Demand and Supply for Money : A Detailed Discussion - The Transaction Motive

• The transaction motive is the principal motive for holding money to carry out day-to-day transactions.
• People receive income at discrete points of time but spend it continuously.
• Since receipts and payments do not occur simultaneously, people need to hold cash balances for transactions.

Suppose a person receives ₹100 at the beginning of every month and spends it evenly throughout the month.

• Beginning cash balance = ₹100
• Ending cash balance = ₹0
• Average cash holding = ₹50
• Monthly transactions = ₹100

Conclusion:
The average transaction demand for money is half of the monthly income (or half of the monthly transactions).

Consider a simple economy with a firm and a worker.

• The firm pays the worker ₹100 as salary at the beginning of the month.
• The worker spends the entire amount on the firm's output.
• Average money held:
  • Worker = ₹50
  • Firm = ₹50
• Total transaction demand for money = ₹100
• Total monthly transactions = ₹200

Conclusion:
The transaction demand for money is only a fraction of the total value of transactions.

\[M_d^T=kT\]

where

\[M_d^T\] = transaction demand for money,
T = total value of nominal transactions in the period,
k = positive fraction of transaction value held as money.

• Velocity of circulation of money is the number of times a unit of money changes hands during a given period.
• In the above example, ₹100 finances ₹200 of transactions because each rupee changes hands twice.

\[\frac{1}{k}M_d^T=T\quad\Rightarrow\quad vM_d^T=T\]

where,

\[v=\frac{1}{k}\] is the velocity of circulation of money (number of times each unit of money changes hands in the period).

• The total value of transactions includes intermediate goods and services, so it is greater than nominal GDP.
• However, there is a stable positive relationship between total transactions and nominal GDP.
• Therefore, an increase in nominal GDP leads to an increase in the transaction demand for money.

\[M_d^T=kPY\]

where 

Y = real GDP

P = general price level (GDP deflator), so PY = nominal GDP.

Conclusion:
Transaction demand for money increases with an increase in real GDP (Y) and the general price level (P).

• Transaction motive means holding money for day-to-day transactions.
• People hold cash because income receipts and expenditures occur at different times.
• Transaction demand is generally a fraction of total transactions.
• Velocity of circulation measures how many times a unit of money changes hands during a period.
• T is a flow variable, Mdᵀ is a stock variable, and v has a time dimension.
• Transaction Demand Formula: Mdᵀ = kT
• Velocity Formula: v = 1/k or vMdᵀ = T
• Modified Formula: Mdᵀ = kPY; transaction demand rises with real GDP (Y) and the general price level (P).