ACCPT1- Intertemporal Choice Flashcards
How many periods does intertemporal choice focus on?
2
What are our 5 basic assumptions for intertemporal choice?
- Assume 2 periods of time
- An individual will have endowments in each period (m1 and m2)
- Assume a common rate of interest r, and a consumer can borrow or save at this rate
- Consumers consume amounts c1 and c2
- Consumers have a utility function U(C1,C2)
Do individuals have to spend all of their endowments in each period?
No, they can borrow or save as well
What goes on our axes instead of y and x?
- C2 goes on the y-axis
* C1 goes on the x-axis
What is our budget constraint?
(m1-C1 )(1+r) + m2 - C2 = 0
What is the slope of the budget constraint?
The slope of the budget constraint = -(1+r)
How do we know that as interest rates increase, point b increases?
∂b/∂r = m1 > 0
How can we directly identify point b?
By setting C1 = 0 in C2 = (m1-C1)(1+r) + m2
Does the budget constraint go through the initial endowment point (m1,m2)?
Yes
What happens if we:
• Spend all our endowment in each period exactly?
• We choose to save?
- We stay at E
* We don’t spend all of our period 1 endowment, so we move closer towards b
What does an increase in the interest rate do?
An increase in the interest rate will rotate the budget constraint clockwise; however it still has to pass through the endowment point.
Where is utility maximised, and how do we work this out?
- Find the tangency between the budget line and the highest indifference curve
- MRS12=(MU1)/(MU2) = (1+r)
If a consumer’s tangency is to the left of their endowment point what are they? What about if they were to the right?
- If their tangency is to the left of their endowment point they are a net saver
- If their tangency is to the right of their endowment point they are a net saver
How do we find the utility maximisung point? List the steps
- Differentiate the utility function to find the MRS
- Remember MRS = (1+r) so plug this back into the budget constraint
- Solve for C1*
How do you work out how the budget maximisation point changes when interest rates change?
- Differentiate C1* with respect to r
- If it is above 0, C1* increases as r increases
- If it is below 0, C1* decreases as r increases
How do we identify the income and substitution effects when r increases?
In order to identify the substitution and income effects and compensating variation we take the new budget line back to the original indifference curve. Then we can see what the SE and IE is
How will a net saver behave when interest rates increase?
We do not know, but we know that their utility will be increased.
