= Get downing ball of money
= Amount of money spent in the first period
= Amount of money spent in the 2nd period
= Interest rate given by the bank
= Amount of money put into an interest-bearing bank history ( )
Finding the best manner of apportioning the budget over the two periods depends on the demand for the good, the existent income and our want for an equal quality of life between the two clip periods.
To explicate our demand for the good we can compare two different types of goods, foremost nutrient. Food is indispensable and the consumer would necessitate to devour it in both clip periods. Second, a belongings on an alien island is inessential, which means the consumer can easy populate without it.
Analyzing the existent income we will sometimes be interested in the beginning sum of money excepting the involvement gained and sometimes for the entire sum including the involvement gained. It will depend on our demand for the good.
The premise I made for apportioning the budget, was deduced in such a manner that it would do the quality of life equal for the two periods. I will presume the good to be nutrient. It is indispensable for life, therefore the consumer will hold a necessary demand for it in both clip periods. I will besides presume that the ball amount is non greater than the sum of nutrient the consumer is able to eat. Since it is nutrient, the fringy public-service corporation is low so there would be no point of inordinate ingestion.
Sing all of this, but largely that the consumer is get downing with merely adequate money needed for normal life, I would state that it is best to split the outgos over the two periods in 50:50 ratio. Looking back at the expression it means that. Puting this into the original expression, and rearranging it, the expression for the sum for disbursement in the first period looks like this:
How would this affect consumers disbursement and salvaging determination? Depending on the degree of involvement rate the consumer will make up one’s mind how much to pass in the first period while seting the remainder of money ( ) into an interest-bearing bank history. The sum put into bank is mathematically shown as:
( graph and explaining )
The graph shows the consumer ‘s salvaging determination. The perpendicular axis shows the proportion of get downing amount of money spent in the first period ( ) , while the horizontal axis shows the proportion of the get downing amount of money spent in the 2nd period ( ) . There are three indifference curves ( ) and the consumer ‘s budget line ( ) . The involvement rate is 10 % ( ) . This can be seen from the point 1.1 on the horizontal axis where budget line meets it. This can be explained through the illustration if the consumer decided to salvage the whole beginning sum of money. Then in the 2nd period he would hold that sum plus the 10 % involvement gained. The y co-ordinate of the point of tangency between and shows the sum the consumer wants to pass in the first period. Subtracting this sum from gives the sum the consumer decided to salvage.
How will different involvement rates affect the consumers salvaging determination? We must retrieve that in this premise the consumer wants the sums of money he spends in each clip period to be equal. The consumer is non interested in entire existent income but in the equal degree of disbursement through clip periods. Therefore as involvement rate increases the consumer would salvage less and pass more in the first clip period. It may non sound like a logical determination, but if the involvement rate is higher the consumer will hold to set less sum of money into a bank to have back the sum equal to the sum received with the lower involvement rate. By seting existent Numberss in the equation it can be seen that proportionate alteration of sum put into bank is smaller than the proportionate alteration of money received in the 2nd period. In economical footings: fringy rate of permutation is smaller than the involvement addition. Analyzing four different involvement rates e.g. a ) 0 % B ) 10 % degree Celsius ) 20 % and vitamin D ) 50 % gives us the undermentioned consequences:
a )
B )
of
of
of
of
entire existent income= of
entire existent income= of
degree Celsiuss )
vitamin D )
of
of
of
of
entire existent income= of
entire existent income= of
The tabular array shows us that when involvement rate additions, the consumer can salvage less while still increasing his entire existent income.
( graph )
The graph shows how the alteration in involvement rates affects the consumer ‘s nest eggs determination. The perpendicular and horizontal axis show us the same proportions as in the first graph. There are four budget lines ( ) and one indifference curve for each of the budget lines ( ) . Since the consumer wants to hold equal outgo over the two clip periods there is a line on the graph. The intent of this line is to demo exact points where budget lines are digressive to the indifference curves. This came to me as an thought so I tried pulling the graphs every bit exactly as I could to happen out if it is true. In instances where involvement rates are 50 % or lower, mathematical equations matched with graphs so I decided to utilize the line. In add-on I realised that the line may besides be an income ingestion curve in this premise where. Although it resembles a monetary value ingestion curve, it is an income ingestion curve. This is because alternatively of cut downing the monetary value of the good in the 2nd period, the involvement rate is increasing the consumer ‘s existent income.
Each budget line reflects different involvement rate.
It can be seen that by increasing the involvement rate, the budget line is going flatter. Since there is no monetary value alteration or any other manner of altering the maximal existent income in the first clip period, the point where the budget line touches y axis is fixed. The budget lines pivots on that point as involvement rate alterations.
By detecting the indifference curves it can be seen that they are closer on the left side and more distant on the right side of the graph. The ground for this is because the budget line is going flatter while holding its left terminal fixed.
Another premise is if the consumer does non wish for equal outgo over the two periods. He might make up one’s mind to pass in the first period merely the minimal sum needed for endurance and salvaging the remainder of the money regardless the involvement rate.
If the consumer believes that for the first period he needs 40 % of the ball amount, the graph would look as follows:
graph +expl
The perpendicular and horizontal axis show the same proportions as earlier graphs. As in the first graph, in this graph there is one budget line ( ) and three indifference curves ( ) . There is one excess horizontal line touching perpendicular axis at since the consumer wants to pass 40 % of in the first period. Traversing point between that line and is the point of tangency. Compared with the first graph it can be seen that the indifference map has shifted to the bottom-left of the graph. It is because the consumer has reduced the outgo in the first period.
In this instance raising the involvement will non consequence the consumer ‘s salvaging determination because he wants to acquire the maximal public-service corporation out of the 2nd period.
graph +expl
This graph is the same as the old one except the extra three budget lines and one indifference curve. Since the consumer decided to pass a minimum sum of money in the first period, he will ever salvage the remainder of the money regardless of the involvement rate. The effect of the increasing involvement rate would be that consumer is holding more money to pass in the 2nd period ( ) while ever passing the same sum in the first period ( ) .
