The New IS-LM Microfoundations allow to –Address the Lucas critique –Perform welfare analysis –Integrate intertemporal budget constraints and expectations. The new microfoundations include –Sticky (but endogenous) prices, usually staggered –A motive for holding money –Monopolistic competition by firms selling differentiated products

The Krugman model Endowmen economy A representative consumer maximizes PDV of utility One must hold enough cash to purchase consumption All variables are constant from t=2 on = the long run

Prices are flexible from t=2 on Prices may be rigid at t=1 The model may be used to analyze the role of a liquidity trap

Preferences

Timing ab tt+1 ab Trade bonds for cash Get M t, B t Trade Consume Pay taxes

The second sub-period: At t-b, I have an endowment y t that I must trade to consume I can’t consume more than my money holdings: P t C t <= M t The government issues money and bonds, levies taxes, and rebates seignorage: Net tax T t = TAX t – (M t+1 – M t ).

The first subperiod People exchange money for bonds Bonds pay a nominal interest rate i t between date t-a and date t+1-a

The budget constraint

The optimization problem

The Euler equation Substituting the value of μ into the FOC for consumption and dividing between two consecutive periods we get the Euler equation

The long run For t >= 1, M t = M*, Y t = Y* Prices are fully flexible  C t = C* = Y t = Y* Assume prices are constant: P t = P* Then i t = i* = 1/δ – 1 from Euler CIA must then be binding This condition determines the price level: P* = M*/Y*

The short run: IS At t=0, variables differ from their long-run values. The Euler equation gives us a relationship between C, i and P It is similar to the IS curve Expectations about future activity play a role Inflationary expectations also play a role

C i IS

The short run: LM If the CIA constraint is binding, then i > 0 and C = M/P. If the CIA constraint is not binding, then i = 0 and C < M/P This defines an L-shaped LM curve

i C LM M/P

The flexible price case The IS and LM curve can be rewritten in the (p,i) plane

Regime 1: CIA binding IS LM M/Y p i

Regime I is like a purely « real » model Price is proportional to money, P = M/Y Real interest rate is determined by intertemporal MRS: 1+r = (Y/Y*) -ρ /δ Nominal interest rate determined by Fisher equation 1+i = (1+r)P*/P =(1+r)(1+π) This regime holds if M < (Y/Y*) -ρ /δ.P*Y

Regime 2: CIA not binding IS LM M/Y p i

Regime II is a Liquidity trap Nominal interest rate is zero  money is useless at the margin The price level is determined by expectations and activity, does not respond to money: P = (Y/Y*) -ρ P*/δ This regime takes place if M >(Y/Y*) - ρ /δ.P*Y

Determination of P Unresponsive to current money Higher if future prices are higher Higher if future activity is higher Higher if current activity is lower

What’s going on? Given the future, the real interest rate must be such that C = Y To understand the adjustment, assume future activity Y* goes up Regime I: I want to consume more, need more money, sell bonds for cash, the nominal rate goes up, so does the real rate, I prefer to postpone consumption. Regime II: I don’t need more money, excess demand for goods, price level goes up, increases the real rate, I prefer to postpone consumption.

Another interpretation There exists an equilibrium rate of return r This defines the maximum rate of deflation; higher rates would imply i<0 The larger M, the larger the rate of deflation at which people are willing to hold it (ROR on money = -deflation) When this required rate is more than the maximum, the economy is in a liquidity trap

LT is more likely when Current consumption is too low relative to real money, i.e. when M is large P* is low Y* is low

Rigid prices P is fixed, and the standard IS-LM diagram is used One is in that regime provided it yields C < Y

Rigid prices: regime I CIA is binding: C = M/P (AD) An increase in M raises C and lowers i An increase in Y* raises C and i An increase in P* raises C and i

Rigid prices: regime II C determined by Euler with i=0 Monetary policy is ineffective One may get rid of the LT by reducing the money stock to move the economy to regime I, but it is contractionary Otherwise, one must increase expectations of future activity and/or inflation

Ricardian equivalence In standard IS-LM, budget deficits shift the IS curve and increase output Here, as long as PDV(taxes)=PDV(expenditure), consumption does not react to the timing of debt Debt accumulation is useless to get you out of the liquidity trap If taxes are distortionary, it can actually be harmful