Question

Inter-temporal Investment/Consumption

a. Summarize Fisher’s separation theorem.

b. Why is this theorem important to both investors and corporations?

c. Why is the existence of a capital market important to the theorem? Illustrate this graphically in the two-period framework and show/explain how consumers will maximize utility.

d. What are some of the assumptions that cause the theorem to hold?

Answer 1

a. Fisher's Separation theoram- This theoram was proposed by the economicst Irving Fisher and was named after him. According to this theoram the primary goal/aim of any corporation will be to increase its present value, irrespective of the shareholder's preferences. It dissimilitude management's focus on productivity opportunities from the market opportunities of the entrepreneu's.

b. This decision is important to both the investors and the company as this theoram leads to company's long term prospirity. Fisher in this theoram argues that management should discard the shareholder's prefernece and should focus on productive opportunities. This will inturn big fruitful results for both the management and the shareholders. The goal will be maximizing profit. Thus, this will increase the comapny's value and will attaract more potential investors.

c. In the capital market there are no frictions that causes the borrowing rate to be different from the lending rate, hence fisher's separation is obtained. It menas that individuals can deligate to the managers of the firm, their investment decisions in which they are the owners.

Assuming r is positive, any fund lent in this period will add up the principal paid back at the end of the period. At any point along the capital market line can be achieved by either lending or borrowing from initial individual position.

Let the principal amount be X0  and X1 be the future value of the principle and the interest rate combined .

therefore, X1= X0 +rX0= (1+r )X0

Present Value of the individual Initial endowment of Y0, Y1 and W0 is

W0 = Y0+ Y1/(1+r)

An Individual's utility is maximised when their subjective rate of time preference is equal to the market rate of interest. The consumption bundle at the point where the individual's subjective time prefernece rate is equal to the market rate of interest is equal to their wealth.

therefore,

W0 = C0 + C*1 /(1+r)

Hence, the equation of the capitalmarket line is

C*1= W0 (1+r) - (1+r)C*0

Figure showing individual's consumption startegy is shown below.

Here, starting with an initila endowmwnr income of Y0 and Y1 at point A, the individual rises its utility. At point D, the rate of return on investment is greater than the borrowing rate, the slope of the capital market line, i.e further investment returns more than it costs to borrow the funds. Thus the individual will continue to invest until the capital market line is tangible to the PPF i.e, point B. Now the individual cn reach any position along the capital market line which is tangible to their own IC. The individual decides to borrow more in the current perios and so his IC curve shifts out to be tangible to capital market line at point C. This is where his utility is maximised.

d. Some of the assumptions of this theoram that put this on hold are first ignoring the preferences of the shareholders. It is entirely impossible for the management to do so. Goal of the shareholders are always taken into consideration.

Secondly, existance of the capital market. In real life scenario the capital market may or may not be present. In the ansence of this, the theoram is not applicable. Third, apart from increasing the present value, the management has to undertake other things into consideration into setting goals.