NHM 373 Consumer Economics
Microeconomics and BehaviorTest TwoResource Allocation Over Time
Notes
Past, Present, and Future Assume we live through time periods
t=0,1,2,3,4, Consumption at time t can influence consumption at
time t+1, t+2, Expenditures at t Reduced resources at t+1, t+2,
Savings at t Increased resources at t+1, t+2, Consumption at time t
can be influenced by expectations about time t+1, t+2, Expectation
of greater income at t+1 increased resources for consumption at t.
Expectation of greater expenditure needs at t+1 Reduced resources
for consumption at t.
Consumption Bundles with Two PeriodsIntertemporal Consumption
BundlesAlternatives combinations of current and future consumption
are represented as points in the C1, C2 plane. By convention, the
horizontal axis measures current consumption; the vertical axis,
future consumption.Two possible bundles of (C1, C2) D (3000,9000) E
(6000,6000)
Consider an Inter-Temporal Decision Suppose your income is
$50,000 in the current period and $60,000 in the future period.
Assumptions Consumption is allocated to two periods only. Life ends
after the second period. No Uncertainty No borrowing constraint At
an interest rate of 20%, that is r=0.2 If you deposit $1 in a bank,
you can receive $1 plus 20 cents on the future period. Future Value
= Principal + Principal*(r) = Principal (1 +r) For every $1.20 you
must repay in the future, you can receive $1 now. Present Value =
Future Value/(1 +r) Consumers affordability limits can be
represented by an inter-temporal budget constraint Two axes:
Current period consumption (C1) & Future period consumption
(C2) First, you can always merely consume your income in each
period. C1=50,000 and C2=60,000 must be a point on the budget
constraint Another option is to deposit all $50,000 and thus
receive 1.2*50,000 = $60,000 in the next period in addition to the
future income $60,000. C1=0 and C2=120,000 is a point on the budget
constraint Another option is to borrow 60,000/1.2 = $50,000 in
addition to the present income $50,000. C1=100,000 and C2=0 is a
point on the budget constraint The Intertemporal Budget
ConstraintFor every dollar by which current consumption is reduced,
it is possible to increase future consumption by $1.2
The Inter-Temporal Budget ConstraintIntertemporal Budget
Constraint with Income in Both Periods, and Borrowing or Lending at
the Rate r:The opportunity cost of $1 of present consumption is
(1+r) dollars of future consumption. The horizontal intercept of
the intertemporal budget constraint is the present value of
lifetime income, M1 + M2/(1+ r). M1 M2: Incomes, periods 1 & 2
C1 C2: Consumption, periods 1 & 2 r : interest rate C2m=M1
(1+r) + M2 Maximum resource available in the future period if you
set all your current income aside C1m = M1 + M2/(1+r) Maximum
resource available in the current period if you dont leave anything
for the future period PV (M2)= M2 1+r Present Value of future
income This is also your borrowing limit
The Slope of the Inter-Temporal Budget Constraint Slope = -(1+r)
It means that a dollars worth of consumption in period 1 can be
exchanged for (1+r) dollars worth of consumption in period 2 As the
interest rate increases, the steeper the slope gets. It is as if
the first period consumption becomes more expensive and second
period consumption less expensive.
Exercise Your future income is $110,000 and the interest rate is
10 percent (r=0.10), what would be the present value of your future
income? $110,000
Assume your current income is $100,000. Draw the budget
constraint.
An Inter-Temporal Indifference MapAs in the atemporal model,
movement to the Northeast represents increasing satisfaction. The
absolute value of the slope of an indifferent curve at a point is
called the marginal rate of time preference (MRTP) at that point.
The MRTP at A is I C2/C1l
The Optimal Inter-Temporal AllocationAs in the atemporal model,
the optimal intertemporal consumption bundle (bundle A) lies on the
highest attainable indifference curve. Here, that occurs at a point
of tangency. Saving and Borrowing Negative Saving = Borrowing
Saving region in the inter-temporal budget constraint Left of the
endowment point Borrowing region in the inter-temporal budget
constraint Right of the endowment point
Patience and Impatience(a) The patient consumer postpones the
bulk of consumption until the future period. (b) The impatient
consumer consumes much more heavily in the current period. But in
equilibrium, the marginal rate of time preference (1+r) is the same
for both types of consumers. Time Preference and Other Motives for
Saving Indifference curves in inter-temporal choice Slope of the
indifference curve shows the consumers time preference Neutral
Present-oriented: = A steep indifference curve = A high marginal
rate of time preference = Impatience = Preference for now over
later Future-Oriented: = A flat indifference curve = A low marginal
rate of time preference = Patience = Deferment of gratitude
Changes in Interest Rate When interest rate goes up:
Inter-temporal budget constraint rotates about the current
endowment point Slope of the budget constraint becomes steeper
Optimal consumption changes Change toward borrowing less or saving
more
Permanent Income Hypothesis: The Effect of a WindfallPermanent
Income, Not Current Income, is the Primary Determinant of Current
ConsumptionThe effect of a rise in current income (from 120 to 240)
will be felt as an increase not only in current consumption (from
80 to 150, but also in future consumption (from 168 to 228). Income
in both periods: $120 Interest rate: r=0.2 Consumer receives a
windfall of $120 in the current period The effect of a rise in
current income (from 120 to 240), with no change in future income,
will be felt as an increase not only in current consumption (from
80 to 150), but also in future consumption (from 168 to 228). Why
doesnt the consumer spend up the transitory income in the current
period? Spreading his windfall over both periods allows him to
achieve a better outcome (a higher inter-temporal indifference
curve.) The effect of a windfall on current consumption will be
even smaller if we consider many future periods. Income and
consumption contain a permanent (anticipated and planned) element
and a transitory (windfall/ unexpected) element. Any transitory
income, either positive or negative, is spread over time. Exercise
1 Karen earns $75,000 in the current period and will earn $75,000
in the future. Assuming that these are the only two periods, and
that banks in her country borrow and lend but at an interest rate
r=0, draw her inter-temporal budget constraint. Karens
Intertemporal budget constraint is C2= 150,000 C1. Her Constraint
has endpoint (C1 = 150,000, C2 = 0) and (C1 = 0, C2 = 150,000).
Now suppose banks offer 10 percent interest on funds deposited
during the current period, and offer loans at the same rate. Draw
her new inter-temporal budget constraint. Her new Intertemporal
budget constraint is C2= 157,500 1.1C1. Her new Constraint has
endpoint (C1 = 143,182, C2 = 0) and (C1 = 0, C2 = 157,500).
Exercise 2 Kathy earns $55,000 in the current period and will
earn $60,000 in the future period. What is the maximum interest
rate that would allow her to spend $105,000 in the current period?
20 percent Interest (See Problem 13; Chapter 5) What is the minimum
interest rate that would allow her to spend $120,500 in the future
period? 10 percent Interest (See Problem 13; Chapter 5)Exercise 3
As the interest rate goes up, an individual becomes:a) More likely
to save
The slope of the inter-temporal budget constraint depends on:d)
Interest Rate
Inflation and Value of Money
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