# Assign 3_answers_2010 - York University Department of...

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York University Department of Economics Faculty of Arts AS / ECON 2450 M Intermediate Macroeconomic Theory II Tasso Adamopoulos Assignment 3 Duration: 2 ½ hours Question 1 (a) By definition, planned expenditure is: E = C + I + G + GX – IM Now separate each of the components above in those that directly depend on Y and those that do not: E = [ C 0 + I 0 – I r r + G 0 + X F Y F + X ε 0 – X r r + X r r F ] + [ C y (1-t) – IM y ]Y The component that does not depend on national income (or real GDP) is autonomous expenditure: A = C 0 + I 0 – I r r + G 0 + X F Y F + X 0 – X r r + X r r F And the coefficient on income is the marginal propensity to expend, i.e., it tells you how much planned expenditure will change if income rises by one dollar: MPE = C y (1-t) – IM y Then we can re-write the planned expenditure line as: E = A + MPE*Y The term A is decomposed into two terms: the baseline level of autonomous expenditure and the term that depends on r: A = = A 0 – ( I r + X r )r The goods market is in equilibrium when planned expenditure (or aggregate demand) is equal to real GDP (or national income): Y = E Combining all these equations we get the IS curve: Y = A 0 /(1-MPE) – ( I r + X r )r/(1-MPE)

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The LM curve gives you all pairs (i,Y) that represent equilibria in the money market. The demand for real money balances is: M D /P = Y/ V L [V 0 + V i (r + π e )] The supply of nominal money by the central Bank is M. The money market is in equilibrium when M D = M. Using this and solving for M we get the LM curve: Y = V L [V 0 + V i (r + π e )] (M/P) The IS-LM diagram represents equilibrium in both the goods and the money market. (b) To derive the AD curve (demand side of the economy) you have to change he price level and see how this changes the equilibrium level of real GDP in the IS- LM diagram. An increase in the price level (P) reduces the real money supply (M/P) in the economy and thus shifts the LM curve to the left. Fig.1 shows shifts in the IS-LM diagram due to price increases, and Fig.2 shows the resulting AD curve by combining the different levels of P with the corresponding equilibrium levels of Y from the IS-LM diagram. Consequently a change in P constitutes a movement along the AD curve. (c) When the central bank follows a Taylor Rule, then this rule becomes the economy’s effective LM curve, i.e., the central bank is willing to supply as much M as is demanded at the r implied by the Taylor rule, to ensure money market equilibrium. Given that with this Taylor rule the central bank does not target the level of real GDP, the effective LM curve is flat in the IS-LM diagram. In this case an increase in inflation increases the real interest rate for every Y and thus the LM curve shifts up, thus reducing the equilibrium level of real GDP. See Fig.3. Connecting the pairs of inflation and the corresponding levels of equilibrium real GDP from the IS-LM diagram from Fig.3 we can derive the economy’s MPRF (monetary policy reaction function) curve. See Fig.4. To derive
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## This note was uploaded on 09/01/2011 for the course ECON 2450 taught by Professor Tasso during the Winter '09 term at York University.

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Assign 3_answers_2010 - York University Department of...

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