal Terms
Calculating with Our Money Demand Function-Part 3
Done in Nominal Terms
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
All variables expressed in nominal dollars, not real dollars.
We use nominal interest rate
rN = rR + ηe + rRηe
Fisher’s Law
Calculating with Our Money Demand Function-Part 3
The Tableau
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
Calculating with Our Money Demand Function-Part 3
Nominal Expressions
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried
Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
25.1)50.5)(50.0(50.050.0
500,417,1$)5.1)(000,630($
000,450$)5.1)(000,300($2
333
222
eR
eRN
RN
RN
rrr
Pww
Pww
Calculating with Our Money Demand Function-Part 3
Wealth in Nominal Terms
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
480$5.1417$25.11
1450$
25.11
10
2
1
z
25.1)50.5)(50.0(50.050.0
500,417,1$)5.1)(000,630($
000,450$)5.1)(000,300($2
333
222
eR
eRN
RN
RN
rrr
Pww
Pww
Calculating with Our Money Demand Function-Part 3
Period 1 Demand
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $(356.4) $801.9 $291.6 $1,093.5 $1,093.5 3.375
6.579625.1
25.11
3
11
96480)
31
(34
1
34
1
11
11
cr
rm
zc
N
N
Calculating with Our Money Demand Function-Part 3
Period 2 Wealth
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
792$5.1417$25.11
16.57$450$)6.345($2
z
Calculating with Our Money Demand Function-Part 3
Period 2 Demand
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
6.12921625.1
25.11
3
11
21678211
3792
)31
(23
1
23
1
22
22
cr
rm
zc
N
N
Calculating with Our Money Demand Function-Part 3
No Free Lunch
• In nominal terms
c2=$216,000
m2=129,600
• In real terms
Calculating with Our Money Demand Function-Part 3
No Free Lunch
• In nominal terms
c2=$216,000
m2=129,600
• In real terms
4.86$5.1$
6.129$6.129$
144$5.1$
216$216$
22
22
Pm
Pc
Calculating with Our Money Demand Function-Part 3
Assets, End of Period 2
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
Assets Plus Real Return $345.6 Plus: Wage Income $450.0 Less: Consumption $216.0 Less: Increase in Money Holdings $72.0 Equals: Assets, end of Period $183.6
Calculating with Our Money Demand Function-Part 3
Period 3 Wealth
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
Calculating with Our Money Demand Function-Part 3
Demand, Period 3
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
Calculating with Our Money Demand Function-Part 3
Period 4
Calculations in Nominal terms
(1) (2) (3) (4) (5) (6) ('7) (8) (9) Non-
monetary Assets Carried Over
Carry over
Plus Real Return
Money Carried Over
Wage Income
Present Value of Future Income
Wealth C Money Holding
s
Assets, End of Period
P
1 $480 $480 $96 $57.6 $(153.6) 1.000 2 $(153.6) $(345.6) $57.6 $450 $1,080 $792 $216 $129.6 $(183.6) 1.500 3 $(183.6) $(413.1) $129.6 $1,417.5 $1,417.5 $1,134 $486 $291.6 $356.4 2.250 4 $356.4 $801.9 $291.6 $1,093.5 $1,093.5 3.375
Calculating with Our Money Demand Function-Part 3
A Threat
Calculating with Our Money Demand Function-Part 3
A Problem
• Assuming no change in prices, Acme Widgets is certain to earn $100,000 next period.
• Newspapers report the interest rate is 8%.
• What is the DPV of next year’s earnings?
593,92$08.1
000,100$DPV
Calculating with Our Money Demand Function-Part 3
Wrong Wrong Wrong
• Assuming no change in prices, Acme Widgets is certain to earn $100,000 next period.
• Newspapers report the interest rate is 8%.
• What is the DPV of next year’s earnings?
593,92$08.1
000,100$DPV
Calculating with Our Money Demand Function-Part 3
Doing it Right
• This calculation mixes real and nominal.
• Suppose the expected inflation rate is 3%
238,95$05.1
000,100$
370,95$08.1
)03.1(000,100$
DPV
DPV
Calculating with Our Money Demand Function-Part 3
Another Problem
• Based on the consensus inflation forecast of 3%, Baker electronics expects to earn $100,000 next year.
• Experts have determined that Baker’s real rate of interest, adjusted for tax and risk considerations, is 5%.
• What is the DPV of Baker’s profits?
Calculating with Our Money Demand Function-Part 3
Baker
238,95$05.1
000,100$DPV
Calculating with Our Money Demand Function-Part 3
Wrong Again
238,95$05.1
000,100$DPV
Calculating with Our Money Demand Function-Part 3
Doing It Right
464,92$05.103.1
000,100$
593,92$08.1
000,100$
DPV
DPV
Calculating with Our Money Demand Function-Part 3
The Point
• Discount real (inflation adjusted) numbers with real discount rates.
• Discount nominal numbers with nominal interest rates.
Calculating with Our Money Demand Function-Part 3
The Threat
Calculating with Our Money Demand Function-Part 3
End
©2004 Charles W. Upton. All rights reserved
