This article explores the concept of optimal money holdings, a crucial decision in personal finance and economics. We will analyze Uma's estimated annual benefits from holding various amounts of money and determine her optimal money holding for different nominal interest rates. Our analysis will demonstrate how individ...
Understanding the Trade-off
Holding money offers benefits such as flexibility and convenience for transactions. However, keeping money in a non-interest-bearing account means forgoing the potential earnings from investing it. This creates a trade-off between the benefits of liquidity and the opportunity cost of forgone interest.
Scenario Analysis: Uma's Investment Strategy
Let's consider Uma's situation, where she has estimated the annual benefits of holding different amounts of money. The provided table shows this relationship:
Average money holdings ($) | Total benefit ($)
---------------------------- | ----------------
500 | 35
600 | 47
700 | 57
800 | 65
900 | 71
1,000 | 75
1,100 | 77
1,200 | 77
Determining Optimal Money Holdings at Different Interest Rates
To determine the optimal money holding for Uma, we need to consider the opportunity cost of holding money, which is the interest rate she could earn by investing the money elsewhere. We will analyze this for three different nominal interest rates: 9%, 5%, and 3%.
Optimal Money Holdings at 9% Nominal Interest Rate
At a 9% nominal interest rate, the opportunity cost of holding $100 for a year is $9 (9% of $100). We need to find the point where the marginal benefit of holding an additional $100 is less than or equal to the opportunity cost. By comparing the marginal benefit and opportunity cost of holding additional money, we can determine the optimal holding:
Average money holdings ($) | Total benefit ($) | Marginal benefit ($) | Opportunity cost ($)
---------------------------- | ---------------- | ------------------- | ------------------
500 | 35 | - | -
600 | 47 | 12 | 9
700 | 57 | 10 | 9
800 | 65 | 8 | 9
900 | 71 | 6 | 9
1,000 | 75 | 4 | 9
1,100 | 77 | 2 | 9
1,200 | 77 | 0 | 9
From the table, we observe that the marginal benefit of holding additional money starts to fall below the opportunity cost at $800. Therefore, Uma's optimal money holding at a 9% nominal interest rate is $800.
Optimal Money Holdings at 5% Nominal Interest Rate
Following a similar approach, we analyze the scenario with a 5% nominal interest rate. The opportunity cost of holding $100 is now $5 (5% of $100).
Average money holdings ($) | Total benefit ($) | Marginal benefit ($) | Opportunity cost ($)
---------------------------- | ---------------- | ------------------- | ------------------
500 | 35 | - | -
600 | 47 | 12 | 5
700 | 57 | 10 | 5
800 | 65 | 8 | 5
900 | 71 | 6 | 5
1,000 | 75 | 4 | 5
1,100 | 77 | 2 | 5
1,200 | 77 | 0 | 5
In this case, the optimal money holding for Uma is $1,000, as the marginal benefit falls below the opportunity cost at this point.
Optimal Money Holdings at 3% Nominal Interest Rate
At a 3% nominal interest rate, the opportunity cost of holding $100 is $3. We repeat the analysis:
Average money holdings ($) | Total benefit ($) | Marginal benefit ($) | Opportunity cost ($)
---------------------------- | ---------------- | ------------------- | ------------------
500 | 35 | - | -
600 | 47 | 12 | 3
700 | 57 | 10 | 3
800 | 65 | 8 | 3
900 | 71 | 6 | 3
1,000 | 75 | 4 | 3
1,100 | 77 | 2 | 3
1,200 | 77 | 0 | 3
With a 3% interest rate, Uma's optimal money holding is $1,200, as the marginal benefit falls below the opportunity cost at this level.
Conclusion
This analysis demonstrates how individuals can determine their optimal money holdings by considering the trade-off between the benefits of liquidity and the opportunity cost of forgone interest. Uma's optimal money holding varies based on the nominal interest rate, with higher interest rates encouraging her to hold less cash and invest more to take advantage of higher potential returns. This approach highlights the importance of understanding opportunity costs and making informed financial decisions based on individual circumstances.