Derive liquidity preference curve : The liquidity preference curve is a concept in macroeconomics developed by John Maynard Keynes.
It illustrates the relationship between the interest rate (or yield) on a particular type of asset, usually money (or cash), and the quantity of that asset that people are willing to hold. The curve reflects people’s preference for liquidity, meaning their desire to hold assets in a form that is easily convertible into cash.
The liquidity preference curve is typically upward-sloping, indicating that as the interest rate increases, the quantity of money demanded (or the willingness to hold money) decreases. This relationship can be derived as follows:
1.Transactions Demand for Money (Md):
The primary reason people hold money is for transactions. They need cash to carry out day-to-day transactions like buying goods and services. The amount of money they want to hold for these transactions is related to their income and the frequency and size of their transactions. Let’s denote this as Md.
Md = k * Y
Where:
- Md is the transactions demand for money.
- k is the proportion of income people want to hold as money.
- Y is income.
2.Asset Demand for Money (Md):
In addition to holding money for transactions, people may also want to hold some money as an asset for precautionary or speculative reasons. The asset demand for money is inversely related to the interest rate (r). As the interest rate rises, people are less inclined to hold money because they could earn more by investing it in interest-bearing assets.
Md = L1 – L2 * r
Where:
- L1 is the amount of money people would hold at a zero interest rate.
- L2 is the sensitivity of the asset demand for money to changes in the interest rate.
3.Total Demand for Money (Md):
The total demand for money (Md) is the sum of the transactions demand and the asset demand for money.
Md = k * Y + L1 – L2 * r
Now, we can derive the liquidity preference curve by plotting the total demand for money (Md) against the interest rate (r). The curve will be upward-sloping because as the interest rate rises (moving to the right along the x-axis), the quantity of money people are willing to hold (Md) decreases (moving down along the y-axis).
In summary, the liquidity preference curve reflects the trade-off between the opportunity cost of holding money (in terms of foregone interest income) and the need for liquidity for transactions and other purposes. As interest rates rise, people are less willing to hold money, leading to a higher interest rate and a lower quantity of money held. Conversely, when interest rates fall, people are more willing to hold money, resulting in a lower interest rate and a higher quantity of money held.