Question

In an economy, the money-domand function is given to be:

M⁴/P =0.50Y−250(r+π²)
The expected rate of infiation, πᵉ, is 0.01 , and the nominal money supply is 9,150 . In this economy the full-employment level of cutput is 1100 .
Using the equibbrium condition for the assel market, delermine the equabon for the LM curve that gives the asset market clearing oulput, Y, giren the price level and the teal interest rato. (Enter your responses rounded to the nearest whole number)

Answer 1

To derive the LM curve equation from the given money-demand function, substitute the expected inflation rate and nominal money supply into the equation, and solve for output (Y) in terms of the price level (P) and the real interest rate (r).

Step-by-step explanation:

To find the LM curve equation that clears the asset market given the price level and the real interest rate, we must use the given money-demand function M4/P = 0.50Y - 250(r + π2) and the data provided. The expected rate of inflation, πe, is given as 0.01 (1%), and the nominal money supply (M) is 9,150. The full-employment output (Y) is 1,100.

Substitute πe for π in the equation and solve for Y to obtain the LM curve equation. Given:

• πe = 0.01
• M = 9150

We can derive the following:

• 91504/P = 0.50Y - 250(r + 0.012)

By solving the above equation for Y in terms of P and r, we can determine the equation for the LM curve that shows the relationship between output (Y), price level (P), and the real interest rate (r).