Consumer Theory Application - Intertemporal Choice Flashcards
How can we think of the Intertemporal Budget Constraint?
- As a two period model: Period 1 (P1) and Period 2 (P2)
- In P1, the consumer receives an income m1.
- In P2, the consumer receives an income m2
- To simplify the consumption choice, we’ll consider a composite good, C, with a price normalised to 1.
Hence, consumer must decide how much of this good to consume in period 1, c1, and how much to consume in period 2, c2.
What are the differing ways a Consumer can consume in P1 and P2 without borrowing?
- Consume all his income in each of the periods if
he wishes. That is, c1=m1 and c2=m2 - Can save some positive amount of money in P1,
(m1-c1)>0, which will then increase his P2 income by an amount equal to (1+r)(m1 - c1)
How do we find the Budget Constraint? (Without Borrowing)
The logic follows that:
In P2, the consumer cannot consume more than his total P2 income which consists of period 2 specific income plus the final value of any P1
savings.
So, implies a budget constraint of:
c2 ≤ m2 + (1+r)(m1-c1)
This can be drawn (SEE DIAGRAM IN NOTES) B
How do we calculate optimal choice for the intertemporal choice?
-Doing the Lagrangian Method
-By introducing a well-behaved utility function over consumption in P1 and P2,
U(c1, c2), we can then set up a Lagrangian to find the optimal choice.
SEE IN NOTES
What is the tangency condition in this context?
-The MRS between consumption in P1
and consumption in P2 must equal the slope of the budget constraint, MRT.
What is the MRS known as for Intertemporal Choice?
the Marginal Rate of Time
Preference, (MRTP). It just reflects how patient the consumer is
In what situation is the the consumer a borrower?
If c1* > m1
In what situation is the consumer a lender?
If C1*
What is the effect of an increase in the interest rate?
The budget constraint steepens because it has a gradient, -(1+r).
However, as the consumer can always consume at the point, (c1=m1, c2=m2),
the budget constraint actually rotates around this point.
SEE DIAGRAM IN NOTES
What are revealed preference arguments?
Based on the idea that under our consumer choice assumptions we can not only predict behaviour for a given set of preferences, but we can also infer preferences from observed behaviour.
What is an economic example to explain Revealed Preference Arguments?
Suppose that we observe that a consumer selects
A from feasible set L1 then, given our assumptions, he must prefer A to all other possible bundles under L1.
If then we also observe that the consumer selects B from feasible set L2 we know that he must prefer B to all other possible bundles under L2 including
C.
Therefore, as the consumer has revealed that she prefers a to b under L1 then
she must also prefer A to C and indeed A to all bundles in the shaded area.
SEE DIAGRAM IN NOTES
What are some comparative statics results?
If a consumer is a lender (c1
Why does a lender remain a lender after an increase in R?
Before the increase, the consumer preferred e1 to borrowing at any point on line g. After the increase,
any point on g would never be chosen because e1 would still be available. Further, g is now unavailable because the set of points with borrowing has
shrunk. So the consumer would never want to become a borrower.
SEE DIAGRAM IN NOTES
How do we compare differing payoffs in the future?
Calculate what the value of the payoffs are in the current time period (their present value)
PV = X/(1+R)
Where:
- X is income payment of £x in 1 year’s time
What is the P.V Formula generally?
𝑷𝑽 =
𝒙/(𝟏 + 𝒓)z
Where z is to the power of and represent time period
SEE EXAMPLE IN NOTES
