1.3 Fisher Model Flashcards
What are the elements of the Fisher model?
How do we design an indifference curve diagram?
- Trade-off between consumption in period 0 and period 1.
- The curve shows the values of c0 and c1 that the individual is indifferent between.
- Slope of the curve, the MRS of c1 for c0 shows how many units of c1 an individual is willing to trade off for units of c0 at a given utility level.
What characteristics do the utility curves have? How do we know this?
MRS is always negative: you must sacrifice units of c1 to be able to consume c0, there is a budget restriction between the two.
MRS falls in absolute value, left to right: diminishing marginal returns
Array of indifference curves
Moving to the upper-RHS corner = higher utility level
How can we illustrate different investment preferences? How would we show a more impatient investor?
Different points on the models and different preferences
Draw a Fisher model diagram for the example
For the example, assume Mark wishes to invest in A, B, and part of C; Lucy wishes to invest in A and part of B. What do their utility curves look like?
What happens if there is no capital market?
Each investor want to invest in projects that are tangential between their utility curve and the investment curve (transformation curve).
They invest in all projects with a higher return than their time preference rate (e.g. willingness to trade consumption today for consumption tomorrow).
Time preferences vary → disagreement on which projects to undertake. Decision on the “optimal” investment programme cannot be separate from individual consumption preferences.
What does a capital market look like? (model)
What does the line represent in the capital market model?
The sloping line is the present value line of all cashflows discounted or compounded.
What is the slope in capital market model?
The slope is -(1 + r)
where: r is the interest rate, E is the maximum consumption in period 0.
What do alpha, beta, and gamma represent here?
Alpha = level of income in years 0 and 1
A shift to Beta = investing in markets to delay year 0 consumption to year 1
A shift to Gamma = borrowing money and spending in year 0
What does the present value line represent?
All cashflow and consumption possibilities with an equal present value
The set of all investment and financing possibilities of all investors in a perfect capital market
Perfection - to be able to borrow and lend at the same interest rate r, and to find a counter-party at any point on the line.
How can you move alone the present value line? What movements are associated with which actions?
Move along the line by borrowing or investing at interest rate r.
Investing → compounding the interest → moving to the left and upwards
Borrowing → discounting the interest → moving to the right and downwards
How would they invest with a capital market?
Invest on the projects where the rate of return is equal to or greater than the capital market interest rate.
Assume interest rate in CM is 40%, construct a complete Fisher model diagram
