1. How is the IS curve derived and what factors determine its slope? What happens to the slope of the IS curve if consumption is interest elastic?


 Ashlie Dennis
 1 years ago
 Views:
Transcription
1 Chapte 7 Review Questions 1. How is the IS cuve deived and what factos detemine its slope? What happens to the slope of the IS cuve if consumption is inteest elastic? The IS cuve epesents equilibium in the goods maket (eal pat of the economy). Consumption is a linea function of disposable income. C = a + c ( T ) Investment is negatively elated to the inteest ate and detemined by a set of autonomous factos Θ. I ( ) = I,Θ Govenment spending and lump sum taxes ae exogenously detemined by the fiscal authoity (govenment). G = G T = T Equilibium in the goods maket is whee supply = demand, o output = expenditue. ( T ) + I( Θ) G = a + c, + a ct + I = 1 c (, Θ) + G Altenatively output equals the poduct of the multiplie ( k = 1 c) autonomous expenditues ( AE = a ct + I(, Θ) + G). 1 and the sum of = kae The IS cuve plots the elationship between equilibium output and inteest ates. An incease in inteest ates educes investment and autonomous expenditue, which leads to a multiplied eduction in output. ( Θ) Δ ΔAE ΔI = k = k, Δ Δ Δ
2 ( ) ΔI, Θ If Δ = φ then Δ Δ = φk The IS cuve plots an invese elationship between inteest ates and output. The gadient of the IS cuve is detemined by the multiplie and the inteest sensitivity of investment. 1 IS 1 Suppose consumption is inteest elastic due to the substitution and income effects of inteest ate changes (i.e. most people ae net boowes so an incease in inteest ates has both a negative income and substitution effect on cuent consumption.) C = a + c ( T ) γ Autonomous consumption, and hence autonomous expenditues, is now also detemined by inteest ates. Δ Δ ΔAE = k Δ = k ( φ + γ ) The slope of the IS cuve is now flatte because autonomous expenditues ae moe sensitive to inteest ate changes. This means a given change in inteest ates has a lage impact on equilibium output.
3 . How is the LM cuve deived and what factos detemine its slope? What happens to the LM cuve is thee is an incease in the cost of liquidating financial assets? The LM cuve epesents equilibium in the money maket, o whee demand and supply of money ae equal. The money supply is set by the monetay authoity. M s = M The demand fo money is a positive function of income (tansactions) and a negative function of inteest ates (cost of liquidity pefeence). M d = a b The LM cuve plots the combination of income and inteest ates whee: s M = M d M = a b = 1 b ( a M ) The slope of the LM cuve is Δ = Δ a b LM 1 1 The slope is detemined by two factos.
4 Paamete a is the income sensitivity of the demand fo money. As this inceases a given change in income leads to a lage incease in the demand fo money. The inteest ate will then have to ise by a lage amount in ode to estoe equilibium to the money maket. The LM cuve becomes steepe. Paamete b signifies the inteest sensitivity of money demand. This detemines the size of the inteest ate esponse equied to estoe money maket equilibium as income ises. As this paamete inceases the LM cuve becomes flatte, because fo any change in income the equied inteest ate change is smalle. 1 The fom of LM cuve we have used has abstacted fom the cost of liquidating assets. (This is explained in chapte 5). An incease in the cost of liquidating inceases aveage money holdings at each level of income. Theefoe, at each money supply equilibium inteest ates ae highe so the LM cuve shifts upwads. M LM ( c ) 4 LM ( c 1 ) 1 L ( 1, c, ) ( c ) L, 1, 1 L (, c, ) ( c ) L,, 1 1. Using the ISLM model, explain how the equilibium ate of inteest and level of output will espond to the following: a. Expectations of a futue incease in unemployment If consumption is fowadlooking, then an expected incease in futue unemployment will lead to a fall in cuent consumption and a leftwad shift in the IS cuve. At the cuent level of inteest ates thee is now a position of excess supply in the money maket, which leads to an incease in bond pices and a fall in inteest ates. The economy settles at a lowe inteest ate and level of income.
5 LM 1 IS 1 b. Financial deegulation leading to the abolition of eseveasset atios A eduction in the eseve action asset atio inceases the money multiplie and leads to an incease in money supply at each level of high poweed money stock. The LM cuve will then shift downwads as the equilibium level of inteest ates is lowe at each level of output. The eduction in inteest ates leads to an incease in investment and a multiplied incease in income. Oveall inteest ates ae lowe and equilibium output is highe. LM 1 LM 1 1 c. A fall in copoate pofits This would be expected to lead to a fall in investment. This could be because of lowe intenal funds available to spend on investment pojects o lowe business optimism.
6 As a esult the IS cuve will shift inwads and equilibium output and inteest ates will fall. This can be epesented with the same diagam in pat a. d. A house pice boom An incease in house pices leads to an incease in asset wealth, and if it can be liquidated though motgage equity withdawal consumption will ise. The IS cuve will then shift outwads. At the existing level of inteest ates thee is now excess demand in the money maket. As a esult bonds ae sold, and falling bond pices push up inteest ates and cowds out some of the initial incease in output. Oveall, output and inteest ates ae highe. LM 1 IS 1 e. A pogam of investment in new ATMs This will lowe the cost of liquidating bank deposits, so would be expected to educe the demand fo money. Consequently, the LM cuve will shift downwads and put downwad pessue on inteest ates. This is because lowe money demand will lead to an incease in bond puchases and a ise in bond pices. As a esult of the lowe inteest ates investment will be stimulated and output will incease. The new equilibium position in the economy sees lowe inteest ates and highe output. The same diagam used in pat b applies. Suppose the cost of liquidating financial assets wee to incease. Theefoe aveage money holdings would ise and the money maket equilibium will yield highe inteest ates at each level of output. The LM cuve would shift upwads, the ise in inteest ates will lead to a contaction in investment. The new equilibium would esult in highe inteest ates and lowe output.
7 LM LM 1 1 IS 1 4. How is the effectiveness of monetay and fiscal policy affected by? a. The slopes of the IS and LM cuves The effectiveness of fiscal policy and the slope of the LM cuve A fiscal expansion consists of eithe a eduction in taxes o a ise in govenment spending. As a esult the IS cuve shifts hoizontally to the ight. As output inceases the money maket moves into a position of excess demand which foces the inteest ate up. The issue is how much the inteest ate must ise in ode to estoe equilibium as this detemines how much investment is cowded out and the oveall effect of policy on equilibium output. LM 1 1 LM IS IS 1 1
8 When the demand fo money is inteest inelastic, the inteest ate must ise consideably to emove excess money demand. As a esult the LM cuve is steep and the cowding out effect is stong. If though the demand fo money is elatively inteest elastic only a small ise in inteest ates ae equied to estoe equilibium in the money maket. Consequently the LM cuve is flatte and the cowding out effect is weake. In this case fiscal policy has a lage impact on equilibium output. The effectiveness of fiscal policy and the slope of the IS cuve An expansive fiscal policy leads to a ightwad shift in the IS cuve and an incease in equilibium inteest ates. The ise in inteest ates leads to some cowding out of investment which limits the impact of fiscal policy on equilibium output. If investment was elatively inteest inelastic the IS cuve would be steep. Theefoe, the ise in inteest ates would have small cowding out effects. If though investment was inteest elastic the IS cuve would be flatte. Theefoe cowding out is stonge and fiscal policy is less effective. IS1 IS LM LM 1 1 IS 1 1 The effectiveness of monetay policy and the slope of the IS cuve An expansion in the money supply leads to the pivate secto holding lage money balances than demanded at the pevailing inteest ate, the money maket is in a position of excess supply. Excess money holdings ae used to puchase bonds which foces bond pices upwads and inteest ates downwads. Because equilibium inteest ates ae now lowe at evey level of output the LM cuve shifts downwads. The impact of lowe inteest ates on investment depends on the inteest elasticity of investment. When investment is inteest elastic the IS cuve is elatively flat and
9 output expands stongly. When investment is inteest inelastic the IS cuve is steepe and the eduction in inteest ates is less influential on equilibium output. LM 1 LM 1 LM LM 1 1 IS IS 1 1 The effectiveness of monetay policy and the slope of the LM cuve LM 1 LM 1 1 LM 1 LM 1 1 Following an expansion in the money supply how is the excess supply in the money maket coected? When the demand fo money is inteest inelastic the LM cuve is steep. Hee, inteest ates must fall consideably to encouage the pivate secto to hold the exta money balances. A lage fall in inteest ates means that the LM cuve shifts downwads to a geate extent encouaging a lage incease in investment and equilibium output.
10 The low inteest esponsiveness of money demand gives a clue as to why monetay policy is effective in this situation. The emoval of excess supply equies an incease in money demand which comes mainly fom the tansactions pespective though a lage ise in income. If the demand fo money was pefectly inelastic, the LM cuve would be vetical. The only way the money maket equilibium can be estoed is fo output to ise sufficiently so that the demand fo money inceases to estoe balance. When the demand fo money is moe inteest elastic monetay policy is less effective in influencing equilibium output. Only a elatively small eduction in inteest ates is equied to eequilibate the money maket following an expansion in supply. Theefoe the LM cuve is flatte and only shifts downwads by a small magnitude. When the demand fo money is pefectly elastic the economy is often in a position known as the liquidity tap. Hee the inteest ate has fallen to such a low level that the pivate secto finds the compensation fom holding bonds is not sufficiently attactive to fogo the benefits of liquidity (holding money). An expansion in the money supply will have no impact on the inteest ate and the LM cuve, which is in this case is hoizontal, will fail to shift downwads. Monetay policy in this case would be completely ineffectual. b. A positive elationship between pices and the deviation of output fom its full employment level LM 1 LM LM LM IS IS (a) ˆ 1 (b) ˆ 1 The Neoclassical ISLM model assumes that thee is a full employment level of output ˆ such that pices espond in the same diection as the deviation of actual output to this level, P& = π ( ˆ ). Because pices ae no longe fixed then this has a long un implication fo monetay and fiscal policies. In panel (a) the case of a monetay policy expansion is shown. The LM cuve shifts downwads and equilibium inteest ates fall and output expands. Howeve, because
11 output is above its full employment level pices begin to ise. This has the consequence of educing the eal value of the money stock which pushed the economy back towads its oiginal equilibium. Theefoe, in the long un monetay policy is neutal. The money stock is highe, but as the pice level has isen the eal money supply and eal vaiables in the economy ae left unchanged. Panel (b) consides the case of a fiscal expansion. The IS cuve shifts ightwads and equilibium output ises above the full employment level. The subsequent incease in pices will lowe the stock of eal money shifting the LM cuve upwads and moving the economy back to equilibium. In tems of levels, pice adjustment means that fiscal policy is neutal in the long un, but not in tems of composition. Eithe govenment spending (if an incease in govenment spending) o consumption (if a cut in taxes) will be highe, but highe equilibium inteest ates will cowd out an equal amount of investment. The effectiveness of both policies depends on how quickly pices adjust, and whethe o not the policy has an impact on the full employment level of output. If pices adjust slowly, pehaps due to impefect competition factos in labou and poduct makets, output in the shot un can deviate fom its full employment level fo a consideable peiod of time. Hysteesis type effects might also lead to an outwad shift in the full employment level of output (inceased poductivity fom using peviously unemployed factos of poduction, highe paticipation due to geate job oppotunities) may make the effects of policy moe pemanent in the medium to long un. Moe advanced poblems 5. Conside the following: C = d d = T T = 100 I = G = 100 (M/P) d = M = 1000 P = 1 Whee C is consumption, d is disposable income, is income, T is the level of lump sum taxes, I is investment, is the inteest ate, G is govenment spending, (M/P) d is eal money demand, M is the money supply and P is the pice level.
12 a. Calculate the IS and LM cuves and find the equilibium level of inteest ates and income. What is the level of investment in equilibium? The IS cuve: = C + I + G ( 100) = * + ( 1 0.4) = = The LM cuve: 1000 = = + Equilibium is whee IS = LM = 5000 = = 1 1 = 0. I ( 0.) 180 = * = ( 0.) = * = 1066 (fom the IS cuve) o 1 ( 0.) = 1 + * = 1066 (fom the LM cuve) b. Concened that the cuent level of investment is too low the govenment announces an expansionay fiscal policy and inceases govenment spending by 00. Find the new equilibium values of output, inteest ates. By how much has investment been cowded out? Govenment spending inceases to 00 giving the new IS cuve:
13 = Equilibium is whee IS = LM = = Equilibium inteest ates ae = = 0.5 Investment in equilibium is: I ( 0.5) 146 = * = Equilibium output: ( 0.5) = * = (fom the IS cuve) o ( 0.5) = + * = (fom the LM cuve) Following the fiscal expansion thee is an incease in output and inteest ates, but investment is cowded out. c. The level of income in b is the full employment level. What might be expected to happen if the govenment doesn t incease govenment spending by 00 as in b? If output is below the full employment, < ˆ then pices would be expected to fall P, but by how much? The full employment level is taken fom pat b. ˆ = What is equilibium inteest ate at ˆ = ? Fom the IS cuve,
14 1 = = ( ) 1666 = ˆ = Fom the LM schedule, the eal money supply equied to delive inteest ates of 15.% is: M P ( ) *( 0.15) 000 = * = Theefoe, the pice level needs to fall to: 1000 = 000 P = P 1 As a esult of lowe inteest ates investment expands : I ( 0.15) 46 = * = 6. Suppose the govenment changes the tax system away fom lump sum taxes to a popotional income tax. Tax evenue is now equal to t whee t is the maginal tax ate. a. Wite down the new consumption function and deive the IS cuve Consumption is still a linea function of disposable income d = ( 1 t) C = a + c( 1 t) Substituting into the IS cuve using a simila fom fo investment and govenment spending ( 1 t) + I( Θ) G = a + c, +
15 ( 1 c( 1 t) ) = a + + I(, Θ) G + a + I = 1 (, Θ) + c( 1 t) G b. Use the ISLM diagam to show how changes in maginal tax ate affect the equilibium level of output? Changes in the tax ate lead to pivots in the IS cuve. Fo a given level of autonomous expenditue, the multiplie effect on output would be geate when the tax ate is lowe. This leads to pivots because if inteest ates ae high autonomous expenditues (investment) ae lowe, so the effect of the tax ate cut on output is smalle. Likewise, as inteest ate falls the ise in autonomous expenditues has a geate effect the highe the multiplie (lowe the tax ate). 0 LM 1 IS 1 ( 1, Θ) + c( 1 t ) a + I G 1 =, 1 1 ( 1, Θ) + c( 1 t ) a + I G =, t 1 > t 1 At the inteest ate 1, a cut in taxes would lead to a pivot in the IS cuve and output inceases to. Howeve, the money maket is now in a position of excess demand, hence inteest ates ise, investment is cowded out and the economy moves to a new level of equilibium output at.
16 7. The economy is chaacteised by the following set of elations: C = d d = t t = 1/6 I = G = 100 M d = 9000 M = 00 Whee C is consumption, d is disposable income, is income, t is the tax ate, I is investment, is the inteest ate, G is govenment spending, M d is money demand and M is money supply. a. Deive the IS and LM schedules The IS cuve, = C + I + G: ( 1 ) = * 6 ( 1 ) = = The LM cuve, M = M d : = = b. Calculate the equilibium level of income () and inteest ate () in the economy. Equilibium income and inteest ates ae whee the IS and LM cuves intesect epesenting a geneal equilibium of the goods and money makets = = 7500
17 The equilibium inteest ate is = = 0.1 o 10% The equilibium level of output is ( 0.1) 600 = * = fom the IS cuve ( 0.1) 600 = * = fom the LM cuve c. At the equilibium in (i) the economy is below its full employment level of output * = 750. By how much does the govenment have to incease its expenditue in ode to each this level of income? What is the budget deficit/suplus at this point? What is the new equilibium ate of inteest and how much is investment cowded out? If ˆ = 750 then what is the equilibium inteest ate? Fom the LM cuve: ( 750) = * = 9000 = = 0.1 Given this inteest ate, what level of G will geneate ˆ = 750? Fom the IS cuve 1 ( 750 ( 750) ) * ( 0. ) + G 750 = * 6 1 G = Hence the equied incease in govenment spending is ΔG = = 8. The budget deficit is the diffeence between govenment spending and tax evenues, G  T then T = 1 *( 750) = 15 If = Govenment deficit ( G T ) = = 58. At the new equilibium inteest ate I = *(0.1) = 1
18 Thee is actually disinvestment, implying at these inteest ates the existing capital stock is above its optimal level. d. Suppose the govenment decides against a fiscal expansion and decides to implement a monetay expansion. What incease in the money supply would be equied to each the taget * = 750. What is the govenment deficit/suplus at that point? A monetay expansion to achieve = 750 Given the oiginal IS cuve, what inteest ate is equied to meet the taget? 750 = = = 0.05 What money supply will achieve this inteest ate? Fom the LM cuve: M ( 750) 9000 * ( 0.05) 1050 = * = Hence the equied incease in the money supply is ΔM = = 750 The govenment deficit: G = 100 and T = 1 ( 750) = 15 ( G T ) = = 5 6 A suplus! Although govenment spending hasn t changed tax evenues have isen due to the highe level of equilibium output. Incidentally, lowe inteest ates mean that investment is highe at I = =. ( ) 50 e. The govenment s fiscal ules imply that it must un a balanced budget. What combination of fiscal policy (inceasing G) and monetay policy (inceasing M) would enable it to each the full employment level of output whilst maintaining the balanced budget? What combination of monetay and fiscal policy will achieve the full employment level of output and maintain a balanced fiscal budget? At = 750 T = then ( 750) 15 1 = 6
19 Hence, balanced budget equies G = 15 implying ΔG = = 5 Substituting this into the IS cuve: ( ( 750) ) = * = 75 = = This is the inteest ate that is simultaneously consistent with G = T and = 750. Fom the LM cuve: M ( 750) 9000 * ( 0.075) 85 = * = Hence, the change in the money supply equied to achieve the inteest ate that satisfied full employment and a balanced budget is ΔM = = What policies could the govenment use to keep income at its pevious level following: a. an incease in cedit cad faud Cedit cads ae a way of dawing on cuent accounts. As a esult of inceasing faud the demand fo money (liquidity pefeence) ises at each income level. The LM cuve shifts upwads as the domestic inteest ates ae highe at each level of output. Theefoe the economy moves fom equilibium a to equilibium b, and output falls fom 1 to. Thee ae two ways in which this could be offset. One would be an expansive monetay policy to lowe equilibium inteest ates and evese the shift in the LM cuve. This would move the economy back to point a. Hee cedit cad faud inceases the demand fo money, so an expansion in the money supply means that the pivate secto can hold exta money balances without having to sell bonds which would foce up inteest ates. Altenatively, thee could be an expansion in the IS cuve though pehaps a ise in govenment spending o a tax cut. This will move the economy to point c. This fiscal expansion diectly offsets the output effect of the cedit cad faud.
20 LM LM 1 1 c b a IS 1 b. An incease in the maginal popensity to save LM 1 LM a 1 b c IS IS 1 This is the same as a fall in the maginal popensity to consume, which ceates an inwad pivot in the IS cuve fom IS 1 to IS. This is because the multiplie effect of the autonomous expenditues is educed by geate leakages fom savings. As a esult the economy moves fom point a to point b and output falls. To evese this, the govenment could unleash a fiscal expansion and shift the IS cuve to IS, o move the economy to point c though an expansionay monetay
21 policy. In doing so they must howeve note that the multiplie is now lowe because of the highe saving popensity. An altenative would be to ty and diectly offset the impact of the highe saving popensity and pevent the IS cuve fom pivoting. If thee ae popotional income taxes then the IS cuve may take the following fom. a + I + G = 1 c(1 t) Following a fall in the popensity to consume, c, the IS cuve can be pevented fom pivoting if the multiplie is left unchanged. This could be achieved though a compensating fall in the tax ate t. Although households save a lage popotion of thei disposable income, a tax cut will incease the level of disposable income leaving consumption unchanged. 10. Using the ISLM model, suggest a suitable policy mix to achieve the following: a. an incease in income whilst keeping inteest ates constant LM 1 LM b 1 a c IS 1 This could be achieved by a fiscal expansion (eithe a ise in govenment spending o a eduction in taxes) with the inteest ate accommodated by an expansion in monetay policy. The fiscal expansion will shift the IS cuve to the ight. The incease in output will lead to an incease in the demand fo money fo tansactions puposes. To achieve this, the pivate secto will sell bonds, loweing bond pices and focing up inteest ates. Theefoe the economy moves fom point a to point c. In ode to pevent this,
22 policymakes must incease the money stock sufficiently so that the pivate secto can satisfy thei liquidity pefeence without selling bonds. This will shift the LM cuve downwads and the economy will move to point c. Output expands futhe, because the subsequent fall in inteest ates eveses the cowding out effects of the initial fiscal expansion on investment. b. a decline in the fiscal deficit while keeping output constant LM 1 LM 1 a b c IS 1 To close a fiscal deficit will equie eithe an incease in taxes o a eduction in govenment spending. Eithe of these will shift the IS cuve inwads. Howeve, to pevent this fom educing output the govenment will need to unleash a monetay expansion and shift the LM cuve downwads. This example demonstates why coodinating monetay and fiscal policies might be offe advantages when an economy needs to coect a fiscal deficit. The fiscal etenchment will educe out and move the economy fom point a to point b. Theefoe, unless monetay policy is simultaneously loosened, moving the economy to point c, output will fall. This might be a consideation when choosing to delegate monetay policy to an independent cental bank because monetay and fiscal policies ae now opeated by sepaate bodies coodinating them to such extent may become difficult. In this case the fiscal authoity may be discouaged fom attempting to deal with a deficit in the fist place if it knows that an offsetting monetay policy stance isn t necessaily fothcoming. c. an incease in the shae of investment in GDP See the answe to pat b. Hee a fiscal etenchment and a monetay expansion keeps output at the same level, but lowes the pevailing domestic inteest ate in
23 equilibium. As a esult investment expands and epesents a highe popotion of GDP. If the fiscal contaction was a ise in taxes, household consumption will be lowe, o altenatively the fiscal contaction epesented a fall in govenment spending as a popotion of output. 11. It is agued that the following equation is a moe accuate desciption of investment behaviou: I = I + β Investment is equal to a fixed quantity I and positively elated to income. a. What factos might justify this fom of investment function? Fist, this functional fom suggests that investment is insensitive to inteest ates. This is not an unconventional thought. Fist, inteest ates may not epesent the tue cost of capital which also needs to take into consideation elements such as depeciation and capital gains. It is also widely consideed that inteest sensitivity is low in its own ight, and changes in output ae much moe significant. Fo example, if the economy is expected to ente into a sevee ecession fims may be unwilling to undetake lage investment pojects egadless of how low cuent ates of inteest actually ae. Vicevesa, if the economy is expanding stongly fims may be willing to undetake investment pojects even if the inteest ate is ising. Thee ae vaious easons as to why investment might be positively elated to income. It is widely acknowledged that indicatos of business optimism and confidence ae impotant dives of investment, and these in themselves tend to be pocyclical. Also, q valuations of investment pojects ae likely to ise if the economy is pefoming well, and this is an indicato that the economy will continue to pefom well in the futue. Finally, it might be agued that because financial makets ae impefect due to asymmetic infomation, the availability of cedit may be a moe impotant facto than the cost of cedit. When cuent output is stong, it would be expected that fims will have geate pofitability and can theefoe finance moe investment pojects fom intenal funds. b. Using this new investment equation, constuct an IS cuve. What happens to the size of the multiplie? Substituting the new investment equation into the typical fom gives: ( ) = a+ c T + I + β + G
24 ( 1 c β ) = a ct + I G + a ct + I + G = 1 c β = kae whee 1 k = and AE = a ct + I + G 1 c β Note, that because investment now esponds positively to output movements the multiplie in the economy is much geate. Changes in autonomous expenditue than geneate output movements will now have feedbacks though both consumption and investment. c. Using the new IS cuve, examine the effects of fiscal policy on equilibium output. Fiscal policy is vey effective, fo two easons. Fist, the multiplie is lage, so fo a given fiscal expansion the ightwad shift in the IS cuve is much geate. Second, because investment is inteest insensitive thee is no cowding out effect. So, oveall fiscal policy can have a significant impact on the economy. In fact, in this case fiscal policy actually cowds in, athe than cowds out, investment expenditues. IS LM 1 1
25
CHAPTER 10 Aggregate Demand I
CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income
More informationProblem Set # 9 Solutions
Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new highspeed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease
More informationControlling the Money Supply: Bond Purchases in the Open Market
Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises
More informationAgenda. Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy, Part 2. The supply of and demand for the dollar
Agenda Exchange Rates, Business Cycles, and Macoeconomic Policy in the Open Economy, Pat 2 How Exchange Rates ae Detemined (again) The ISLM Model fo an Open Economy Macoeconomic Policy in an Open Economy
More informationPersonal Saving Rate (S Households /Y) SAVING AND INVESTMENT. Federal Surplus or Deficit () Total Private Saving Rate (S Private /Y) 12/18/2009
1 Pesonal Saving Rate (S Households /Y) 2 SAVING AND INVESTMENT 16.0 14.0 12.0 10.0 80 8.0 6.0 4.0 2.0 0.02.04.0 1959 1961 1967 1969 1975 1977 1983 1985 1991 1993 1999 2001 2007 2009 Pivate Saving Rate
More informationQuestions for Review. By buying bonds This period you save s, next period you get s(1+r)
MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the twopeiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationOpen Economies. Chapter 32. A Macroeconomic Theory of the Open Economy. Basic Assumptions of a Macroeconomic Model of an Open Economy
Chapte 32. A Macoeconomic Theoy of the Open Economy Open Economies An open economy is one that inteacts feely with othe economies aound the wold. slide 0 slide 1 Key Macoeconomic Vaiables in an Open Economy
More informationHow Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes
How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk  Risk to shaeholdes esulting fom the use of debt. Financial Leveage  Incease in the vaiability of shaeholde etuns that
More informationThe Supply of Loanable Funds: A Comment on the Misconception and Its Implications
JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently FieldsHat
More informationDefinitions and terminology
I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve
More informationChapter 11: Aggregate Demand II, Applying the ISLM Model Th LM t
Equilibium in the  model The cuve epesents equilibium in the goods maket. Chapte :, Applying the  Model Th t C ( T) I( ) G The cuve epesents money maket equilibium. M L(, ) The intesection detemines
More informationThe LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
More informationGESTÃO FINANCEIRA II PROBLEM SET 1  SOLUTIONS
GESTÃO FINANCEIRA II PROBLEM SET 1  SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 20102011 Chapte 1 The Copoation 113. What is the diffeence
More informationConverting knowledge Into Practice
Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading
More informationEpisode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
More informationDefine What Type of Trader Are you?
Define What Type of Tade Ae you? Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 1 Disclaime and Risk Wanings Tading any financial maket involves isk. The content of this
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationFirstmark Credit Union Commercial Loan Department
Fistmak Cedit Union Commecial Loan Depatment Thank you fo consideing Fistmak Cedit Union as a tusted souce to meet the needs of you business. Fistmak Cedit Union offes a wide aay of business loans and
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationIntertemporal Macroeconomics
Intetempoal Macoeconomics Genot Doppelhofe* May 2009 Fothcoming in J. McCombie and N. Allington (eds.), Cambidge Essays in Applied Economics, Cambidge UP This chapte eviews models of intetempoal choice
More informationEconomics 326: Input Demands. Ethan Kaplan
Economics 326: Input Demands Ethan Kaplan Octobe 24, 202 Outline. Tems 2. Input Demands Tems Labo Poductivity: Output pe unit of labo. Y (K; L) L What is the labo poductivity of the US? Output is ouhgly
More informationJapan s trading losses reach JPY20 trillion
IEEJ: Mach 2014. All Rights Reseved. Japan s tading losses each JPY20 tillion Enegy accounts fo moe than half of the tading losses YANAGISAWA Akia Senio Economist Enegy Demand, Supply and Foecast Goup
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first nonzero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
More informationFI3300 Corporate Finance
Leaning Objectives FI00 Copoate Finance Sping Semeste 2010 D. Isabel Tkatch Assistant Pofesso of Finance Calculate the PV and FV in multipeiod multicf timevalueofmoney poblems: Geneal case Pepetuity
More informationChapter 7: Equilibrium in the Flexible Price Model
Copyight MHHE 2005 Chapte 7: Equilibium in the Flexible Pice Model knowing what has happened to consumption spending. But consumption spending depends on income, which in tun depends on the levels o net
More informationFXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
More informationUNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + =   
More informationEquity compensation plans New Income Statement impact on guidance Earnings Per Share Questions and answers
Investos/Analysts Confeence: Accounting Wokshop Agenda Equity compensation plans New Income Statement impact on guidance Eanings Pe Shae Questions and answes IAC03 / a / 1 1 Equity compensation plans The
More informationElectricity transmission network optimization model of supply and demand the case in Taiwan electricity transmission system
Electicity tansmission netwok optimization model of supply and demand the case in Taiwan electicity tansmission system MiaoSheng Chen a ChienLiang Wang b,c, ShengChuan Wang d,e a Taichung Banch Gaduate
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationChannel selection in ecommerce age: A strategic analysis of coop advertising models
Jounal of Industial Engineeing and Management JIEM, 013 6(1):89103 Online ISSN: 0130953 Pint ISSN: 013843 http://dx.doi.og/10.396/jiem.664 Channel selection in ecommece age: A stategic analysis of
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More information1.4 Phase Line and Bifurcation Diag
Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes
More informationAlgebra and Trig. I. A point is a location or position that has no size or dimension.
Algeba and Tig. I 4.1 Angles and Radian Measues A Point A A B Line AB AB A point is a location o position that has no size o dimension. A line extends indefinitely in both diections and contains an infinite
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationLINES AND TANGENTS IN POLAR COORDINATES
LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Polacoodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and
More informationThe transport performance evaluation system building of logistics enterprises
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194114 Online ISSN: 213953 Pint ISSN: 2138423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
More informationContinuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
More informationLab #7: Energy Conservation
Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 14 Intoduction: Pehaps one of the most unusual
More informationSemipartial (Part) and Partial Correlation
Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated
More informationGauss Law. Physics 231 Lecture 21
Gauss Law Physics 31 Lectue 1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationTrading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract
Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi email: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,
More informationExam #1 Review Answers
xam #1 Review Answes 1. Given the following pobability distibution, calculate the expected etun, vaiance and standad deviation fo Secuity J. State Pob (R) 1 0.2 10% 2 0.6 15 3 0.2 20 xpected etun = 0.2*10%
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationLoyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques
Loyalty Rewads and Gift Cad Pogams: Basic Actuaial Estimation Techniques Tim A. Gault, ACAS, MAAA, Len Llaguno, FCAS, MAAA and Matin Ménad, FCAS, MAAA Abstact In this pape we establish an actuaial famewok
More information9:6.4 Sample Questions/Requests for Managing Underwriter Candidates
9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated
More informationThings to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
More informationYIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE
YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE Septembe 1999 Quoted Rate Teasuy Bills [Called Banke's Discount Rate] d = [ P 1  P 1 P 0 ] * 360 [ N ] d = Bankes discount yield P 1 = face
More informationNBER WORKING PAPER SERIES FISCAL ZONING AND SALES TAXES: DO HIGHER SALES TAXES LEAD TO MORE RETAILING AND LESS MANUFACTURING?
NBER WORKING PAPER SERIES FISCAL ZONING AND SALES TAXES: DO HIGHER SALES TAXES LEAD TO MORE RETAILING AND LESS MANUFACTURING? Daia Bunes David Neumak Michelle J. White Woking Pape 16932 http://www.nbe.og/papes/w16932
More informationExperiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
More informationPHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013
PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80kg physics book is placed next to you on the hoizontal seat of you ca. The coefficient of static fiction between the book and the seat is 0.650,
More informationChapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43
Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More informationAMB111F Financial Maths Notes
AMB111F Financial Maths Notes Compound Inteest and Depeciation Compound Inteest: Inteest computed on the cuent amount that inceases at egula intevals. Simple inteest: Inteest computed on the oiginal fixed
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance the availability
More informationPhysics HSC Course Stage 6. Space. Part 1: Earth s gravitational field
Physics HSC Couse Stage 6 Space Pat 1: Eath s gavitational field Contents Intoduction... Weight... 4 The value of g... 7 Measuing g...8 Vaiations in g...11 Calculating g and W...13 You weight on othe
More informationThe Binomial Distribution
The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between
More informationRevision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams
More informationINITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS
INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in
More informationOffice of Family Assistance. Evaluation Resource Guide for Responsible Fatherhood Programs
Office of Family Assistance Evaluation Resouce Guide fo Responsible Fathehood Pogams Contents Intoduction........................................................ 4 Backgound..........................................................
More informationTransformations in Homogeneous Coordinates
Tansfomations in Homogeneous Coodinates (Com S 4/ Notes) YanBin Jia Aug, 6 Homogeneous Tansfomations A pojective tansfomation of the pojective plane is a mapping L : P P defined as u a b c u au + bv +
More informationSUGGESTED SOLUTIONS. 21404 Strategic Financial Management. CA Professional (Strategic Level II) Examination June 2014
SUGGESTED SOLUTIONS 21404 Stategic Financial Management CA Pofessional (Stategic Level II) Examination June 2014 THE INSTITUTE OF CHARTERED ACCOUNTANTS OF SRI LANKA All Rights Reseved Answe No. 01 (a)
More informationSpirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
More informationA THEORY OF NET DEBT AND TRANSFERABLE HUMAN CAPITAL
A THEORY OF NET DEBT AND TRANSFERABLE HUMAN CAPITAL Bat M. Lambecht Lancaste Univesity Management School Gzegoz Pawlina Lancaste Univesity Management School Abstact Taditional theoies of capital stuctue
More informationVoltage ( = Electric Potential )
V1 Voltage ( = Electic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage is
More informationThe force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges
The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee
More informationPRICING MODEL FOR COMPETING ONLINE AND RETAIL CHANNEL WITH ONLINE BUYING RISK
PRICING MODEL FOR COMPETING ONLINE AND RETAIL CHANNEL WITH ONLINE BUYING RISK Vaanya Vaanyuwatana Chutikan Anunyavanit Manoat Pinthong Puthapon Jaupash Aussaavut Dumongsii Siinhon Intenational Institute
More informationThe Role of Gravity in Orbital Motion
! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State
More informationThe Incidence of Social Security Taxes in Economies with Partial. Compliance: Evidence from the SS Reform in Mexico
The Incidence of Social Secuity Taxes in Economies ith Patial Compliance: Evidence fom the SS Refom in Mexico Gecia M. Maufo Abstact Looking at impovements in social secuity benefits in Mexico, this pape
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More informationThe impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011
The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility
More informationProblem Set 6: Solutions
UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 164 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway 29.55 Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance
More informationPY1052 Problem Set 8 Autumn 2004 Solutions
PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ighthand end. If H 6.0 m and h 2.0 m, what
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.7. find the vecto defined
More informationHour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and
Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon
More informationExperiment MF Magnetic Force
Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuentcaying conducto is basic to evey electic moto  tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating
More informationThe Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?
The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity
More information81 Newton s Law of Universal Gravitation
81 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,
More informationAP Physics Electromagnetic Wrap Up
AP Physics Electomagnetic Wap Up Hee ae the gloious equations fo this wondeful section. F qsin This is the equation fo the magnetic foce acting on a moing chaged paticle in a magnetic field. The angle
More informationGravitational Mechanics of the MarsPhobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning
Gavitational Mechanics of the MasPhobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This
More informationInstructions to help you complete your enrollment form for HPHC's Medicare Supplemental Plan
Instuctions to help you complete you enollment fom fo HPHC's Medicae Supplemental Plan Thank you fo applying fo membeship to HPHC s Medicae Supplement plan. Pio to submitting you enollment fom fo pocessing,
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationTheory and practise of the gindex
Theoy and pactise of the gindex by L. Egghe (*), Univesiteit Hasselt (UHasselt), Campus Diepenbeek, Agoalaan, B3590 Diepenbeek, Belgium Univesiteit Antwepen (UA), Campus Die Eiken, Univesiteitsplein,
More informationSkills Needed for Success in Calculus 1
Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell
More informationUnit Vectors. the unit vector rˆ. Thus, in the case at hand, 5.00 rˆ, means 5.00 m/s at 36.0.
Unit Vectos What is pobabl the most common mistake involving unit vectos is simpl leaving thei hats off. While leaving the hat off a unit vecto is a nast communication eo in its own ight, it also leads
More informationConcept and Experiences on using a Wikibased System for Softwarerelated Seminar Papers
Concept and Expeiences on using a Wikibased System fo Softwaeelated Semina Papes Dominik Fanke and Stefan Kowalewski RWTH Aachen Univesity, 52074 Aachen, Gemany, {fanke, kowalewski}@embedded.wthaachen.de,
More informationIn the lecture on double integrals over nonrectangular domains we used to demonstrate the basic idea
Double Integals in Pola Coodinates In the lectue on double integals ove nonectangula domains we used to demonstate the basic idea with gaphics and animations the following: Howeve this paticula example
More informationRegulatory requirements and commercial banks' lending rate: some theoretical perspectives
Saat C. hal (India ans and an Systems, Volume 5, Issue 2, 200 Regulatoy equiements and commecial bans' lending ate: some theoetical pespectives Abstact This pape demonstates theoetically how the egulatoy
More informationShaping the future of diabetes care
Shaping the futue of diabetes cae 1 Heino von Pondzynski Head of Roche Diagnostics 2 The idea Roche Diagnostics, the woldwide leade in Diabetes monitoing, and Disetonics, the woldwide numbe 2playe in
More informationDeflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
More informationCONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest
CONCEPT OF TIME AND VALUE OFMONEY Simple and Compound inteest What is the futue value of shs 10,000 invested today to ean an inteest of 12% pe annum inteest payable fo 10 yeas and is compounded; a. Annually
More information9.5 Amortization. Objectives
9.5 Aotization Objectives 1. Calculate the payent to pay off an aotized loan. 2. Constuct an aotization schedule. 3. Find the pesent value of an annuity. 4. Calculate the unpaid balance on a loan. Congatulations!
More informationIntroduction to Electric Potential
Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic
More informationRune Stenbacka Tuomas Takalo. Switching costs and financial stability
Rune Stenbacka Tuomas Takalo Switching costs and financial stability ank of Finland Reseach Discussion Pape 06 SWITCING COSTS ND FINNCIL STILITY* Rune Stenbacka** Tuomas Takalo*** 4 Januay 06 We establish
More informationMERGER SIMULATION AS A SCREENING DEVICE: SIMULATING THE EFFECTS OF THE KRAFT/CADBURY TRANSACTION
MERGER SIMULATION AS A SCREENING DEVICE: SIMULATING THE EFFECTS OF THE KRAFT/CADBURY TRANSACTION Enique Andeu, Kisten Edwads, Aleando Requeo 1,2 Novembe 2010 Abstact In this aticle we pesent a method that
More informationReal Estate Equity Derivatives
Real Estate Equity Deivatives Geltne Mille 2 nd Edition Chapte 26 Section 26.3 Real Estate Deivatives (Index Retun Swaps) Real Estate Equity Deivatives A deivative is an asset whose value depends completely
More information