Question three assuming a constant velocity of money while...

QUESTION THREE Assuming a constant velocity of money while the money supply is growing 10% per year, real GDP is growing at 4% per year, and the real interest rate is r = 8%. Assume that actual Inflation is equal to expected inflation. a) Find the value of the nominal interest rate in this economy b) If the central bank increases the money growth rate by 4% per year, find the change in the nominal interest rate Ai C) Suppose the growth rate of Y falls to 2% per year. What will happen to inflation? What must the central bank do if it wishes to keep inflation constant?

Transcript

00:01 So here we have some questions about money, and we're told a few things, right? we're told that the money supply is growing at plus 10 % per year.

00:10 We're told that real gdp is growing at 4 % per year, and we're told that the real interest rate is 8%.

00:18 Great.

00:19 So we also assume that inflation is equal to expected inflation, right? so a, the nominal rate is defined by the fisher identity.

00:27 Right the fisher identity says as you are hopefully familiar with that the real rate is equal to the nominal rate minus expected inflation which we know is equal to inflation here so i know the real rate i need to get expected inflation how do i get expected inflation well i appeal to the quantity equation right this is the quantity equation it tells us the amount of money spent m times v has to be equal to the amount of money spent p times y right and v is the amount of money used to buy stuff p y is the amount of stuff sold so what are we told we're told that velocity is constant we're told that m is growing at 10 percent we're told that y is growing at 4 percent and that implies that p has to be growing at 6 percent which is equal to inflation right the rate of change of prices so if this is 6%, we can now solve, right? we often call this r, i, and pi.

01:39 So if i have the real rate is 8%, is equal to the nominal rate minus 6%.

01:46 That means that the nominal rate has to be 14%.

01:50 Great.

01:52 So for b, now money supply is going to grow at 14%.

01:57 Well, let's go back to the quantity equation.

02:00 V is equal to py.

02:02 This is constant.

02:03 We know that money is going to be growing at 14%.

02:06 We know that output is still growing at 4%.

02:09 And that means that prices have to grow at 10%.

02:12 Right.

02:13 So we have inflation equal to 10 % now, right? the bank is going to print more money.