The IS-LM Model. Underlying model due to John Maynard Keynes Model representation due to John Hicks Used to make predictions about

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1 The S-LM Model Underlying model due to John Mynrd Keynes Model representtion due to John Hicks Used to mke predictions bout nterest rtes Aggregte spending ( ggregte output) mportnt ssumption: price is fixed The Fixed Price model Essentilly dels with short run determintion of output nd interest rte The Sequence Output determintion in the goods mrket Goods mrket equilibrium condition: S Money mrket equilibrium condition: LM Objective: nlyzing effects of policies on interest rte nd ggregte income Fiscl policy: control of government spending nd txes Monetry policy: control of interest rte nd money supply 2

2 Keynes: The Context How government policy could be used to increse employment in sitution similr to the GD Emphsis of the demnd side Not restricted to nlyzing GD-type ctstrophes Mcroeconomic model to understnd movements in ggregte output in short-run Mcroeconomic stbiliztion policies 3 Aggregte Demnd Totl quntity demnded of n economy s output is the sum of four types of spending: C G NX Equilibrium occurs when: producers cn sell their outputs nd hve no reson to chnge their production Emphsis on Effective demnd if is not enough ( > ) the economy is producing more thn there is demnd for output below the full employment level To understnd output fluctutions, need to understnd the components of ggregte demnd 4

3 Consumption Function (C) Disposble income: D T ggregte income ggregte output T txes The consumption function: utonomous consumption expenditure consumption spending when C mrginl prepensity to consume Why is utonomous consumption positive? Exmples: students, welth, unemployment benefits. Ex: 0.8 if D increses by $, then 80 cents out of tht will be spent, nd 20 cents sved Keynes ssumed: is constnt C ( D ) D is equl to D 0 5 6

4 Plnned nvestment Spending () Economist s view of nvestment Adding something NEW (ex: new mchine) Buying of ssets such s stocks re NOT investment Fixed nvestment Spending by firms on equipments (ex: mchines) nd structures (ex: office buildings) Spending on residentil housing nventory nvestment Spending by firms on ditionl holdings of intermedite nd finished goods (holdings t the beginning of period holding t the end of the period) 7 Plnned versus Unplnned Fixed investment lwys plnned nventory investment cn be Plnned ( P ): prt of, hence prt of Unplnned ( U ): not prt of, hence not prt of Only Plnned items constitute, the component of, ( fixed investment) (plnned inventory investment) Plnned investment spending depends on nterest rtes Business s expecttions bout the future 8

5 C G NX Simple model : let, G 0, NX 0 C f T0, D C. 9 Simple model : G 0, NX 0 0

6 Output Response to Chnges in components Simple model: C, [ Q G 0, NX 0] How chnge in C nd (nd lter on, other components) chnge ggregte output? Wht kind of chnges to be expected? Chnges in investment Chnges in utonomous consumption Why not chnges in consumption other thn utonomous consumption? NOTE: lter on we ll lso discuss chnges in other components of. For simple model only C nd. A rise in or shifts the upwrds Mgnitude of output response: multiplier Output Response: Chnge in > 2

7 Expenditure Multiplier Components of ggregte demnd: C C n equilibrium: output, does not depend on but, C f () initil effect is, When Chin of events follow fter the initil effect As there is n increse in, we hve C incresed As C increses, lso increses, gin, nd so on The finl effect on ( ) higher thn the initil 3 Expenditure Multiplier: Exmple Suppose, 0.5, for everyone Consider n exogenous $000 in Sr s income (sy, due to some investment spending by some firm) nitil increse in income is $000 Chin of events spending $000 Finl increse in income $2000 Chin of Events Sr buys from Hsn Hsn buys from Gerldo Gerldo buys from Tyrone Tyrone buys from ng ng buys from Polo Polo buys from Nigel Nigel buys from Rvi Rvi buys from Avi Avi buys from Ahtunowhiho Ahtunowhiho buys from Tkeshi Totl Spending (dollrs)

8 5 Expenditure Multiplier: Derivtion C C ) ( hve, we ) ( ) ( LHS ) ( ) ( so, ) ( but, 6 Expenditure Multiplier: Derivtion , 2 0.5, 0.5, : Exmple, nd 0 ) ( old new ) ( new plce) took before (i.e.,, old > > > < < >

9 Expenditure Multiplier ncome is, After Note n ( ) tht, ( ) increse in { { 4243 output increse multiplier investment expenditure increse spending, Wht if there is n increse in inste. Sy,? 7 Expenditure Multiplier ( ) Could the sme tke plce if, inste of, we hve of the sme mgnitude? Aggregte demnd: { ( ) Any chnge in the utonomous component will hve the sme kind of effect where, { { A output incresein 4243 increse multiplier utonomous spedning utonomous 8

10 Full Model 4 4 2G 4 4NX 3 ( ) utonomous A Alterntive expression, Multiplier effect, Multiplier, ( G NX ) A A > ( ) G NX C 9 Expenditure Multiplier Output Contrction A When utonomous spending increses by A, output increse by times A Wht hppens when utonomous spending DECREASES by A? Output DECREASES by times A. A lrger thn A decline in output. 20

11 Keynes s Explntion for GD 2 Keynes s Prescription to GD Decline in utonomous spending Cnnot rely on utonomous C or to increse ncrese G, under government s control Fiscl Policy 22

12 Government: The Full Tretment Consumptio n function : No txes With txes, C D D T C Consumptio n function with txes, ( ) ( ( T )) ( T ) ( ) ( T ) G ( ) utonomous A [ ( T ) G] D Txes C A $ in txes C by the mount of ( T ) [Ex: if 0.5, then $ in txes C by 50 cents] T is n utonomous (like G ) but effect dmpened by 23 Government Spending vs Txes G shifts up T shifts down G more effective thn T G T > 0 24

13 Explining the Digrm C C G NX ( ( T )) ( T ) ( ) Consider the stright line on (, ) plne, [ ( T ) G ] { ntercept on (, ) plne slope Exmple: 0.5, G400, T400 G intercept of increses by 400 shifts up by 400 T intercept of decreses by (0.5*400)200 shifts down by 200 There is net increse in, in the equilibrium 25 The nterest Rte So fr, we hve tlked bout income determintion, nd wht hs been missing is, interest rte (i) The connection between i nd is investment () We need to figure out: i ( ) First we ll discuss investment schedule: Then we ll use the Keynesin cross digrm Combining these two will give us: i i ( ) 26

14 The nvestment Schedule Negtive reltionship between i nd plnned investment () 27 The nvestment Schedule For firms with no surplus funds, interest rte (i) is the cost of borrowing For firms with surplus funds, they cn put their funds in two things Plnned investment spending (which will yield return) Buy bonds (which will lso yield return) f (i) is high they re more likely to buy bonds Thus, in either cse we hve tht, ( i ). () n words: i nd re negtively relted. 28

15 The Keynesin Cross Digrm Chnges in Due to Chnges in 29 30

16 The S Curve & the LM curve The S curve gives us the combintion of ( i, *) The S curve tells us wht the ssocited level of i for ech *. n other words: for ech goods mrket equilibrium wht is the level of interest rte ssocited with tht? So, wht we hve is ( i, *) Once we hve ( i *, ), Combining these two we cn hve ( i *, *). The LM curve will give us ( i *, ). This comes from the money mrket equilibrium. 3 Money Mrket: Liquidity Preference Model Keynesin money demnd function, M f ( i, ) P ( ) ( ) nterest rte (i) is the opportunity cost of holding money As income () increses, money demnd increses Supply of money is fixed exogenously given quntity 32

17 Derivtion of the LM Curve 33 The S Curve & the LM curve The LM curve gives us the combintion of ( i*, ) The LM curve tells us wht the ssocited level of for ech i*. n other words: for ech money mrket equilibrium wht is the level of ggregte output ssocited with tht? Now tht we hve the S curve with ( i, *), nd the LM curve with ( i *, ), crossing them will give us the economy-wide ( i *, *). 34

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