(Ma’s fav version of the equation)(1/V) * Y = M/PQuantity 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/PWhy doesn’t velocity change over time? Most of the economic activities happen on a regularbasis (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 buybonds●Let’s say I decide to buy $30 worth of bonds and hold $70 inmy 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 muchmoney 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 isconstant), the demand for money positively depends on Y,which can be shown mathematically as a fixed # times Y

k*Y = M/Pfrom1/V * Y = M/PMoney 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 inflationInterest rate:Classical model, “r” (real interest rate, is determined already from the goods marketequationY-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 rate3% = 2% + 1%●i = nominal interest rate●r = real interest rate●= inflation rate (% change in P)πi = r +Fisher’s equationπClassical model: r is determined alreadya fixed #⇒M goes up by 1%P goes up by 1%⇒goes up by 1%i goes up by 1%π⇒→ if M goes upby 1%, the nominal interest rate goes up by 1%→ 1 to 1 relationship between i andπFisher effect:affects iπQuantity theory of money (equation):k*Y = M/Pk = 1/V(assume V is fixed unless otherwise stated in the question)

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

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