Will aggregate demand curve be vertical in the liquidity trap? Can you prove a point?

1 is vertical. In the liquidity trap, if the LM curve is horizontal, then H->; It is infinite, so r = a (constant) The first method: because LM equation is r = a, it is brought in to get f (y), so the ad curve is y = constant, so it is the second vertical method: the derivative of ad curve is obtained from IS-LM model. When P changes, that is, the edge of the LM curve is the trajectory formed by the intersection of P and Y, that is, the ad curve. Therefore, when P changes, because LM is horizontal and the position of the LM curve remains unchanged, Y is always a fixed value, so ad is vertical.

2. liquidity trap refers to that when the nominal interest rate is reduced to zero, people prefer to hold wealth in the form of cash or savings, rather than investing in it in the form of capital, or consuming it as a means of personal enjoyment. Any increase in the country's money supply will be absorbed in the form of "idle capital", just like falling into a "liquidity trap", so it has no impact on overall demand, income and prices. Therefore, when economists reduce interest rates to a very low level, it is impossible to stimulate the economy only by adjusting monetary policy. Extremely low interest rates and gross national expenditure levels will not change, which is called "liquidity trap".

First, the liquidity trap is a hypothesis put forward by Keynes, which means that when the interest rate level can't be lower in a certain period of time, the elasticity of money demand will become infinite, that is to say, no matter how much money is added, it will be stored by people. When the liquidity trap appears, the loose monetary policy cannot change the market interest rate, which makes the monetary policy invalid. The wallet in a citizen's hand is like a "black hole", which can absorb any substance. It mercilessly devours all the money allocated by the state to citizens, causing a "liquidity trap" with unlimited demand for money.

Second, under the condition of market economy, people generally understand the liquidity trap from the effect of reducing interest rates to stimulate economic growth. According to the principle of monetary economic growth (including negative growth), a country's central bank can change interest rates by increasing the money supply. When the money supply increases (assuming that the money demand remains unchanged), the price of funds, that is, the interest rate, will inevitably fall. The fall in interest rate can stimulate exports, domestic investment and consumption, thus driving the growth of the whole economy. If the interest rate has dropped to the lowest level, the central bank will first increase the money supply and then lower the interest rate, and people will not increase investment and consumption, then the simple monetary policy can not achieve the purpose of stimulating the economy, and the level of gross national expenditure will no longer be affected by the reduction of interest rates. Economists call it a "liquidity trap".