Mas fav version of the equation 1v y mp quantity

(Ma’s fav version of the equation)
(1/V) * Y = M/P
Quantity theory of money:
Assume velocity is a fixed #
(unless question explicitly says velocity increased/decreased)
1/V is also a fixed # ⇒
1/V = k ⇒
⇒ k*Y = M/P
Why doesn’t velocity change over time? Most of the economic activities happen on a regular
basis (pay rent to the landlord at the end of every month)
k*Y = M/P
● M/P is money supply over a price index → M/P = real money supply = real (money)
balances
● Since M/P is the real money supply, k*Y must be the real demand for money
● k*Y = demand for money in real terms -Proof that this is demand for money:
○ Demand for money (How much you want to spend on goods)
■ Individual receives $100 as income for the month
● The $100 can go into checking deposit or can be used to buy
bonds
● Let’s say I decide to buy $30 worth of bonds and hold $70 in
my checking account
● My demand for money is $70
○ Demand for money = how much money an individual wish to hold
(alternative is bond)
■ = it depends on
● Interest rate (negatively/inversely)
○ The higher the rate, the more you put in bonds
● For transactions- positively on income → Y
○ (transactional motive for holding money)
○ Amount of money you demand depends on how much
money you need to hold for spending
○ Demand for money depends positively on Y (income)
■ Demand for money = (fixed #)*Y
● Ignoring the impact of interest rate (assume interest rate is
constant), the demand for money positively depends on Y,
which can be shown mathematically as a fixed # times Y

k*Y = M/P from 1/V * Y = M/P
Money market equilibrium (in the quantity theory of money)
Quantity theory of money (equation): k*Y = M/P (other versions)
Combine with the classical model:
Y-bar = MPC*(Y-bar - T-bar) + I(r) + G-bar (review: we determine the value of r)
Y = Y-bar = a fixed #
k*Y-bar = M/P ⇒
● The left side of the equation is fixed
● So if M goes up by 1%, P must go up by 1%
● (k*Y-bar)*P = M ⇔
○ B*C = A
○ % change in B + % change in C = % change in A
○ (k*Y-bar) is B, P is C, M is A
○ But k*Y-bar never changes so % change in k*Y-bar is 0
○ → % change in M = % change in P
● If M goes up by x% P goes up by x% ⇒
○ This is our formal link between money supply and inflation
Interest rate:
Classical model, “r” (real interest rate, is determined already from the goods market
equation
Y-bar = MPC*(Y-bar - T-bar) + I(r) + G-bar ← solve this for r
(When we say assume r is a constant, we are saying it was already determined here)
Recall:
Nominal interest rate = real interest rate + inflation rate
3% = 2% + 1%
● i = nominal interest rate
● r = real interest rate
● = inflation rate (% change in P) π
i = r + Fisher’s equation π
Classical model: r is determined already a fixed # ⇒
M goes up by 1% P goes up by 1% ⇒
goes up by 1% i goes up by 1% π ⇒
→ if M goes up by 1%, the nominal interest rate goes up by 1%
→ 1 to 1 relationship between i and π
Fisher effect: affects i π
Quantity theory of money (equation):
k*Y = M/P k = 1/V (assume V is fixed unless otherwise stated in the question)

[P*Y = M*V]
M/P = money supply in real terms
k*Y = demand for money dependent only on real income ⇒
k*Y = M/P money market equilibrium ⇒
Combining with the classical model: