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# Intermediate Macroeconomic Theory ECON 302

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This 16 page Class Notes was uploaded by April Jerde on Thursday September 17, 2015. The Class Notes belongs to ECON 302 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 13 views. For similar materials see /class/205163/econ-302-university-of-wisconsin-madison in Economcs at University of Wisconsin - Madison.

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Date Created: 09/17/15

Ditcuuion Weekb Econ302Lecture2 Prof Yongseok Shin Date 102006 TA Seung Gyu Sim Absolute Convergence vs Conditional Convergence Consider a group of economies that have the same steadystate values K and Y Does absolute convergence ipoor economies growing faster than rich ones ihold for AKK Suppose that Poorland s production technology saving rate depreciation rate and the current level of capital are yk0395 s01 6005 and k3 respectively while Richland s arey3k0395 s01 6005 and k4 a Solve for the steady state of each country 1 Which county grows faster c Does absolute convergence hold Growth Accounting YK12L 12 YAK12L 12 ltEXERCISEgt 1 Labor productivity is de ned as YL the amount of output divided by the amount of labor input Start with the growthaccounting equation and show that the growth in labor productivity depends on growth in total factor productivity and growth in the capital Iabor ratio In particular show that AYL g a AKL Y L A K L 2 In the economy of Solovia the owners of capital get twothirds of national income and the workers receive onethird a Suppose that the labor force increased by 5 percent while all other conditions are mehanged What would happen to the measured output of the economy Does labor productivity idefined as output per worker increase decrease or stay the same Does total factor productivity increase decrease or stay the same b In year I the capital stock was 6 the labor input was 3 and output was 12 I diale a lace weekend In year 2 the capltal stock was 7 the labor 1nput was 4 and output was 14 What happened to total factor productivity between the two years IS 7 LM Model The IS Curve depicts all combinations of the real interest rate r and real output levels Y in which the goods market and loanable funds markets are in equilibrium Keynesian Cross Diagram to determine equilibrium level of output for a given interest rate setting planned expenditure equal to output Y Output Production E Planned Expenditure CabY7T IIg11r GG0G1r TT ECIG E abY7T0Ig 11rGg G1r In equilibrium there are no inventory changes and the level of production is equal to the level of planned expenditure YE C 1 6 abY7T0Ig IlrG0 G1r abY ng 10 11rGg G1r 2 Y bY a bT0 10 IlrGg G1r 1 bY a10 G0 11G1r7bT0 2 1 Y a10G011G1r7bT0 l b YiaIGIGr77T My 7 7 lt gt H Keynesian Multiplier is llb llMPC Keynesian Tax Multiplier is blb MPClMPC The LM Curve depicts all combinations of the real interest rate r and real output levels Y in which the money market is in equilibrium M S Real Money Supply M D LrY Real Money Demand To trace out the LM curve we vary the level of output Y in the real money demand equation and trace out the real interest rate and output combinations that result from the equilibrium in the money market 1 Assume a close economy can be described by the following equations Note This setup is different than the one above as we now have progressive taxes rather than an autonomous taX level C100008YT I 12 000 600r G 2 000 501 T 200 025Y S K 4000 P D K 3 670 02Y 3 500r a Solve for the IS curve Y E c 1 G 1000 08Y T12000 600r 2 000 50r 15 000 08 Y 200 025Y 650r 15 000 08 200 0 75Y 650r 15160 06Y 650r 2 04Y 15160 650r 2 Y 2515160 650r 379001625r b Solve for the LM curve M s M 5 5 4 000 3 670 02Y 3 500r 02Y 330 3 500r Y 5 3303500r Y165017500r c What is the equilibrium interest rate and output level Is Curve Y 379001625r LM Curve Y 1 65017500r 37 900 1 625r 1 65017500r 36250 19125r r 1895 Y 1 650 1 7 5001895 34 820 Y 37900 1 6251895 34820 d What is the equilibrium level of consumption private savings and national savings in the closed economy C100008Y T 1000 08 Y 200 02519 1000 08200 0 75Y 1 160 0 6Y 1 160 0 634 820 22 052 SP Y C T Y 22 052 200 02519 0 75Y 21852 0 7534 820 21852 4 263 NS I 12 000 600r 12 000 6001 895 10 863 NS SP SG SP T G Alternative Method of Solving 4 063 200 025Y 2000 50r 1 863 0 2534 820 501 895 18638705 95 10 863 2 Assume a close economy can be described by the following equations IS Curve Y 10000 100r LM Curve Y 8 000 150r C 50075Y T a What is the equilibrium interest rate and output level IS Curve Y 10 000 100r LM Curve Y 8 000 150r 10000 100r 8000 150r 2 000 250r re 8 K 8 000 1508 9200 b What is the new IS Curve if autonomous government expenditure increases by 50 It may be useful to graph an initial Keynesian Cross and think about what happens to expenditure with the change in G abTG0Ig IrGr 7abTGgAGIg IlrG1r 7 abTGIIrGr AG C IMPC 7 AG IMPC Y 1 50450200 1075 NewIS CurveY 10200100r c Intuitively and qualitatively what will happen to the equilibrium level of output and real interest rate with the new IS curve It may be useful to graph the initial IS curve new IS curve and the LM curve 15 Z 15 New 4 LM 2 0 Real Interest Rate r I O Real Output In Thousands With a shift right in the IS curve the equilibrium level of output will increase and the equilibrium real interest rate will increase as well This happens as a result of the expenditure function shifting upwards in the Keynesian cross causing the IS curve to shift right With the shift right of the IS curve we have a higher levels of output which cause the interest rate to rise and the level of output to fall back to a new equilibrium level higher than before but less than what would be predicted by the Keynesian Cross d What will happen to the LM Curve if money supply increases in the economy Compared to our initial equilibrium and using the original IS curve do we know the change in the interest rate and the change in the output level Compared to our initial equilibrium and using the new IS curve do we know the change in the interest rate and the change in the output level With a shift light in the money supply curve we know that the equilibrium interest rate in the money market will fall for every level of output Thus the LM curve will shift rightw ards Compared to the initial equilibrium we know that a LM shift right will cause the real interest rate to fall and the level of output to increase using the original IS curve Compared to the initial equilibrium we know that a LM shift light will cause the level of output to increase using the new IS curve but the change in the real interest rate is ambiguous and it depends on the magnitudes of the shifts Both of the graphs below depict a LM curve shift to the light but they have contradicting predictions on the equilibrium real interest rate 2 l4 f 12 m Is 2 8 gt smew g 6 LM 4 LMN 2 W O Real Output In Thousands 15 W S New A LM LVl New Reall Interest Rate H O Real Output In Thousands Positive AS curve YfaULP Y actual output 3 natural rate of output or parameter indicating the responsiveness of output to unexpected changes in price level P price leve P expected price level 3 explanations l Sticky Wage Model When prices change nominal wages are stuck Thus an increase in price level will push down the real wage causing unemployment rms will hire more workers and output to increase P and Y positively related Problem The real wage goes down when output increases this countercyclical behavior is not supported in the data 2 Imperfect Information Model Temporary misconceptions about relative price levels compared to overall price level changes If the overall price level increases rms expect it is due to relative prices and not overall prices and as such increase their prices 3 Sticky Price Model Firms are price setters and want to set prices according to p P 0Y l7where an overall higher price level P will cause rms to set higher prices and a higher level of output relative to what is expected will increase prices as production increases and marginal costs increase A fraction of the rms s have sticky prices and set prices based on expectations p P2 01Y2 172 The remaining rms have exible prices and set their price on the YfaUhP desired price End result S wh J l ereai 0L ls AD curve shifts from ISLM framework The IS Curve depicts all combinations of the real interest rate r and real output levels Y in which the goods market and loanable funds markets are in equilibrium Keynesian Multiplier is llb llMPC Keynesian Tax Multiplier is blb MPClMPC Changes in the IS Curve G0 IS curve shifts right by llb T0 IS curve shifts left by blb a IS curve shifts right by llb Io IS curve shifts right by llb 11 IS curve shifts right and steeper by llb at rl What happens if there is an increase in b IS tilts atter slope changed to b in IS curve steeper implies higher Y for every r in comparison The LM Curve depicts all combinations of the real interest rate r and real output levels Y in which the money market is in equilibrium To trace out the LM curve we vary the level of output Y in the real money demand equation and trace out the real interest rate and output combinations that result from the equilibrium in the money market Changes in the LM Curve M LM curve shifts right P LM curve shifts left L LM curve shifts right Go To a Io 11 b Change in Y movement along If the IS curve shifts out then the level of output increases for every price level holding the LM curve fixed and as such the AD curve shifts out If the LM curve shifts out due to monetary policy or changes in money demand then the level of output increases for every price level holding the price fixed for the LM curve 1 Salaw Gmwlh Madzl Steady State Akquot sf m e 5411g kquot 0 sf m 5ng w At the steady state our new rnvest s lnvestment level and the eaprtal per effectlve worke rnent r exacd to r ls rnterpretatron The speclflc values forthrs graph are y and s 0 3 y equal our break even eonstant A graph ls below for k 5n003g0025005 a What ls the steady state level of eaprtal per effectlve Worker glven the above rnforrnahon7 sk5ng w 031t 50 l1t Oulput per effec 39 0 3 6 9 12 15 18 21 24 Capital per effective worker k r What would happen lf you were not rnrtrally m a steady state7 Conslder the ease lfkwere less than k Explam whathappens over trrne If k is smaller than k we know that our investment exceeds our break even investment Thus in each period we will have an increase in the stock of capital per effective worker Over time we will approach the steady state level of capital given the production function savings rate depreciation rate labor growth rate and technological efficiency growth rate ii Consider the case if k were greater than k Explain what happens over time If k is larger than k we know that our break even investment is greater than our new investment Thus in each period we will have a decrease in the stock of capital per effective worker Over time we will approach the steady state level of capital given the production function savings rate depreciation rate labor growth rate and technological efficiency growth rate Golden Rule of Capital Steady State In a steady state so Ak sf k 7 5ng k 0 Maximize consumption to nd the best steady state for individuals c y i y sfk y 5ng k fk 5ng k Derivative at maximum is MPK k 5ng At the steady state our new investment is exactly equal to our break even investment level and the capital per effective worker is constant However we can have many different steady state levels each of which depends on a unique savings rate s b What is the golden rule steady state level of capital per effective worker given for the above information MPK5ng 05 01 kgaldos 5 limos 25 kquot gold Steady State y c39 m g N s gold y 6ngk o 51015 20 25 30 35 40 Steady Siate k k gold 25 What ls true about the savings rate if the eurrent steady state w ls greater than k gd If the steady state m is greater than k wuwe lsan that the savings rate is greater than the gn er savings rate This is true because a higher savings rate is required tn reach a higher steady statelevel nfczpital What 5 true about the MPK at steady state kquot If kls greater than leggy che steady state m is greater than k muwe lsan that the MIFK k39 is less than the MI k mu This is true because the slupe ur the prndnc nn functinn diminishes and far higher levels at k the lvwer the level at MIFK What ls required to transition to the golden rule level of eaprtal if the eurrent steady state kquot if v ls ess than law 7 Speclflcally what happens to the level of consumption immediately and a ernme7 If the steady state k is less than kg01d we know that the savings rate is lower than the golden rule steady state savings rate In order to transition to the golden rule we must save more By saving more with the current level of output we must be consuming less and the level of consumption must immediately fall However we know that over time the consumption level will increase compared to the initial level as we are moving toward the golden rule steady state level of capital 2 Simple Aggregate Demand Aggregate Supply Model Aggregate Supply Price and Real Output combinations of goods and services supplied Short Run AS SRAS Prices are xedsticky which results in a horizontal curve Long Run AS LRAS Real output is fixed which results in a vertical curve Aggregate Demand Price and Real Output combinations for a fixed nominal output level combinations of goods and services demanded AD Use the quantity theory of money to realize that nominal output PY is also equal to MV Thus changes in either money supply M or the velocity of money V result in shifts to the AD curve Supply Shocks Supply shocks are in the form of price shocks that can be favorable or non favorable Demand Shocks Demand shocks are in the form of exogenous changes in money supply or in the velocity of money Monetary policy can shift the AD curve Stabilization Policy Monetary Policy actions which can affect the AD curve and counter shifts in the SRAS This will maintain the level of real output in the economy as a cost of changing prices LRAS A u A in m 39 r SRAS2 m T gt lt12 1 1 a SRAS o 3 5 0 Q4 0 39n 2 l I I I I AD1 Y2 Y1 7 Real Output Y a Consider the graph above and describe what happened from the initial equilibrium if a stabilization policy was used after the initial shift Initially we are in equilibrium at price level P1 and the full employment level of output Y1 on the LRAS curve However there was an adverse price shock and the SRAS curve shifts up from SRAS1 to SRASZ We move along the aggregate demand curve to a higher price level P2 and lower level of real output Y2 However once we moved to the higher price level and lower output level a stabilization policy was enacted to shift the aggregate demand curve to the right AD2 This was done by increasing the money supply in the economy through the purchase of bonds on the open market operation We then return to the initial level of output Y1 but at a higher price level P2 Ditcuuion Week1 Econ302Lecture2 Prof Yongseok Shin ISLM Model Why do we study the lSLM model Date 102706 TA Seung Gyu Sim MPC Y CIG Suppose that due to an exogenous shock the interest rate goes up ltEXERCISEgt Suppose that the government increases its expenditure Analyze the impact on IS curve Movement Along vs Parallel Shift Quantitative Analysis ltEXERCISEgt Multiplier Suppose that the interest rate increases from 002 to 005 The marginal Suppose that the government expenditure goes up by AG Then propensity of consumption is 05 11001000r and G100T Y WCXY7TIG aYandYAY b Investment Multiplier c Sketch the IS curve ltEXERCISEgt Suppose that the government spending goes up by 10 The marginal propensity of consumption is 05 r002 130010000r and the initial G100T a Y and YAY7 b Fiscal Policy Multiplier ave a lace weekend c Sketch the IS curves d

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