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2. Based on the following model: Endogenous variables: M,, , P,,\'; The quantity

ID: 1130083 • Letter: 2

Question

2. Based on the following model: Endogenous variables: M,, , P,,'; The quantity equation Real GDP from growth model (classical dichotomy) Y-Y Exogenous and constant velocity Exogenous money supply M,V, = P,Y, M' = M Exogenous variables/parameters: M, ,'/, a. b. c. d. Solve for the equilibrium price level, assume that V is constant. What happens to the price level if the real GDP increases? Why? What happens to the price level if the money supply increases? Why? Based on the quantity equation, give a formula for the inflation rate of the economy. What does it mean?

Explanation / Answer

a). The “Quantity equation” is given by “Mt*Vt = Pt*Yt, => Pt = Mt*Vt / Yt, where “Yt” be the real GDP, “Mt” be the money supply and “Vt” be the velocity of money. So, the equilibrium price is "Pt = Mt*Vt / Yt".

b). So, we got that “Pt = Mt*Vt / Yt”, as “Yt” increases given that everything remain same “Pt” will fall.

Here “Y” is in the denominator and “M” and “V” are same => if “Y” will increase, =>”P” will decreases to maintain the equality.

c). So, we got that “Pt = Mt*Vt / Yt”, as “Mt” increases given that everything remain same “Pt” will also increase.

Here “M” is in the numerator and “Y” and “V” are same => if “M” will increase, =>”P” will also increase with the same proportion to maintain the equality.

d). Consider the quantity equation, “Mt*Vt = Pt*Yt”, => log(Mt) + log(Vt) = log(Pt) + log(Yt), by taking “log” both side of the quantity equation.

=> dlog(Mt)/dt + dlog(Vt)/dt = dlog(Pt)/dt + dlog(Yt)/dt, by differentiating with respect to “t”.

Now, we can write the same equation in the following form.

=> Growth(Mt) + Growth(Vt) = Growth(Pt) + Growth(Yt),

=> Growth(Pt) = Growth(Mt) + Growth(Vt) – Growth(Yt), where Growth(Pt) = rate of inflation.

Now, if “Vt” and “Yt” are fixed, =>Growth(Vt) = Growth(Yt) = 0, => Growth(Pt) = Growth(Mt).

=> the rate of inflation is same as the growth in the money supply, so if “Mt” increases by “1%”, the rate of inflation is also “1%”, if “Mt” increases by “5%”, the rate of inflation is also “5%”.