1 Econ 202 Problem Set 5 Solutions Meetings 18 to 20 Reading Unit 5 Macroeconomic Policy: Inflation and Unemployment 1) Correlation and Causation Any two variables for which we have data can be: • positively correlated, i.e. move in the same direction. • negatively correlated, i.e. move in the opposite direction. • Not correlated, i.e. move in unrelated directions. a) Suppose two variables are positively correlated . For example, people with higher income tend to be healthier. What does this correlation imply about causality ? What do you think is the causal relationship between income and health? The positive correlation between income and health by itself doesn’t imply anything about causality. Correlation is not causality! We need to have a theory of why one variable causes another. The positive correlation between income and health c ould imply: • higher income causes better health: because people have more resources to spend on health care and good food and exercise. • Better health causes higher income because healthier people don't miss work due to sickness. • Income and health are correlated with another variable such as education and its education that causes both higher income and better health I think all three of these causal stories can be at play in explaining the relationship between income and health! b ) Exercise 5.1 in the textbook gives a link to the Spurious Correlation Website: https://www.tylervigen.com/spurious - correlations . What is a Spurious Correlation? Give an example from the Spurious Correlation Website. Why do you think this correlation is “spurious”? A spurious correlation is when two variables are highly correlat ed but there is no plausible causal explanation for the correlation. For example, the Spurious Correlation Website shows that the distance between Neptune and the sun is highly negatively correlated with Burglary rates in the US : 2 I can’t think of any causal mechanism or explanation that would generate this correlation, so I consider it a “spurious correlation”! c) What correlation does Figure 5.1 from our textbook show between inflation and the ruling party margin of victory? Is this correlation spurious or is there a plausible causal explanation for this observed correlation? Figure 5.1 shows a negative correlation between inflation and the ruling party’s margin of victory. This correlation is probably not spurious since there is a plausible causal explanation for the observed correlation: voters dislike higher inflation and ho ld the ruling party response for inflation. Hence voters vote against the ruling party in times of higher inflation. Hence higher inflation tends to cause the ruling party to lose elections. d ) Below is figure 5.2 from our textbook. This graph shows the negative correlation between the size of government as a share of GDP and the size of fluctuations in the real GDP growth rate. Is this correlation spurious or is there a plausible causal explanation for this observed correlation? (Hint: Consider using th e Multiplier Model in your answer) 3 This c orrelation is probably not spurious because the multiplier model provide s plausible causal explanation for the correlation According to the multiplier model fluctuations in real GDP growth are due to fluctuations in aggregate demand Government spending fluctuates less than other components of aggregate demand suc h as consumption and investment . As the government spending share of GDP increases so consumption and investment share of GDP are decreasing this make Aggregate D emand (AD) more stable thus causing more stability in real GDP growth (since Y=AD). 2) Fiscal and Monetary Policy a) What is fiscal policy? Who controls fiscal policy? How does fiscal policy influence aggregate demand? Fiscal policy concerns taxes (t), government spending (G) the government budget deficit and government debt The Government budget deficit = government spending minus tax revenue plus the interest payments on government debt (GBD = G - tY + interest payments o n government debt) 4 If the government runs a budget deficit it must finance the deficit by either borrowing w hich adds to government debt . S ome governments can also print money t o finance budget deficits F iscal policy in United States is set at the Federal Level by Congress subject to the veto of the P resident . At the state and local levels, fiscal policy is set by state and local legislative bodies subject to the veto of governors and mayors depending on state and local political institutions. As we saw in the M ultiplier M odel , fiscal policy influences Aggregate demand via changes in income tax rates and government spending An increase in government spending directly increases aggregate demand : ↑ G →↑ AD A cut in income taxes increases disposable income which increases consumption which increases a ggregate demand : ↓ t → ↑ (1 - t)Y → ↑ C → ↑ AD b ) What is monetary policy? Who controls monetary policy? How does monetary policy influence aggregate demand? What is a typical goal for monetary policy? Monetary policy set s the “ nominal policy interest rate ” . In the US the nominal policy interest rate is the federal funds rate, which we'll talk more about later in the course Setting the nominal policy interest rate then influences all interest rates that you and I care more directly about such as auto loan rate s, student loan rates and mortgage rates Monetary policy is under the control of the central bank . In the United States the central bank is called the Federal Reserve System For the E uro area the central bank is called the European Central Bank As we saw in the multiplier model aggregate demand depends on investment w hich depends on interest rates , in particular the real interest rate (r). Increases in the real interest rate cause a decrease in investment and hence a decrease aggregate demand : ↑ r → ↓ I → ↓ AD D e creases in the real interest rate cause a n in crease in investment and hence a n inc rease aggregate demand : ↓ r → ↑ I → ↑ AD Fo r most central bank s the goal of monetary policy is to keep inflation close to a “ target inflation rate ” with for most central banks in rich countries is 2% As we will see i n the next question , central banks Influence real interest rates by setting the nominal interest rate 3) Nominal interest rates, real interest rates, expected inflation and the Fisher Equation a) The nominal interest rate ( i ) is the interest rate in terms of money. For example, suppose at the beginning of 2025, Bala lends Abby $100 for one year at a nominal interest rate (i) equal to 10% How much is Abby (the borrower) supposed to re pay Bala (the lender) at the beginning of 2026 ? If 𝒊 = 𝟎 𝟏𝟎 then Abby is supposed to repay Bala ( 𝟏 + 𝒊 ) $ 𝟏𝟎𝟎 = 𝟏 𝟏𝟎𝒙 $ 𝟏𝟎𝟎 = $ 𝟏𝟏𝟎 at the beginning of 2026. 5 b) Given you r answer to part b ) suppose Bala only cares about cups of coffee and price of coffee at the beginning of 2025 is $5/cup. How many cups of coffee is Bala giving up at the beginning of 2025 when he lends $100 to Abby? Suppose Bala expects prices to be constant. What is Bala’s expected rate of inflation 𝜋 𝐸 ? What “real interest rate” is Bala expecting to get when Abby repays her loan? To lend $100 to Abby Bala is giving up $100/($5/cups) = 20 cups of coffee. B ala expects the rate of inflation to equal z ero, so Bala is expecting the price of coffee to remain at $5 a cup Hence when Abby repays her loan with $110 at the beginning of 2026 Bala expects to be able to purchase $110/$5/cup = 2 2 cups of coffee This implies a real interest rate , that is an interest rate in terms of goods and services of 10% Hence if inflation = 0 the “ex post real interest rate ” = nominal interest rate. c) S uppose Bala is willing to lend at 10% nominal interest rate if he expects inflation to equal zero. This means Bala is willing to lend a t a real interest rate of 10% What nominal interest rate would Bal a be willing to lend at if he expect s inflation to equal 5 % ? Explain why Bala wants to earn a real interest rate of 10%. Since Bala expects inflation to equal 5 % then he will want a nominal interest rate of about 15 %. Then at the beginning of 2026 Abby pays Bala $1 15 . Bala expects coffee to cost 5.25 /cup so at the beginning of 2026 Bala expects to be able to purchase $1 15 /$5. 2 5/cup ≈ 22 cups of coffee . Since Bala lent the equivalent of 20 cups of coffee at the beginning of 2025 this implies a real interest rate = 10% d) Given your answers to b) and c) write down an equation for the relationship between real interest rates and nominal interest rates. (Hint: This is the Fisher Equation) Part c) above impl ies that we can think of real interest rates as the nominal interest rates minus expected inflation : 𝒓 = 𝒊 − 𝝅 𝑬 This is called the “ Fisher E quation ” e ) Use the Fisher equation to c alculate the real interest for Japan during the following four period s ( Source The Economy 1.0) 1996 - 2000 2001 - 2005 2006 - 2010 2011 - 2015 nominal interest rate 1.50% 1.40% 1.30% 1.20% Expected inflation - 1.90% - 0.90% - 0.50% 1.60% Real interest rate 3.40% 2.30% 1.80% - 0.40% 4 ) Monetary Policy can red u ce the rate of infl ation but it may require a recession! Suppose that due to past increases in aggrega t e demand inflation has ended higher that where the Federa l R e serve System (th e US central bank ) would like it to be A historical example of this i s the US in the late 19 70s 6 a) To use a numerical exampl e, suppose in year 1 the b ar g aining gap is 0 and expected inflation equals 10%. The n in year 2 , the c entral bank use s mone tary pol icy to reduce i nflation to 4% . In year 3 the c entral bank use s monetary policy to stabil ize inflation at 3%. Ass ume that expected inflation is unanchor ed for year s 2 and 3 so 𝜋 𝑡 𝐸 = 𝜋 𝑡 − 1 . Complete the f ollowing table: Year Bargaining gap Expected inflation Actual inflation 1 0 % 10% 10% 2 - 6 % 10% 4% 3 0% 4% 4% b ) Monetary policy involves setting the poli cy interest rate. How will the central bank change the interest rate in year 2 to decrease inflation to 4 %? How will the central bank change the interest rate in year 3 to keep inflation at 4 %? In year 2 , the central bank will increase the interest rate (↑r) to reduce AD to make the bargaining gap < 0 (i.e. cause a recession) to bring down inflation . In year 3 , the central bank lower s the policy interest rate (↓r) to return the bargaining gap to zero in order to keep inflation at 4 %. c) Given your answers to part a) and b) draw the the Phillips Curve and the Multiplier Graph, show how the curves shift and indicate the equilibriums for years 1 , 2 and 3 7 d) Use two flow diagram s (one for multiplier graph and one for Phillips Curve graphs) to give the intuition for what happens from year 1 to 3 to aggre gate demand , Real GDP , employment , income, con sumption and inflation. Intuition for the multiplier graph year 1 to 2 : PC ( 𝜋 𝑒 = 10 % ) 𝑦𝑒𝑎𝑟 1 , 2 Q of inflation Q of Employment 4 % PC ( 𝜋 𝑒 = 4 % ) 𝑦𝑒𝑎𝑟 3 10 % Q of Output (Y) Q of AD A D curve year 1 & 3 Y=AD curve ) AD curve year 2 N SSE 8 In year 3 , the central bank decreases interest rates to return AD to its initial level . This returns output and employment to the s upply side equilibrium values thus returning the bargaining gap to zero and stabilizing inflation at 4 %. Intuition for the Labor market and PC graphs for years 1 to 2 5 ) In addition to keeping inflation close to a “target inflation rate” another goal of Monetary and Fiscal Policy is to keep unemployment as low as possible without increasing inflation This means us ing monetary and fiscal policy to keep employment as close as possible to the supply side ↓Q of AD = C+I+G+ X - M Firms ↓ production ( ↓ Y) → ↓employment so ↑ unemplo yment ↓ income ( ↓ Y) ↓C CB ↑ r → ↓ I ↓ tax revenue = tY ↓ i M ports = m Y ↑ NX = X - M HR can ↓ W and still get worker s to not shir k Given ↓ W the marketing dep t ↓ P to maintain the profit margin. ↓ P → lower inflation “Wage Price Spiral” Since in year 3 AD decreases, firms ↓production ↓Y and fire workers: ↓ employment & ↑unemployment → bargaining gap < 0 i.e. - 6% → ↓ COJL ↓inflation → ↓expected inflation (PC curve shifts down ) 9 equilibrium value for employment This is equivalent to trying to keep the bargaining gap equal to 0 w ith as many workers employed as possible a) G iven the goals stated above how will fiscal policy respond to an event that decreases aggregate demand? Illustrate your answer by drawing the multiplier model graph Label the initial equilibrium point A. Then suppose some event decreases a ggregate demand such as a decline in autonomous consumption or decline in autonomous investment Indicate how the aggregate demand curve shifts and label the new equilibrium point B W hat fiscal policy response s and monetary policy responses will offset the decline in aggregate demand and return the economy to the initial equilibrium. S how this in your multiplier model graph To make a recession less severe the government can use monetary and fiscal policy to offset declines in aggregate demand. The central bank can cut interest rates. The government can increase government spending and or cut income tax rates. This mix of monetary and fiscal policy this is often used to make recessions less severe both in United States and elsewhere 10 b) Use a flow diagram to give the intuition for the transition from the initial equilibrium point A to the e quilibrium point B in due to the decline in autonomous consumption and autonomous investment as you show in your graph for Part a). c) Use a flow diagram to give the intuition for the transition back to the initial equilibrium point A due to the fiscal and monetary policy response to the decline in aggregate demand as you show in your graph for Part a). 11 6 ) Negative (inflationary) supply shock and the Monetary Policy Dilemma From Problem Set 4, question 10 we saw that a negative supply shock , for example due to an increase in oil prices : • Causes Firms to increase prices so inflation rises: • causes the supply side equilibrium value of employment to decrease. • causes a positive bargaining gap (G ap>0 ) • If expected inflation remains anchored at the target 𝜋 𝑡 𝐸 = 2% , then inflation rises by the amount of the G ap , but doesn’t continue to rise. • If expected inflation is un anchored so 𝜋 𝑡 𝐸 = 𝜋 𝑡 − 1 , then i nflation to continue to rise a) The goal of monetary policy is to keep inflation close to an inflation target, for example close to 2% What does the central bank have to do in response to a negative supply shock to bring inflation back down to the inflation target ? Why does this pose a dilemma if there is a negative supply shock rather than a positive demand shock ? Assum e inflation is initially at its target value (for example 2%) and the economy is in a supply side equilibrium. T hen regardless of whether there's a negative (inflationary) supply shock or a positive demand shock, the resulting positive bargaining gap implies inflation increases. To bring inflation back down to the target value, monetary policy must increase the real interest rate resulting in a decrease in aggregate demand and hence a decrease in employment. In the case of a positive demand shock, this just brings employment back to where it was before the shock occurred. In the case of a negative supply shock to keep inflation at the target inflation requires employment to decrease to the new lower supply side equilibrium value. 12 T he dilemma for monetary policy : keeping inflation at the inflation target requires a lower level of employment and higher unemployment, if the negative supply shock lasts while keeping unemployment from increasing would result in increasing inflation, particularly if expected inflation is “unanchored”. b) To illustrate the Monetary Policy Dilemma of responding to a negative supply shock , r eproduce the WS - PS and PC graph s from the answer to problem set 4 question 10b). Below these two graphs draw the multiplier model graph and indicate what must happen to aggregate demand to keep inflation at the inflation target assuming the supply shock lasts 13 Following problem set 4 question 10 , the negative supply shock causes inflation to increase from 2 % to 5% point s A to B in the above graphs. If expected inflation remains anchored at 2% , then the central bank needs to raise interest rates to bring inflation back down to 2% Higher interest rates reduce investment spending resulting in a shift down in the AD curve This is shown by moving from point B to C in the above graphs. Employment and output both decrease so long as the supply shock lasts I f e xpected inflation becomes unanchored before the central bank raises interest rates , then inflation starts to accelerate, and the economy moves from points B up to D and so on Starting from point D, the central bank can stabilize inflation at 5% by increasing real interest rate s. T his is shown in the movement from point D to E in the graph s. Once inflation is stabilized at 5% , th e n to bring inflation back down to 2% require s the central bank t o increase interest rates yet again , causing a recession with eventually the economy returning to Point C with inflation at 2% c ) Monetary Policy Dilemma numerical example with Anchored Expected Inflation To further illustrate the Monetary Policy Dilemma of dealing with a negative (inflationary) supply shock consider the following numerical example. The central bank has an inflation target = 2% and assume that expected inflation is anchored at the inflation target 𝜋 𝑡 𝐸 = 2% Suppose in year 1 the economy is in a supply side equilibrium. Then in year 2 a negative supply shock hits the economy causing a bargaining gap = 3%. In year 3 suppose that the central bank increases real interest rates to return inflation to the inflation target. What is the value of the bargaining gap in year 3. In year 4 the economy is in the new supply side equilibrium. Given all these assumptions complete the table below Year (t) 𝐺𝑎𝑝 𝑡 Anchored inflation 𝜋 𝑡 𝐸 = 2% 𝜋 𝑡 1 0% 2 % 2 % 2 3% 2 % 5 % 3 0% 2 % 2 % 4 0 % 2 % 2 % d ) Monetary Policy Dilemma numerical example with Unanchored Expected Inflation Now suppose that expected inflation in unanchored so 𝜋 𝑡 𝐸 = 𝜋 𝑡 − 1 Again, assume that t he central bank has an inflation target = 2% Suppose in year 1, the economy is in a supply side equilibrium with 𝜋 1 𝐸 = 2% Then in year 2 a negative supply shock hits the economy causing a bargaining gap = 3%. In year 3 suppose that the central bank increases real interest rates to return inflation to the inflation target. What is the value of the bargaining gap in year 3 and 4 In year 4 the economy is in the new supply side equilibrium. Given all these assumptions complete the table below How do your answers compare to your answers to part c? Year (t) 𝐺𝑎𝑝 𝑡 Una nchored inflation 𝜋 𝑡 𝐸 = 𝜋 𝑡 − 1 𝜋 𝑡 1 0% 2 % 2 % 2 3% 2 % 5 % 3 - 7 % 5 % 2 % 4 0 % 2 % 2 % Comparing the answers to d) with the answers to c) shows that Expected inflation becomes unanchored then returning inflation to the inflation target requires a recession that is a 14 negative bargaining gap. Real interest rates in year 3 must be increased more if expected inflation is unanchored than when expected inflation is anchored. 7 ) The impact of macroeconomy Policy depends on the size of the multiplier. a) What determines the size of the multiplier? How does the size of the multiplier determine the impact of increases in government spending or cuts in real interest rates? Hint: Use the answers to problem set 3, question 10. In problem set three question 10 solved for the multiplier k: 𝒌 = 𝟏 𝟏 − 𝒄 𝟏 ( 𝟏 − 𝒕 ) + 𝒎 Hence the multiplier i s bigger ( ↑ k) if • the marginal propensity to consume increases ( ↑ 𝒄 𝟏 ) , • if the tax rate decreases ( ↓ t) • if the marginal propensity to import decreases ( ↓ m). Since 𝜟𝒀 = 𝒌 × ( 𝜟 𝒄 𝟎 + 𝜟 𝒂 𝟎 − 𝒂 𝟏 𝜟 𝒓 + 𝜟 𝑮 + 𝜟 𝑿 ) , t he impact on output of an increase in government spending or a cut in real interest rates is larger the larger is the multiplier: 𝜟𝒀 = 𝒌 × 𝜟𝑮 𝜟 𝒀 = − 𝒂 𝟏 𝜟 𝒓 b) As the economy goes into a recession, what is likely to happen to the fraction of households facing credit constraints? How does this change the multiplier and hence the impact of monetary and fiscal policy on aggregate demand? As the economy goes into recession the fraction of households facing credit constraints , that is having difficulty borrowing against future income , is likely to increase This results in an increase in the marginal propensity to consume which , in turn , increases the value of the multiplier A higher multiplier increases the impact of a given change in monetary or fiscal policy This suggests that monetary policy and fiscal policy are likely to have a bigger impact on aggregate demand in a recession. 8 ) “Automatic Stabilizers”, Recessions and Government Austerity Policy a) What happens automatically, ( that is without the government changing government spending on goods and services (G) or income tax rates (t) ) , to the government budget deficit ( 𝐺𝐵𝐷 = 𝐺 − 𝑡𝑌 ) when the economy goes into a recession? What happens to government debt due to the changes in the government budget deficit ? Recession → ↓ Y → ↓ tax revenue = tY → ↑ 𝑮𝑩𝑫 = 𝑮 − 𝒕𝒀 Hence recessions automatically result in bigger government budget deficits 15 If a government budget deficit is financed by borrowing, then bigger budget deficits lead to more government debt. b) S ome people argue that government budget deficits are always a bad thing, and that the government should always “ live within its means ” that is , always have a balanced budget even when the economy is in a recession Suppose the economy goes into a recession What would the government have to do with government spending and /or tax rates to keep the budget balance d? Would this make the recession better or worse ? Since a recession → ↓ Y → ↑ GBD, k eep ing GBD = 0 would require the government to ↓ G and/or ↑ t → ↓ AD → further ↓ Y making the recession worse! c) Does your answer to part b) explain why many economists (for example John Maynard Keynes) argue that budget deficits are OK in a recession ? When would be a good time to have a balanced budget ? Ye s, the answer to part b) suggests that a llowing the government budget deficit to increase in a recession is a good thing since it makes the recession less severe relative to trying to keep the budget balance d. A good time to balance the budget is when the economy is not in a recession a nd the central bank can offset declines in aggregate demand due to fiscal austerity ( ↓G and/or ↑t) by cutting interest rates 9 ) The invisible hand and the paradox of thrift O ne of the paradoxical ideas of microeconomics is the notion of the invisible hand The invisible hand argument claims that under certain conditions , such as perfect competition and no externalities , that each individual acting in their own self - interest results in a socially optimal outcome A short way of saying this is the invisible hand claims that individual private vice (individual greed ) can lead to social virtue (the collective good) Invisible hand argument: individuals acting in their own self interest results in the collective good. A paradoxical idea of macroeconomics is the “paradox of thrift”. According to the paradox of thrift argument, if each individual acts in their self - interest in choosing how much to consum e the resulting aggregate spending may result in a recession and high unemployment . This is an outcome that no one would choose. To summarize: Invisible hand argument: individuals acting in their own self - interest results in the collective good ( for example if there is sufficient competition between firms then there will be lots of high - quality goods at low prices) Paradox of Thrift argument: individuals acting in their own self - interest may result in a collective bad (recession, high unemployment) a) To illustrate the paradox of thrift argument, suppose some event such as a decline in autonomous investment causes the economy to go into a recession What happens to aggregate demand, output, employment, and c onsumption ? ↓ 𝒂 𝟎 → ↓ AD →↓ Y & ↓ N ( ↓output, ↓ employment) → ↓ income → ↓ Consumption 16 b) Given your answer to part a) what might individuals believe is their individual self - interest to do ? Will this lead to a good outcome from the standpoint of s ociety as a whole ? Why is this a p aradox of thrift? Given an economy with falling income and employment those individuals who are still employed might decide it's in their individual self - interest to de crease consumption, even though their incomes have yet to change , to try to increase their saving s so they can provide themselves self - insurance in an event that they too become unemployed This implies a decrease in autonomous consumption Since a decrease in autonomous consumption ( ↓c 0 ) further decreases aggregate demand make s the recession worse Hence everyone who is still employed deciding to try to save more results in more people becoming unemployed and having lower income s. This makes it likely that they will not be successful in saving more, particularly if they become unemployed This is a paradox of trying to be thrifty ! 10 ) The zero lower bound (on nominal interest rates) Our textbook argues that since people can always hold currency w hich doesn't pay interest , this implies that n ominal interest rate s cannot be below zero. For example , suppose Bala has a $100 bill which he is thinking about lending to Abby for one year . If Bala puts the $100 bill in his mattress and pulls it out one year later then he'll have a $100 bill (assuming the mattress didn't catch fire !). This implies that the nominal interest rate on currency equals zero. If Abby borrow s Bala’s $100 bill and offer s Bala a negative n ominal interest rate , for example i= - 5% this would imply that Abby in one year will pay Bala (1+i)$100 = $95. Since Bala could keep the $100 bill and earn i = 0 this suggests there is a “zero lower bound” on nominal interest rates: 𝑖 ≥ 𝑖 𝑍𝐿𝐵 = 0% a) Recall the function for investment spending and the Fisher Equation. How can central banks increase or decrease aggregate demand. Hint: The investment function was in problem set 3, question 7. The Fisher Equation which was discussed in question 3 above. Investment S p ending function : 𝑰 = 𝒂 𝟎 − 𝒂 𝟏 𝒓 implies that investment increases if real interest rates decrease ( ↓ r →↑ I) and investment spending increases if real interest rates increase ↓ r →↑ I) Fisher Equation: 𝒓 = 𝒊 − 𝝅 𝑬 implies that real interest rates equal the nominal interest rate minus expected inflation The central bank directly controls the nominal policy interest rate as we will discuss later in the course Expected inflation is just whatever people expect inflation to be in the future which is not controlled by the central bank but might be influenced by the central bank ’ s inflation target Hence according to the Fisher equation , the central bank can increase or decrease the real interest rate by increasing or decreasing the nominal policy interest rate assuming no change in expected inflation 17 b) How can Monetary Policy respond to m ake a recession le ss severe ? Does the zero lower bound on the nominal policy interest rate , limit what a central bank can do to make a recession less severe ? Suppose s ome event → ↓ AD → ↓ Y. To make the recession less severe the central bank must o ffset the decrease in aggregate demand. Decreasing nominal interest rates will decrease the real interest rate and increase investment spending and aggregate demand (central bank ↓i → ↓r →↑I → ↑AD). However, once the nominal policy interest rate hits zero ( ↓i to 𝒊 = 𝒊 𝒁𝑳𝑩 = 0%) then the central bank can no longer decrease the nominal policy interest rate. Hence the zero lower bound on nominal policy interest rates potentially limits the ability of central banks to make recessions less severe 1 1 ) Fear of Deflation a) Suppose some event decreases aggregate demand. What happens the bargaining gap, inflation and expected inflation, if expected inflation is unanchored? ↓ AD → ↓ Y & ↓ N → G ap <0 → ↓ 𝝅 → ↓ 𝝅 𝑬 b) How will monetary policy respond to a decrease in aggregate demand? What limits the monetary policy response. The central bank will ↓i → ↓r →↑I → ↑AD to try to offset the ↓AD The limit to this is 𝒊 ≥ 𝒊 𝒁𝑳𝑩 = 0%. c) Suppose that expected inflation is unanchored and the central bank has decreased the nominal policy interest rate to the zero lower bound, but output and employment are still below their supply side equilibrium values. What will be true about the bargai ning gap? What will be true about inflation, expected inflation, real interest rates and aggregate demand over time? Hint: You’ll need to use the Fisher Equation If 𝒊 = 𝒊 𝒁𝑳𝑩 = 0%. Then the Fisher equation implies 𝒓 = 𝒊 − 𝝅 𝑬 = − 𝝅 𝑬 so This process continues potentially leading to a deflationary spiral. Deflation is when inflation is negative. 1 2 ) Investment Spending revisited: investment and present value 18 So far, we’ve used the investment function 𝐼 = 𝑎 0 − 𝑎 1 𝑟 . This says that investment spending (purchases of new equipment and structures) increases if real interest rates decrease or if autonomous investment increases. An increase in expected profit from investment will increase autonomous investments. Now we're going to dig a little deeper into how to think about investment spending. a) Bala is considering an investment project which involves buying a piece of equipment that will cost $I today, wears out in one year, and provides a profit for sure of $X in one year. Bala’s alternative is to lend $I for one year and earn a real interest rate of r. Under what conditions should Bala buy the piece of equipment today ? With $I in funds today used for either lending or purchasing the equipment, Bala will get either: $X in one year if Bala buys the equipment today $I(1+r) in one year if Bala lends today Bala should buy the equipment if $X > $I(1+r) This is equivalent to saying Bala should buy the equipment if 𝑵𝑷𝑽 = 𝑿 𝟏 + 𝒓 − 𝑰 ≥ 𝟎 Where NPV stands for Net Present Value b) Now Bala is considering the same project as before, but he is uncertain about the returns from purchasing the equipment. Now Bala expects his profits to be $ 𝑋 𝐸 in one year. In addition, Bala now requires an additional return, a risk premium (RP), on the investment project to get him to purchase the equipment. Bala’s alternative is to lend $I for one year and learn a real interest rate of r, which given his risk aversion he values the safe return at his “discount rate” 𝑑 = 𝑟 + 𝑅𝑃 . Under what conditions should Bala buy the piece of equipment today? With $I in funds today used to either lending or purchasing the equipment, Bala will either buy the equipment or lend. If Bala buys the equipment today, he e xpects to get $ 𝑋 𝐸 in one year I f Bala lends today he values his future safe returns in one year as $ 𝑰 ( 𝟏 + 𝒓 + 𝑹𝑷 ) Bala should buy the equipment if $ 𝑿 𝑬 > $ 𝑰 ( 𝟏 + 𝒓 + 𝑹𝑷 ) This is equivalent to saying Bala should buy the equipment if 𝑵𝑷𝑽 = 𝑿 𝑬 𝟏 + 𝒓 + 𝑹𝑷 − 𝑰 ≥ 𝟎 Where NPV stands for Net Present Value c) Given your answer to part b) what can say about what will cause investment spending to increase or decrease? Since firms’ investment if 𝑵𝑷𝑽 = 𝑿 𝑬 𝟏 + 𝒓 + 𝑹𝑷 − 𝑰 ≥ 𝟎 , Investment spending increases if ↑ 𝑿 𝑬 , ↓ 𝒓 and/or ↓ RP. Investment spending decreases if ↓ 𝑿 𝑬 , ↑ 𝒓 and/or ↑ RP 1 3 ) Monetary policy and exchange rates Our textbook defines the nominal exchange rate (e) as the ratio of local currency per unit of foreign currency For example, for the US this would be U.S. dollars per euro 𝑒 ≡ $/€ 19 What matters for spending on US exports (Europeans buying US goods and services) and US imports (Americans buy Euro area goods and services) is the “real exchange rate” which out textbook denotes “c” 𝑟𝑒𝑎𝑙 𝑒𝑥𝑐 ℎ 𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑒 ( 𝑐 ) ≡ 𝑒 𝑃 ∗ 𝑃 Where 𝑃 ∗ is the foreign price level (for example €/euro good) and P is the local price level ($/US good). a) What causes the real exchange rate to increase (↑c)? In this case , are local goods (US goods) or foreign goods (Euro goods) becoming relatively more expensive? What happens to local exports and local imports? ↑c if ↑e, ↑ 𝑷 ∗ or ↓P a “real depreciation” of the local currency relative to the foreign currency because: ↓ e → ↓ amount of local currency ($) it takes to buy foreign currency (€) → local currency is depreciating, becoming less valuable relative to foreign currency → local goods become relatively cheaper than foreign goods. ↑ 𝑷 ∗ →↑ amount of foreign currency (€) it takes to buy foreign goods → holding e, and P constant local goods become relatively cheaper than foreign goods. ↓ P → ↓ amount of local currency ($) it takes to buy local goods → holding e, and 𝑷 ∗ constant local goods become relatively cheaper than foreign goods Hence if ↑ c “real depreciation” of the local currency relative to the foreign currency then local exports increase and local imports decrease. b) What is the relationship between the nominal exchange rate (e) and local int erest rates relative to foreign interest rates? If the central bank of the local country, (for example the Federal Reserve if the local country is the US), increases the policy interest rate then, everything else equal, portfolio managers will shift their funds out of the foreign country and into the local country. Portfolio managers will have to sell foreign currency for local currency, since local currency is needed to buy local bonds. An increased demand for the local currency will cause the local currency to appreciate. That is, it will take less loc al currency to buy a unit of foreign currency so the nominal exchange rate will go down: the local currency appreciates relative to the foreign currency therefore local country exports decreases and local country imports increase 20 1 4 ) Draw a flow diagram for the monetary policy transmission mechanism, showing how changes in the real policy interest rate change consumption, investment and net exports.