Lecture: THE KENESIAN MODEL IN THE SHORT AND LONG RUN In the short run actual GDP,, may be lower or higher or equal to full-employment GDP,. The aim of the Keynesian model in the short run is to explain short-run fluctuations in production around a long-run trend. The reason why actual GDP may deviate from full-employment GDP in the short run, is that prices and nominal wages are assumed to be not fully flexible in the short run. We start by assuming that P and W are fixed in the short run. In this case aggregate demand determines output at a fixed price level. Thus, we assume that the short-run supply curve (the MC-curve) is horizontal. A flat MC-curve is not unreasonable as when firms increase output they in reality increase both K and L as some part of the stock of physical capital is often unused in a recession. In a recession firms close production plants, which makes both machines and workers unemployed. When firms expand production they open up closed plants and employ workers. So MC needs not increase a lot because diminishing MPL. Lecture: BUILDING THE KENESIAN MODEL: The simple Keynesian model for a closed economy without its own currency: Assumption: The short-run supply curve is horizontal (= P is fixed), which implies that aggregate demand alone determines output. The model also assumes that the real interest rate is fixed; and that planned investment is an exogenous variable. The money market plays no explicit role here. The model is thus relevant for small economies without monetary authorities that are not or far from full-employment. If economies are at full-employment government spending cannot increase aggregate production. For example: the model is relevant for small municipalities within Sweden or small countries within the Euro-area or small states within the US states. If they are big, expansionary fiscal policies might increase the real interest rate. The model how income is determined for given levels of the exogenous variables: government purchases (G), net taxes (T) and planned investment, I (planned). Actual expenditure () is the amount households, firms, and the government spends on newly produced goods and services (GDP). Planned expeditures is the amount households, firms and the government would like to spend on newly produced goods and services. The economy is in equilibrium when Actual expenditures () = Planned expeditures (E) NOTE: AGGREGATE DEMAND (AD) = PLANNED EXPENDITURES (E)
, E Actual Expenditure, = Planned Expenditure, E = C(-T)+ I(pl.) + G 2 1 Income, Output, Actual expenditures () = Planned expenditures (E) + involuntary inventory investment (positive or negative). Actual investment = I(planned) + involuntary inventory investment (which is zero, negative or positive). Planned Expenditure (E) = AD = C( T) I ( pl.) G C MPC ( t) I ( pl.) G Note that: I ( pl.) I ( planned ). We could add NX as an exogenous variable. If we rewrite the equation above: E AD I( pl.) G, where 0<MPC<1. C MPC 1 t Intercept How is the equilibrium achieved? Slope At 2 planned expenditures (E) > actual expenditures () involuntary depletion of inventories, I( pl.) > I (actual) firms increase production, At 1 planned expenditures (E) < actual expenditures () involuntary inventory build-up, I( pl.) < I (actual) firms decrease production,
The goods market Equilibrium implies: = E (=AD) E AD C I( pl.) G MPC (1 t) The effect on of increased government spending (G):, E Actual Expenditure, =E G A B Planned Expenditure, E = C(-T) + I(pl.) + G0 1 Income, Output, E AD I( pl.) G C MPC 1 t Intercept Slope An increase in government purchases of G raises planned expenditures (E) = Aggregate Demand (AD) by that amount for any given level of income (): the E-schedule shifts up. The equilibrium moves from A to B and income rises. Note that the increase in income exceeds the increase in government purchases G. Thus, fiscal policy has a multiplied effect on income. This is because a higher income increases private consumption, C((1-t)). =C + G. The multiplier process: If government spending (G) increase by 1 $, you might expect equilibrium output () to also rise by 1$. But it does not: Initially planned expenditures (E) increases by G, and income increases by the same amount. A higher income increases consumption (and thereby planned expenditures/ad) by MPC(1-t)G, which raises again. This second increase in income of MPC(1-t)G again raises consumption: by (MPC(1-t))(MPC(1-t)G), which raises income and so on.
The change in equilibrium is: G(1 MPC(1 t) MPC(1 t) MPC(1 t)...) Using the expression for the sum of an infinite series: 1 MPC G, 0<MPC<1. E.g., MPC=0.8 G 1 1 t 1 MPC 1 1 t 1 The multiplier effect operates fully if the factors of production are not fully utilized; that is, when the short-run aggregate supply curve is horizontal. Lecture: Solving for equilibrium mathematically and deriving multipliers: Goods market Equilibrium: = E=AD E AD C( t) I ( pl.) G NX E AD C MPC (1 t) I ( pl.) G NX This is one equation with one unknown variable (one endogenous variable):. 1 I( pl.) G NX MPC t C (1 1 ) C I( pl.) G NX MPC t C I( pl.) GNX 1MPC 1 t is equilibrium, the value of which implies equilibrium in the goods market. The solution implies that the unknown/endogenous variable,, is expressed as a function of the exogenous variables; the variables that are determined outside the model.
What happens to equilibrium when the exogenous variables change? C I ( pl.) GNX 1MPC 1 t The government spending multiplier If Ct I ( pl.) 0 G 1 1 t MPC G 1 MPC 1 1t 1 Summary: Factors that increase AD and thereby the equilibrium income (): Increased I ( pl.), C, G, MPC, and NX, and lower t. The saving function: Households use their disposable income to saving and consumption: T t S C S C MPC (1 t) Thus, the private-saving function (S) is S C (1 MPC) ( t) A LESSON IN THIS MODEL: If government spending increases by 1 dollar, aggregate demand and output may increase by more than 1 dollar. Of course if is at fullemployment there is complete crowding-out. Leftist parties talk often about multipliers, when they want a larger government sector. They rarely mention that increased G may crowd out I and NX, as well as create inflation.
THE KENESIAN MODEL IN THE SHORT RUN CONTINUED: INTRODUCING THE MONE AND BOND MARKET INTO THE MODEL THE IS-LM-MODEL If the closed economy has its own currency and a central bank, the model below is relevant. Now we have 2 markets: the goods market and the money (and bond) market, which interact: For example: A higher income () increases the real money demand which results in a higher interest rate (= real interest rate) when M/P is fixed, which lowers I(planned): Our equilibrium requires both these markets to be in equilibrium. As the bond market is in equilibrium when the money market is in equilibrium it is sufficient that we only explicitly study the money market. Assumptions: Short run: P is fixed. 2 markets: Equilibrium in the goods market: =E=C(-T)+I(r)+G.. Equilibrium in the money market: M/P = L(r,) Real interest rate (r)=nominal interest rate (i) inflation rate = nominal interest rate Note: since P is assumed to be constant, the inflation rate is 0, and the real interest rate equals the nominal interest rate. Equation system with the endogenous variables:, r, I(r), C(-T). Exogenous variables determined outside the model: M determined by the central bank.g, t are determined by the government. P is fixed in the short run. A simpler and more realistic model than IS-LM-model would be to assume that the Central Bank sets the nominal interest rate instead of chooses nominal money supply (M). That is, the central bank chooses the nominal interest rate and provides whatever money supply that is consistent with the chosen interest rate. Such a model is more realistic and another advantage is that we do not assume that the P is constant. Instead we assume that inflation is sticky. THE IS-MP (=Monetary Policy)-model In the short run: i t, r t because t sticky/constant AD i, r t because t sticky/constant AD t
THE IS-LM-model continued: Lecture: Analysis of expansionary fiscal policy: a higher G., E Actual Expenditure, =E G+ A B Planned Expenditure, E = C(-T) + I(r0) + G0 1 Income, Output, If G AD= (C(-T) + I(r)+G) at given level of When AD the real money demand, L(r,) r I. In the new short run equilibrium (B): r is higher, I is lower, G, C, and higher than before. increases by less than G 1 MPC (1 t) crowded out ) due to a higher interest rate. because private investment falls ( is
i M/P i i M/p PPP L(i,1 L(i,0 ))' ) M/p PPP Variable Old short-and long-run Equilibrium (A) New short-run Equilibrium (B) G G0 <G1 0 < 1 Interest rate R0 <R1 I I0 >I1 C C(0-T) <C(1-T) P P0 =P1 National saving S0=I0 >S1=I1
Lecture: Short run effects of expansionary monetary policy Assume that nominal money supply (M) is increased: Note that the picture shows the opposite, a lower nominal money supply. Recall that the price level (P) is assumed to be constant in the short run. r Supply' Supply M/P Demand, L (r,) M/P If M (M/P) nominal interest (=real interest rate when P is constant) I(r), AD= (C(-T) + I(r)+G) at a given level of P, which increases, which increases real money demand; which pushes up the interest somewhat., E Actual Expenditure, =E + A B Planned Expenditure, E = C(-T) + I(r0) + G 1 Income, Output,
Variable Old short-and long-run Equilibrium (A) New short-run Equilibrium (B) 0 < 1 Interest rate R0 >R1 I I0 <I1 C C(0-T) <C(1-T) P P0 =P1 M/P M0/P0 <M1/P0 A MORE FORMAL APPROACH TO THE KENESIAN MODEL IN THE SHORT RUN FOR A CLOSED ECONOM: THE IS-LM-MODEL. 2 markets: Equilibrium in the goods market: =C(-T)+I(r)+G Equilibrium in the money market: M/P=L(i,) Real interest rate(r) =nominal interest rate (i)-inflation rate=i Note: since P is assumed to be constant, the inflation rate is 0, and the real interest rate equals the nominal interest rate. Assume now: planned investment depends on the real interest rate: I(r). An increase in the interest rate (in graph a), lowers planned investment, which shifts planned expenditure downward (in graph b) and lowers income (in graph c). (a) r (b) E (c) r =E Planned Expenditure, E = C + I + G Income, Output, The IS curve shows the equilibriums in the goods market. I(r) Investment, I IS Income, Output,
If r I(r) so that AD (= planned expenditures) at the old equilibrium AD< at the old equilibrium Lecture: Mathematical Derivation of IS-curve: Equilibrium in the goods market: Before: E AD C MPC ( t) I ( pl.) G NX Now if I depends on r: E AD C MPC ( t) I d r G NX where d>0. I G NX I G NX C d r C d r 1MPC 1 t 1MPC 1 t 1MPC 1 t The equation above is the EQUATION FOR THE IS-CURVE: When r=0, then C I GNX 1 1 t MPC If C, or I, or G, or t or NX this intercept increases. When =0, then r C I G NX d
Real money demand: d ( M / P) L( r, ) The quantity of real money demanded is negatively related to the nominal interest rate (because it is the opportunity cost of holding money) and positively related to income (because of transactions demand). Along a LM-curve real money supply, M/ P, equals real money demand: M / P L( r, ) The LM-curve has a positive slope as an increase in increases Real money demand, which means that the interest rate has to increase to lower real money demand to the same extent so that it continues to be equal to the real money supply ( M/ P), which is fixed along a given LM-curve. Nominal money supply ( M ) is assumed to be exogenous as it is determined by the Central Bank. The price level is also assumed to be fixed. Thus, the supply of real money balances, M/ P, is assumed to be exogenously given; that is, determined outside the model. The cost of holding real money is actually the nominal interest rate and not the real interest rate. However, as the price level is fixed in the model, the real interest rate equals the nominal interest rate.
Note: i = r (=real interest rate) as P P =0 as P is assumed to be fixed. If M/ P, LM-curve shifts to the right. Mathematical derivation of the LM-curve: Assume: L( r, ) e f r, where e> 0 and f > 0. In equilibrium; that is, along the LM-curve: M / P L( r, ) e f r Solving for r: r 1 (M / P ) e f f Intercept Slope The equation above is the equation for the LM-curve. If / M P, the intercept becomes more negative. Thus, the LM-curve shifts to the right.
r IS LM(P 0 ) r 0 0 The intersection of of the the IS IS curve/equation, = C (-T) + I(r) + G and the the LM curve/equation M/P = L(r, ) ) determines the the level of of aggregate demand. The intersection of If C(-T) at a given level of, e.g. if T of the the IS IS and LM curves, or if I(r) at a given r, if G represents simultaneous equilibrium in in the the market for for goods and services and in in the the market for for real money balances for for given values of of AD government at a given level of : the IS-curve shifts to the right. spending, taxes, the the money supply, and the the price level. A change in the exogenous variables and parameters: government (G), Money supply (M), the price level (P), the tax rate (t), the autonomous level of investment ( I ), C and MPC changes the short run equilibrium.
+G Consider an increase in government purchases. This will raise the level of income by G/(1- MPC) r IS IS LM A B The IS curve shifts to the right by G/(1- MPC) which raises income and the interest rate. increases by less than G 1 MPC because private investment falls ( is crowded out ) due to a higher interest rate. Here we assume fixed T; that is, a T that does not depend on. The economic mechanism: If G aggregate demand at given level of real money demand r investment Comparing equilibrium A with equilibrium B: 0 < 1 C(0-T) < C(1-T) R0 < r1 I(r0) > I(r1) National saving0 > national saving1 Note that national saving=-c-g=i
+M Consider an increase in the money supply. r IS LM LM A The LM curve shifts downward and lowers the interest rate which raises income. Why? Because when the Fed increases the supply of money, people have more money than they want to hold at the prevailing interest rate. As a result, they start depositing this extra money in banks or use it to buy bonds. The interest rate r then falls until people are willing to hold all the extra money that the Fed has created; this brings the money market to a new equilibrium. The lower interest rate, in turn has ramifications for the goods market. A lower interest rate stimulates planned investment, which increases planned expenditure, production, and income. B M P r so that real money demand and becomes equal to M/ P I(r), If / aggregate demand at a given level of.. Comparing equilibrium A with equilibrium B: 0 < 1; C(0-T) < C(1-T) R0 > r1; I(r0) < I(r1) National saving0 < national saving1 DO EXERCISE 11.3
THE KENESIAN MODEL IN THE SHORT RUN: FROM IS-LM-curve to the AD-curve in the P-diagram. We use the P-diagram to analyze long-run effects: ou probably noticed from the IS and LM diagrams that r and were on the two axes. Now we re going to bring a third variable, the price level (P) into the analysis. We can accomplish this by linking both twodimensional graphs. r P P 2 P 1 IS B B LM(P 2 ) A A LM(P 1 ) AD To derive AD, start at point A in the top graph. Now increase the price level from P 1 to P 2. An increase in P lowers the value of real money balances, and, shifting LM leftward to point B. Notice that r increased. Since r increased, we know that investment will decrease as it just got more costly to take on various investment projects. This sets off a multiplier process since -I causes a. The - triggers -C as we move up the IS curve. The +P triggers a sequence of events that end with a -, the inverse relationship that defines the downward slope of AD.
Lecture: The Short run equilibrium in the IS-LM-model in one equation: Equilibrium in the goods market; that is, along the IS-curve: I G NX I G NX C d r C d r 1MPC 1 t 1MPC 1 t 1MPC 1 t In equilibrium; that is, along the LM-curve: M / P L( r, ) e f r Solving for r: r 1 (M / P ) e f f Intercept Slope Now substitute the LM-curve into the IS-curve to solve for equilibrium as a function of the exogenous variables and parameters: 1 d e C I G NX d M / P (1 MPC (1 t )) f 1 MPC (1 t) (1 MPC (1 t)) f I G NX d ( M / P) (1 MPC (1 t)) f f (1 MPC) d e C f (1 MPC 1 t) 1 MPC (1 t) f ( CI G NX ) d M / P f (1 MPC (1 t)) d e f (1 MPC 1 t) d e This is the AD-curve in the P-diagram. If C, or MPC, or t, or I, or G, or NX or M equilibrium increases. The AD-curve in the P diagram shifts out. If P equilibrium : Movement along the AD-curve in the P-diagram.
Solving for equilibrium r by inserting the expression for equilibrium into the equation for the equation that shows equilibrium in the money market: r 1 / e ( ) M P f CI GNX d M / P f f f (1 MPC (1 t)) d e f (1 MPC) d e which can be simplified: THE LONG RUN EQUILIBRIUM IN THE LONG RUN PRICES AND WAGES ARE FLEXIBLE The Keynesian model in the long run = classical model see ch. 3 When is larger (lower) than the full-employment, the nominal wages increase (decrease) which shifts the MC-curve/SRAS-curve upwards (downwards), which increases (decreases) the price level. A higher (lower) price lowers (increases) M/P which increases (decreases) the real interest rate, and thereby lowers (increases) private investment.
Short and long run effects of less thriftiness: of C : r IS IS' C LM(P2) LM(P0) Short Run: Long Run: P P 2 P 0 LRAS C SRAS + P 0 r + C + I - 0 + ++ + --
Short and long run effects of expansionary monetary policy If M : (M/P) nominal interest (=real interest rate when P is constant) I(r), AD= (C(-T) + I(r)+G) at a given level of P, which increases, which increases In the short run: movement from A to B., C(-T), and I(r)=S increase, and r decreases in the short run. For the variables, P and r, you can read the effects right off the diagrams. 0, because rising P shifts LM to left, returning to as required by LRAS. r P +, in order to eliminate the excess demand at P 0. r 0, reflecting the leftward shift in LM due to +P, restoring r to its original level. C 0, since both and T are back to their initial levels (C=C(-T)). I 0, since or r has not changed. P Variable Remember that LR is the movement from A to C. Notice that the only LR impact of an increase in the money supply was an increase in the price level. Old short-and longrun Equilibrium (A) New short-run Equilibrium (B) 0 < 1 2=0 Interest rate R0 >R1 r2=r0 I I0 <I1 I2=I0 C C(0-T) <C(1-T) C(0-T) P P0 =P1 <P2 M/P M0/P0 <M1/P0 M0/P0 A = C New long-run equilibrium (C) In the long run P increases until M/P becomes identical to M0/P0. Thus, An increased nominal money supply has no effect on real variables in the long run P 2 P 0 IS A C B LRAS B LM (P0) LM SRAS AD AD
Lecture: Analysis of expansionary fiscal policy: a higher G. The short and long-run effects on increased government spending (G) P P 0 LRAS A C B = F (K,L) SRAS AD=C(-T)+I(r)+G1 AD=C(-T)+I(r)+G0 Variable Old short-and longrun Equilibrium (A) New short-run Equilibrium (B) G G0 <G1 = G1 0 < 1 2=0 Interest rate R0 <R1 <r2 I I0 >I1 >I2 C C(0-T) <C(1-T) C(0-T) P P0 =P1 <P2 National saving S0=I0 >S1=I1 >S2=I2 New long-run equilibrium (C) In the long run there is no effect on. The increase in G is completely offset by a decrease in I. See chapter 3.
Read by yourselves: The short and long-run effects of lower net taxes (t): If t AD= (C((1-t)) + I(r)+G) at given level of When AD the real money demand, L(r,) r I. In the new short run equilibrium (B): r is higher, I is lower, C, and are higher than before. P P 0 LRAS A C B = F (K,L) SRAS AD=C(-T1)+I(r)+G AD=C(-T0)+I(r)+G Variable Old short-and longrun Equilibrium (A) New short-run Equilibrium (B) New long-run equilibrium (C) t t0 >t1 = t1 0 < 1 2=0 Interest rate R0 <R1 <r2 I I0 >I1 >I2 C C(0(1-t0)) <C(1(1-t1)) >C(0(1-t1)) P P0 =P1 <P2 National saving S0=I0 >S1=I1 >S2=I2 In the long run there is no effect on. The increase in C is completely offset by a decrease in I. See ch. 3
Lecture: THE SMALL OPEN ECONOM (r= r ) with its own currency: THE MUNDELL-FLEMMING MODEL, CH. 12. Short-run effect: 2 equations: Equilibrium in the goods market: = C(-T) + I(r) + G + NX (e) Equilibrium in the money market: M/P = L(r,) Assumption 1: r = r. The small economy assumption. Assumption 2: P($) and changes in e change P ( en ) are assumed to be constant, which means that only e( en /$) P($) en P ( en) en Thus, e, e e=yen/dollar: e () appreciation (depreciation) of dollar Domestic goods become more expensive (cheaper) in foreign currency (en) and foreign goods become cheaper (more expensive) in domestic currency (dollar). Exports, Imports NX The money market equilibrium condition: M / P L( r, ), determines the equilibrium level of output (). M, P and r are exogenously given in the model. The only endogenous variable in the LM-equation is, which then is determined by the exogenous variables M/ P, and r : / (, ) If: M P L r eq M / P L( r, ) e fr M / ep( f / e) r Since M and P determine, fiscal policy (changes in G and T) has no effect on. M P L( r, ) 100 r, where Ex.: The money market equilibrium condition: If M=1000 and P=1, and / L( r, ) r =0.04 1000=-1000.04 = 1000 + 4 = 1004 If M=1100 = 1100 + 4 = 1104 Given P and r, M determines. The economics of a monetary expansion in the standard model above: If M/ Pr : r < r not profitable with financial investments in our country: the demand for our currency the currency depreciates: e NX
Monetary policy has a larger impact on in small open economy compared to the effect in a closed economy because there is no crowding-out of private investment in the open economy model. Fiscal Policy(G,T): Changes in G and T do not impact equilibrium (because eqb. is determined by the equation: C T I r G NX eq ( ) ( eq ) ( ) s M P L r / (, ) eq : Aggregate Demand If e.g. G aggregate demand at a given level of. But AD must be unchanged as eq is fixed. As C( eq T) and Ir ( ) also are fixed, e must increase so that NX by the same amount that G. That is, AD G NX 0 Why does a fiscal expansion increase e? If G aggregate demand at a given exchange rate. When aggregate demand real money demand domestic interest rate, r : r > r profitable with financial investments in our country the demand for our currency the currency appreciates NX Thus: Increased G or increased C(-T) due to lower net taxes crowds out net exports completely even in the short run. (In a richer model, fiscal policy impacts in the short run: A currency appreciation (e) tends to make the price on imported goods and services cheaper in the domestic currency P because prices on imported goods are included in the consumer price index M/ P: Fiscal policy has an effect on.)
Read by yourselves: The short and long run effect of monetary policy If M (M/P) r so that r<r financial investments in domestic country turns less profitable demand for the domestic currency the nominal exchange rate, e, depreciates (e) ( e P) / P NX, AD = (C(-T)+I(r) + G + NX(( ( e P) / P )) Variable Old short-and longrun Equilibrium (A) New short-run Equilibrium (B) New long-run equilibrium (C) 0 < 1 >2=0 Interest rate R0 =R1 =r2=r0 I I0 =I1 =I2=i0 E E0 >e1 <e2=e0 C C(0-T) <C(1-T) >C(0-T) NX NX0 <nx1 >Nx2=nx0 P P0 =P1 <P2 M/P M0/P0 <M1/P0 >M1/P2=M0/P0 Notes: Fixed exchange rates are not included in the course The large open economy is an average of the closed economy and the small open economy. To find how any policy will impact any variable, find the answer in the 2 extreme cases and take an average.