Question

An economy has full-employment output of 1500. Suppose desired consumption and desired investment are
?? = 125 + 0.75(? − ?) − 400?
?? = 200 − 100?
G is the level of government purchases, and T=100

Money demand is
?? ?
= 0.8? − 2000(? + ??)
where the expected rate of inflation, ??, is 0.05. The nominal supply of money M = 2000.

2. Asset market equilibrium and the LM curve.

i) Derive the LM curve when the price level is equal to the solution in part (h) [Hint: Use the price level from the part (2-h) to get the real money supply]

Solution in part H is P = $2

Answer 1

According to the given information, the asset market is reflected by the IS curve and the money market is reflected by the LM curve.

Here we I need to derive the equation of the LM curve when the price level is equal to the solution in part h i.e. P*=2.

Now, from the given informations, we get the Money demand equation as,

Md/P = 0.8Y - 2000(r+πe)

Where, Md= Money demand, πe= Expected inflation rate.

From the given informations, we get

Nominal Money Supply M=2000. Expected inflation rate=πe=0.05.

Now we get the LM curve by putting Md=M or the nominal money demand = nominal money supply.

Hence, The equation of the LM curve is

M/P = 0.8Y - 2000(r+πe)

or, 2000/P=0.8Y-2000(r+0.05)

From solution in part h we get P=$2.

Hence,

  2000/2=0.8Y-2000(r+0.05)

or, 1000 = 0.8Y-2000r-100

or, 0.8Y - 2000r = 1100..........(1)

This is the equation of the LM curve when the price level is $2.

Hence, the equation of the LM curve is

LM: 0.8Y-2000r = 1100.

Hope the solution is clear to you my friend.