1. As an investor, you consider investing in a recently liberalized emerging market
economy. From past post liberalization performance data for this economy you know that investment projects tend to have a pay-off of 11.57% per annum. What assumption
would you have to make to conclude that this figure is a good guide to future investment returns.
One assumption for past sample data to give a guide to the future is that the remaining investment opportunities are of equal quality as the ones earlier exploited. If one assumes that there is a limited pool of such opportunities (not an entirely realistic assumption) it would appear that the more profitable ones get taken first. So, later investment projects may well earn a lower return.
A second reason has to do with diminishing marginal returns to individual production factors and capital saturation in the production process. We will address this in more detail in the context of growth theory next semester. The basic lesson here is that in an applied context one needs to be aware about the factors that influence the probabilities underlying past decision making.
2. How would a change in the market rate of interest affect the allocation of consumption over time?
A rise in the rate of interest would lead to an increase in future consumption and a fall in present consumption. A fall in the rate of interest would likewise lead to a rise in present consumption relative to future consumption. In either case, the market rate of interest is equal to the consumer’s rate of time preference at the new equilibrium point.
3. Assume you and a business partner attempt to agree on an investment project. You have a strong preference for saving while you know your business partner’s preference to be weighted in favour of present consumption. How, if at all, could you agree on the optimum amount to invest in your firm?
Microeconomic theory tells us that you should invest in your firm until the internal rate of return to your investment project has fallen to the market rate of interest. Once this point is achieved, your ‘hedonistic’ business partner can borrow at the market rate of interest to fund his present consumption. You can likewise invest your remaining assets in a bank account. Both of you benefit from this arrangement. Even your business partner does, since the investment project earns a higher rate of return than the market rate of interest, enabling him to consume more over both periods, and re-allocate this higher income at a cost determined by the market interest rate.
4. Consider an income prospect of £749 with a certainty equivalent income level of
£1024. Would an economic agent with risk preferences corresponding to this scenario be risk averse or risk loving?
He would be risk loving, since the amount of certain income creating the equivalent amount of utility (hence certainty equivalent) to a given prospect, is higher than the expected value of this income prospect.
5. Assume that at the end of the course you join the other MSc Finance students for a drink in a local pub. By the end of the evening you have reached a state of intoxication that makes you feel generous so you volunteer to pay for the drinks of all MSc students who have not yet paid for their drink. Do you pay for your own drink?
The operative concepts here are membership of the set of MSc students and ownership of the drinks to be paid for. By the statement above, you should strictly speaking not have paid for your own drink, since you only pay for the drinks of those MSc students who do not pay for their own drinks and you are one of the MSc students. If however you don’t pay for your own drink, then you belong to the subset of those MSc students who have not paid for their drinks so that you would have to pay for it if it were not for the fact that you only pay for the drinks of those who don’t pay for their own drink and this is your own drink after all ….
As should be clear by now the above statement is –in good logic- paradoxical. In general terms, it is not possible in set logic to define a set of all sets that do not contain
themselves since such a set would have to contain itself while it would be simultaneously required that it can’t do so.
This is also known Russel’s paradox. If you go further into this you will find that it closely ties in with the impossibility of creating self contained logical systems. Many of the assumptions made in economic theory are introduced to simplify things. Even if they were not, some assumptions would have to be made as a basis for any theory (and this includes theoretical physics).
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