# Mas fav version of the equation 1v y mp quantity

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(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 = kk*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/PM/P is money supply over a price index → M/P = real money supply = real (money)balancesSince M/P is the real money supply, k*Y must be the real demand for moneyk*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 monthThe \$100 can go into checking deposit or can be used to buybondsLet’s say I decide to buy \$30 worth of bonds and hold \$70 inmy checking accountMy demand for money is \$70Demand for money = how much money an individual wish to hold(alternative is bond)= it depends onInterest rate (negatively/inversely)The higher the rate, the more you put in bondsFor transactions- positively on income → Y(transactional motive for holding money)Amount of money you demand depends on how muchmoney you need to hold for spendingDemand for money depends positively on Y (income)Demand for money = (fixed #)*YIgnoring 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/PThe left side of the equation is fixedSo if M goes up by 1%, P must go up by 1%(k*Y-bar)*P = MB*C = A% change in B + % change in C = % change in A(k*Y-bar) is B, P is C, M is ABut k*Y-bar never changes so % change in k*Y-bar is 0→ % change in M = % change in PIf 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 rater = 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 incomek*Y = M/Pmoney market equilibriumCombining with the classical model:

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