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When the nominal money supply remains unchanged, the rising price level makes the LM curve move to the right? Really or not?
Mistake.

The equation of LM curve is: m=ky-hr, k is the sensitivity of money demand to income change, h is the sensitivity of money demand to interest rate change, m is the actual money supply, m=M/P, m is the actual money supply and p is the price level.

In the title, M is constant and P rises, which makes the actual money supply M fall. The LM curve can be changed to r=(k/h)*y-m/h, so that when Y is constant, the decline of M leads to the rise of R, that is, the LM curve moves up, which is equivalent to moving to the left.

Money supply is a financial process in which the banking system of a country or currency area inputs, creates, expands (or contracts) money into the economy. It is a concept of stock, which is the sum of coins, paper money and bank deposits that are not owned by the government and banks at a certain point in time.

Extended data:

The factors that determine the money supply include the central bank's increasing money issuance, the central bank's adjustment of the amount of funds available to commercial banks, the ability of commercial banks to derive funds, economic development, and the money demand of enterprises and residents. Money supply can also be divided into two forms: nominal money supply expressed in monetary units and actual money supply expressed in goods and services that money in circulation can buy.

Because the money supply is realized by cashing in the deposits of commercial bank customers, the amount of money supply depends entirely on the willingness of non-bank departments to hold money.

Non-bank departments have the right to cash their deposits into money at any time, and commercial banks are obliged to meet the cash deposit needs of non-bank departments at any time. If the non-banking sector's willingness to hold money is not satisfied, commercial banks will be forced to close down or go bankrupt because they cannot fulfill their statutory obligations to guarantee repayment.

Baidu encyclopedia-money supply