Now or later

1
Now or later

• ECO61 Microeconomic Analysis
• Udayan Roy
• Fall 2008

2
Inter-temporal budget constraint

• Two dates 0 (present) and 1 (future)
• Dollar incomes M0 and M1
• Food consumed C0 and C1
• Price of food P0 and P1 dollars
• Money saved in date 0 M0 P0C0 dollars
• Interest rate in date 0 R
• Wealth carried over to date 1 M0 P0C0 (M0
  P0C0) ? R (M0 P0C0) ? (1 R)
• P1 C1 M1 (M0 P0C0) ? (1 R)

3
Inter-temporal budget constraint

• Let m0 ? M0/P0 and m1 ? M1/P1 denote the amounts
  consumed on dates 0 and 1 when there is no saving
  (or dis-saving)
• That is, mt is the amount consumed on date t if
  all of date ts incomeneither more nor lessis
  spent on date ts consumption

4
Inter-temporal budget constraint

• Start with the Inter-temporal budget constraint
• Separate the consumption and income terms
• Divide both sides by P1
• Use the definitions m0 ? M0/P0 and m1 ? M1/P1

5
Interest rates nominal and real

• A loan of 1 on date 0 gets you 1 R on date 1
• R is the nominal interest rate
• The loaned amount (1) could have been used for
  1/P0 units of consumption on date 0
• The 1 R that you get on date 1 would pay for
  (1 R)/P1 units of consumption on date 1
• So, a sacrifice of 1/P0 units of consumption on
  date 0 leads to (1 R)/P1 units of consumption
  on date 1
• So, a sacrifice of (1/P0)/(1/P0) 1 unit of
  saving on date 0 leads to (1 R)/P1 /(1/P0)
  (1 R) P0/P1 units of consumption on date 1

6
Inflation

• Let INFL denote the rate of inflation
• P1 P0 P0 ? INFL P0 ? (1 INFL)
• Example
• Let the rate of inflation be 5
• Then, INFL 0.05
• If P0 2.00, then P1 2.00 ? (1 0.05) 2.10

7
Interest rates nominal and real

• Recall that a sacrifice of 1 unit of consumption
  on date 0 leads to (1 R) P0/P1 units of
  consumption on date 1

8
Inter-temporal budget constraint

• Note, from the second line, that if C0 0, then
  C1 m1 m0(1 Rreal)
• This is the maximum possible consumption in date
  1
• Note, from the third line, that if C1 0, then
  C0 m0 m1/(1 Rreal)
• This is the maximum possible consumption in date
  1
• If C0 m0, then C1 m1, and vice versa.
• That is, the consumer always has the option of
  not saving or dis-saving

9
Inter-temporal budget constraint

• This is just like the usual budget constraintXPX
  YPY M, when
• X is C0, Y is C1
• PX 1, PY 1/(1 Rreal), and
• M m0 m1/(1 Rreal)
• M is also called the present discounted value
  (PDV) of the consumers income stream
• The left-hand-side of the budget constraint is
  the PDV of the consumption stream
• So, the budget constraint is that the PDV of the
  consumption stream must equal the PDV of the
  income stream

10
Inter-temporal budget line
B
A
11
Inter-temporal budget line

• When the real interest rate increases, the budget
  line still passes through the no-saving-no-dissavi
  ng (NSNDS) point, but rotates upward and becomes
  steeper (red line)
• When the real interest rate decreases, the budget
  line rotates downward and becomes flatter (green
  line)

B
A
12
Inter-temporal budget line

• When either m0 or m1 (or both) changes, the
  no-saving-no-dissaving point changes, and the
  budget line moves parallel to the old line, still
  staying on the NSNDS point
• The line moves outward (inward) if M, the PDV of
  the income stream, increases (decreases)
• If M is unchanged, the budget line stays put even
  if m0 or m1 (or both) changes

B
A
13
Preferences for the Timing of Consumption

• Treat identical physical objects as distinct
  goods if they are available at different points
  in time
• Consider a consumer who cares about two goods
  food this year and food next year
• Indifference curves have customary shape
• Slope downward, declining MRS
• Bundles on 45o line indicate equal consumption in
  both years
• If food this year is on horizontal axis, steeper
  indifference curves show greater impatience in
  consumption

10-13
14
Figure 10.4 Preferences for the Timing of
Consumption
10-14
15
Affordable Consumption Bundles

• Consumption bundle is affordable if, through
  borrowing and lending, the consumer can make all
  required payments as they come due
• PDV of consumption stream PDV of income stream
• Slope of the budget line is the negative of the
  ratio of the goods prices

10-15
16
Figure 10.5 Affordable Alternatives
10-16
17
Consumption Choices

• To determine each consumers best choice, apply
  the no-overlap rule
• Brians solution (Figure 10.6(a))
• Chooses point B
• Saves some income in first year to boost
  consumption in second year
• Ryans solution (Figure 10.6(b))
• Chooses point C
• Borrows money in first year to consume more food
  than current income would allow

10-17
18
Figure 10.6 Best Choices with Saving and
Borrowing
For both Brian and Ryan, A is the NSNDS point.
10-18
19
Saving, Borrowing, and the Interest Rate

• When interest rate rises
• Saving becomes more rewarding
• Borrowing becomes more costly
• Do people respond by saving more and borrowing
  less?
• Not necessarily!
• To understand, study how changes in the interest
  rate affect consumers budget constraints
• If consumption at each point in time is a normal
  good and the interest rate rises
• Savers may increase or decrease their savings
• Borrowers definitely reduce their borrowing

10-19
20
Figure 10.7 Effect of a Change in the Interest
Rate on Saving
3. For a saver, like Brian, an increase in the
real interest rate can have an ambiguous total
effect on saving.
2. For Brian, the saver, an increase in the real
interest rate is like an increase in income. When
current consumption is a normal good, this
encourages more current consumption that is,
less saving.
1. The substitution effect of an increase in the
real interest rate encourages less current
consumption that is, more saving.
10-20
21
Figure 10.8 Effect of a Change in the Interest
Rate on Borrowing
3. For a borrower, like Ryan, an increase in the
real interest rate leads to more saving.
2. For Ryan, the borrower, an increase in the
real interest rate is like a decrease in income.
When current consumption is a normal good, this
encourages less current consumption that is,
more saving.
1. The substitution effect of an increase in the
real interest rate encourages less current
consumption that is, more saving.
10-21
22
PDV of Income Stream

• An individual can attain a higher level of
  utility only if her inter-temporal budget line is
  high
• This is possible when the PDV of the consumers
  income stream is high
• Therefore, our focus must be on how the PDV of
  the consumers income stream can be maximized

23
Investment An Example
10-23
24
Net Present Value

• Investment refers to up-front costs incurred with
  the expectation of generating future profits
• E.g. when a firm buys capital goods
• Profitability of investment is computed as the
  difference between the PDV of the revenue stream
  and the PDV of the cost stream, the net present
  value (NPV)
• NPV criterion an investment project is
  profitable when its NPV is positive unprofitable
  when its NPV is negative

10-24
25
Net Cash Flow

• In practice, we usually compute investments net
  cash flows
• Difference between revenue and cost during a
  single year of a projects life
• Then find NPV by computing PDV of projects net
  cash flows

10-25
26
Internal Rate of Return

• Every projects NPV depends on the interest rate
• A projects internal rate of return (IRR) is the
  rate of interest at which its NPV is exactly zero
• If a projects cash inflows occur before its cash
  outflows
• Project is profitable when interest rate
• Unprofitable when interest rate IRR
• For a two-period investment, IRR is easy to
  calculate using NPV equation
• For longer term investments, solve for IRR
  numerically using spreadsheets or other computer
  programs

10-26
27
Investment and the Interest Rate

• When interest rates rise, most potential projects
  become less profitable
• Some become unprofitable
• Causes total amount of investment to fall
• Two reasons
• Future dollars become worth less compared to
  current dollars, this reduces the value of the
  investment relative to its cost
• Putting money in the bank becomes more
  attractive the opportunity cost of funds is
  greater. Thus profit is lower

10-27
28
Choosing Between Investments

• Not all profitable projects should be invested in
• Sometimes projects are mutually exclusive
• Best choice among mutually exclusive alternatives
  is the one with the greatest profit
• For investments, this is the one with the highest
  NPV
• Using criteria other than NPV to compare mutually
  exclusive projects can lead to poor
  decision-making
• E.g., do not compare IRR or payback period

10-28
29
Investing in Human Capital

• Human capital consists of marketable skills
  acquired through investments in education and
  training
• Use standard investment principles to determine
  whether to invest in human capital
• Compute the NPV of the financial costs and
  benefits
• Include opportunity costs
• Economists often summarize the financial returns
  to education by calculating an IRR

10-29
30
The PDV of AttendingBusiness School
10-30