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UO / Economics / ECON 313 / Define okun's law.

# Define okun's law. Description

##### Description: Econ 313 Study guide  Output  ● The most common measure of output is Real Gross Domestic Product
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Econ 313 Study guide

## Define okun's law. Output

● The most common measure of output is Real Gross Domestic Product. ● We also often are interested in Real GDP per person (per capita)

Unemployment

● : the proportion of people in the labor force who don’t have a job but are actively looking for one.

Inflation

● Inflation measures how much prices are increasing over time

● ”hyperinflation” extremely high inflation rates

GDP

● value of final goods and services produced in the economy.

● GDP is also equivalent to the total income (wages, profits, etc) in the economy. ● Value added is simply the final good sales price less the cost of intermediate goods.

Y = C + I + G + (X − IM) GDP is the sum of Consumption, Investment, Government Spending, and net exports.

## How costly it is for the rm to replace a worker? C = consumption I= Investment G=govt spending (X­IM) = exports ­imports

Y Real GDP ­ constant base year prices (better measure) \$Y Nominal­ Price adjusts each year

Employment, Labor force, Working Pop If you want to learn more check out What do companies call a set of benefits that they promise to consumers to satisfy their needs?

Population =P Labor force =L unemployes =U Employed=E NILf= Not in labor force

UR= Unemployment rate LFPR= Labor force participation rate

P= L+NILF L= U+E UR=U/L LFPR= L/P

discouraged workers­unemployed people dropping out of the labor force.

The GDP deflator is the ratio of nominal to real GDP: Pt = \$Yt/ Yt .

The CPI is the price of the ”CPI basket” in current dollars. Inflation is the percent change in these price indices: π =( P−P*)/( P*) P*= last year

Okun’s law​­ I the relationship between output growth and the change in the unemployment rate is negative, linear, and has a slope of about −0.5.

## What are the two main determinants of growth? Phillips curve​­ that there is a tradeoff between unemployment and inflation (at least in the short run).

Together, these relations point to the central lesson of economics: we want high growth, low inflation and low unemployment, but it might be impossible to accomplish all three. Don't forget about the age old question of Why is trn important?

Investment

● Residential investment is all purchases of new homes and apartments by households. I

● Non­residential investment is all purchases of plants, machinery, equipment, software and intellectual property by firms I Don't forget about the age old question of What does a molecular equation show?

● Inventory investment is all final goods and services produced by firms in one year but kept “in inventory” for future years.

Assumptions

● All firms produce a single good, which is used for investment and consumption. I ● Firms are price­takers and are willing to supply any amount of the good at the market price p. I

● The price of goods is fixed in the short run. I

● The economy is closed, so that X = IM = 0.

● Z ≡ C + I + G. is demand equation

Consumption

● The most important determinant of consumption is disposable income (YD) ● C = Co +C1 YD

● c1 is the marginal propensity to consume (MPC).

● c0­ autonomous consumption the portion of consumption which doesn’t vary with income

● C = c0 + c1 (Y − T) with taxes included

Equilibriums

● Y (Output/GDP) = 1 /(1 − c1 ) * (c0 − c1T + I+ G)

● multiplier(x term) autonomous spending(intercept term)

● know how to interpret changes

● Production is determined by demand, production is equal to income and demand is determined by income. If you want to learn more check out What does it mean to be an authority on something?

● The multiplier is the central mechanism by which changes spending affect output.

Investment & savings

● Private savings is S = YD − C

MOney demand

● people can hold their wealth either in money or in bonds.

● Money is a liquid asset that can be used to buy goods and services.

● Money is composed of: I

○ currency, which is provided by the government I

○ checkable deposits, which are provided by the financial sector.

● Bonds are illiquid assets that provide some return, but cannot be used for transactions.

Demand for \$

● If the interest rate is higher, households might be more likely to hold bonds ● How responsive the demand for money is to the interest rate is summarized by the liquidity function: L (i).

● We assume the level of transactions is equal to total (nominal) income. ● We can then summarize the relationship between the demand for money Md and the interest rate as Md = \$YL (i)

● L (i) represents a negative relationship between interest rates and money demand ● . As interest rates rise, households hold more bonds and less money. ● The demand for money increases with aggregate income If you want to learn more check out What do people think of themselves?

\$ supply and equilibrium

● In equilibrium, the supply of money equals money demand, so that M = \$YL (i)

Market operations

● n expansionary monetary policy, it buys bonds from banks and creates new money ● n contractionary monetary policy, it sells bonds, and destroys the money used to purchase them

Bond Prices

● interest rates (also called bond yields) can be calculated based on prices. ● Consider a bond that pays \$100 for sure in 1 year. If you were to pay \$PB for the bond today, then the rate of return is i = (100 − \$PB) /\$PB

● if we have an interest rate, we can figure the bond price from it: \$PB = 100 /(1 + i) ● Buy bonds and decrease rates sell bond and increase rate If you want to learn more check out What are the 2 most important powers of the federal courts?

Banks

● financial intermediaries, pool deposits from a large number of consumers and buy assets (make loans) I

● Not all financial intermediaries are banks, (e.g. mutual funds)

● Banks’ assets consist of loans and bonds. We assume that banks also hold some liquid assets as reserves.

● central bank money­ household currency and reserves of banks

Reserves

● e amount of cash that depositors withdraw might not be equal to the amount that depositors deposit

● required reserve ratios in order to prevent bank runs.

● .Money supply is now currency held by households and reserves held by banks ● Money demand is now the demand for reserves plus the demand for currency Demand for currency

● CUd = cMd D d = (1 − c) Md

Demand for reserves

● R d = θ (1 − c) Md θ= required reserves ratio

Demand for central bank \$

● H d = (c + θ (1 − c)) \$YL (i)

● H s = H d ⇒ H = (c + θ (1 − c)) \$YL (i) equilibrium

Money Multiplier

● Equilibrium: 1/ (c+θ(1−c)) H = \$YL (i)

● money multiplier can be thought of as the change in money supply due to successive purchases of bonds by banks.

ISLM model

● I the IS relation (which describes goods market equilibrium)

● LM relation (which describes money market equilibrium).

● describes how the money market and the goods market interact

IS: Goods Market Equilibrium

● loosen this assumption by allowing investment to depend on both output and the interest rate.

● assume that Investment now depends on two factors: the level of sales (i.e. output), and the interest rate.

● Y = C (Y − T) + I (Y , i) + G

● As before increases in output will increase investment and consumption and hence demand

● increases in the interest rate will lead to decreased investment, which will shift the goods market equilibrium curve downward

● Any change to autonomous spending will result in a shift of the IS Curve. ● Any change in autonomous spending that would shift the goods market equilibrium down will shift the IS curve back

LM relation

● M/ P = YL (i)

● Any change in interest rates or income is exhibited as a movement along the LM curve ● a change in any other variable will shift the LM curve.

Together

● the IS relation ­ which tells us how interest rates affect output IN the ● LM relation ­ which tells us how output affects interest rates.

● overall (general) equilibrium in the economy occurs goods market and the money market are in equilibrium simultaneously.

● Any point on the IS curve is an equilibrium in the goods market; Any point on the LM curve is an equilibrium in the money market

Fiscal Policy

● There are two policies that policymakers can use in the IS­LM model: I ● policymakers can change taxes and spending (fiscal policy) I Or they can change the money supply (monetary policy)

● both new equilibrium interest rate and equilibrium output are lower after fiscal contraction.

● Reducing the deficit will result in both lower output and lower interest rates ● Taxes do not affect the money market equilibrium directly, but they do affect the goods market through consumption.

Monetary policy

● We refer to an increase in the money supply as expansionary monetary policy (or a monetary expansion)

● A decrease in money supply is contractionary monetary policy (or monetary tightening).

● an increase in the money supply ­The equilibrium output in the IS­LM model is higher, and equilibrium interest rates are lower.

● Disposable income increases, so consumption and investment increases ● Since the interest rate falls and output is higher, investment increases as well. Policy mix

● monetary & fiscal authorities coordinate simultaneously using fiscal and monetary policy

● best way for deficit reduction; central bank expand \$ supply, fiscal reduce deficit Liquidity trap

● we have been assuming that the equilibrium interest rate is strictly positive. ● Near­zero interest rates and sluggish growth are rare.

● led to a large spike in the risk premium

● ”risky” bonds, lead to an increase in borrowing costs for firms, leading to to decrease in investment

● also led to a decrease in consumer confidence, leading to consumption decrease ● At an interest rate of zero, however, households are indifferentbetween purchasing bonds and holding money, since both have the same return.

● Graphically, the money demand curve becomes horizontal at an interest rate of zero. ● This is the liquidity trap ­ the central bank can increase liquid assets (liquidity) only so far before interest rates run into the ZLB and the Central bank loses its ability to increase output.

● fiscal policy is still effective at the zero lower bound.

● Additionally, central banks may be able to engage in ”unconventional monetary policy”.

Midterm 2

Econ 313

Labor market

● The unemployment rate is U /LF

● LFPR is (U+E)/P , and employment

● population ratio is E/P

● The household survey is designed to measure the unemployment rate ● The Establishment survey is designed to track employment (the number of jobs)

● If fewer hires, the chance of an unemployed worker finding a job falls ● If firms layoff workers, the employed experience a higher risk of losing their jobs

Wages

We now consider how wages are determined. This could be done in a

number of different ways:

● I Collective Bargaining is common for unionized jobs

● I Employers will often post wages (they set the wage, workers can take it or leave it) ● I If workers have scarce skills, they will often be able to negotiate for higher wages

The bargaining power of a worker depends on:

● How costly it is for the rm to replace a worker

● Required job skills

● How difficult it is for a worker to nd another job

● Labor market conditions

W = Pe F (u; z)

(­, +)

W denotes aggregate nominal wage

Pe denotes the expected price level

u denotes the unemployment rate (inversely related to wages)

z denotes all other variables that are positively correlated with wages

We can use this to establish a relationship between real wages and the markup over marginal cost, called the price­setting relation W/P=1/(1+m)

● At the natural rate of unemployment, we get the natural level of employment ● Nn = L(1 ­un) Yn = L(1 ­ un)

● Rearranging this equation, one can show that un = 1 ­ Yn/L Aggr Supply

● aggregate supply relation captures the effects of output on the price level, ● P = Pe(1 + m)F (1­Y/L, Z)

● This gives us a relation between the price level P, the expected price level Pe and output.

● the price level also depends on the markup m, the size of the labor force L and the catchall z, which includes, e.g. unemployment benets. Aggr Demand

● The aggregate demand relation captures the effect of the pricelevel on equilibrium output in the goods and money markets.

● Y = Y (M/P, G, T )

We can think of two equilibria then ­ a short run equilibrium, where

Pe is fixed, and a medium run equilibria where Pe is flexible.

short run, Pe isn't equal to the true price Medium run, wage setters revise expectations In the short run,

● I Output can be above or below the natural level of output

● I Changes in any of the variables that enter the AS or AD relation lead to changes in output and to changes in the price level

In the medium run,

● I Output returns to the natural level of output

● I This adjustment works through changes in the price level

● I When output is above the natural level of output, the price level increases which decreases demand and output

Monetary policy

● In the short run, expansionary monetary policy decreases interest ratesand increases output. It also slightly increases prices.

● I As time goes on, however, wage setters adjust their price expectations.If monetary policy pushed output past its natural rate, then the AS curve will shift up as price expectations catch up with real prices.

● I In the medium run, output cannot be pushed above its natural rate. Infact, the only medium run effect is an increase in prices.

Deficit reduction Philpis Curve

Let π denote the inflation rate and πe denote the expected inflationrate. Then with some annoying algebra, one can show that

● π = πe + (m + z) − αu

Substituting πe = 0 into Equation (2) yields

● πt = (m + z) − αut

wage­price spiral:

1. Low unemployment leads to higher nominal wages

2. This leads firms to increase prices and a higher price level

3. An increase in the price level leads workers to ask for higher wages nexttime wages are set 4. The higher nominal wage leads to further increases in the price level,etc.

● that before about 1960,inflation was more likely tooscillate around 0. ● After 1960, inflation is bothconsistently positive and morepersistent

πt = θπt− 1 + (m + z) − αut

If θ = 0, then we just have the original Phillips Curve.

If 0 < θ < 1, then inflation depends on last periods inflation, but on aless than one for one basis.

For θ = 1:

As the value of θ increased from0 to 1, the original Phillips curverelationship disappeared. This relation is often called the expectations augmented Phillips curve.

πt − πt− 1 = −α(ut − un)

● When unemployment is above its natural rate, inflation is decreasing;when unemployment is below its natural rate, inflation is increasing.

● At ut = un, inflation isn’t changing.

● Hence another name for the natural rate of unemployment is oftenthe NAIRU ­ the non­accelerating inflation rate of unemployment.

since 1970 in the U.S., the average rateof unemployment required to keep inflation constant has been equalto 6%.

Neutrality of Money

If unemployment is at it’s natural level, then the aggregate demandrelation becomes Yn = Y(M/P, G, T)

● Let gM be the growth rate of money. Assume that π, the growth rate of prices (inflation) is above zero. Then ∆M P= 0 → π = gM

● In the medium run, the rate of inflation is determined by the rate of money growth

Nothing about the Phillips curve relationship we’ve studied requires itto be constant over time, nor across different countries.

he natural rate of unemployment depends on factors that affectwages (z), firms’ markups over marginal cost (m), and the response of

inflation to unemploymentThere’s no reason these are the same across countries.

Lucas Critique​: estimates of relationships from past data may notaccurately predict future outcomes if people’s expectations change

Wage Indexation: a provision thatautomatically adjusts wages for inflation ● This leads to a stronger response of inflation to unemployment

the PhillipsCurve relation breaks downwhen there is deflation.

Expectations

Nominla vs Interest rate

real interest rates

● Real interest rates are expressed in terms of units of goods

● if we borrow 1 unit of goods at a real interest rate ofr = 0.05, we agree to pay back 1 +r= 1. 05 units of goods in the future.

● nominal interest rates are real interest rates adjust for expected ination

1 +r=(1 +i) /(1 +et+1)

R = i­ π t+1

investment will depend on the real interest rate

r=i­ π^e

The interest rate that central banks can affect is the nominal interest rateI The interest rate that affects output is the real interest rateI

So the effectiveness of monetary policy depends on how changes in the nominal interest rate translate into changes in the real interest rate.

Discounted present values

● the value ofnunits of goods next year in terms of today'sconsumption is n/(1+r)

● the present value of consuming n units in two periods

1/(1+rt)(1+rt+1) * n

● The expected discounted present value of a flow of consumption is V=zt+1/(1 +rt) zet+1+ 1/(1 +rt) (1 +ret+1) zet+2

households care only about consumption ofgoods,so they discount by the real interest rate: V(YeL­TeL) =1/(1 +ret) (Yet+­Tet) +1/ (1 +ret)(1 +ret1)+ (Yet2 ­Tet2)….

assume that consumption depends on both current disposable income, as well as the discounted present value of future disposable income:

C=C(Yt­Tt, V(YeL­TeL))

Econ 313 post midterm 2

Long run growth

∙ Our measure of the standard of living in a country is then output per person  not total output.

Across counties: Exchange rates vary a lot over time and this variation does not re  exchanges in the standard of living in a country

∙ Wide exchange rate swings are quite common

∙ Exchange rates only tell us about the relative price of tradable goods.

Cost of living - the price of tradable and non-tradable goods and services - varies  across countries

We can do this by calculating GDP using a common set of prices for all countries -  including non-tradable goods - purchasing power parity

Convergence: the further away from the “steady state” a country is, the faster its  growth rates.

∙ Its hard to make general statements, but Asian countries exhibited  convergence & not African countries

∙ As China begins to catch up to richer countries like the US and the EU, it will  almost surely see its growth rates decline

Solow Model

two main determinants of growth –

1. capital accumulation,

2. technological progress.

aggregate production function: Y= F(K,N)

∙ Capital is the total amount of physical plants, machinery and software used in production

∙ Labor is the number of workers employed by firms.

Assume

∙ constant returns to scale (CRTS): if we double both the number of workers  and the amount of capital in the economy, output will double:

∙ diminishing returns to capital Each additional unit of capital we add to the  economy produces a smaller increase in output (production function is  concave)

Y/N is output per worker or average output; K/N is the capital-labor ratio

Growth in Solow Model

∙ Increases in capital per worker – capital accumulation

∙ Improvements in the state of technology – technological progress

∙ Capital accumulation by itself cannot sustain growth permanently (decreeing  returns)

Assumption 1: size of the population is constant, and all people work (so that N is  constant)

Assumption 2: There is no technological progress

Assumption 3: The economy is closed

Assumption 4: Public saving is equal to zero

Assumption 5: Private saving is proportional to income

absent any investment, capital depreciates (wears out) at a fixed rate δ. (Kt+1/N) – (Kt/N) = sf( Kt/N) – δ( Kt/N)

The change in capital per worker from year to year depends on:  ∙ Investment per worker in the previous period, sf (Kt/N)

∙ Deprecation per worker in the previous period, δ(Kt/N)

State which output per worker & capital per worker are not changing =steady  state the economy

∙ Y*/N = f (K*/N)

How does the saving rate affect the growth rate of output per worker? 1. The saving rate has no effect the long run growth rate of output per worker,  which is zero.

2. The saving rate determines the steady state level of output per worker in the  long run

3. increase in the saving rate leads to higher growth of output per worker for a  time, not forever

Saving Rate & consumption

Governments can affect the saving rate through policy

∙ directly: Public saving is affected by government spending adjustments ∙ indirectly: Private saving is affected by changes in taxes

What should the saving rate be?

∙ If the saving rate is zero (and always has been) there is no capital  accumulation and hence no output. This in turn implies that consumption is  zero.

∙ If the saving rate is one, people save all their income - capital accumulation  and hence output is very high, but consumption is zero

∙ There must be some value of the saving rate between zero and one that  maximizes the steady-state level of consumption; this is golden rule  savings rate

Technology

∙ lead to more output for a given quantity of inputs

∙ lead to a larger variety of product

State of Technology - how much output can be produced from given capital and  labor at any time.

∙ AN is called effective labor (or sometimes “effective worker”) ∙ When add in technology, interested in output per effective worker, capital per effective worker

Y/AN = f (K/AN)

Including assumption that public saving is zero= Y/AN = sf (K/AN)

Let δ be the depreciation rate of capital

gA be the rate of technological progress

gN be the population growth rate

Assume the population is composed of workers, population growth rate same as the growth rate of the labor force- the growth rate of effective labor is gA + gN

capital accumulation per effective worker (t are time subscripts)   (Kt1/ At1 Nt1) – (Kt / At Nt) = sf (Kt/ At Nt ) – (δ +ga +gn ) (Kt/ At Nt) ∙ graphically this parallels the Solow growth model graph from the previous  chapter

∙ in a steady state, output per effective worker does not grow at all ∙ output per worker grows at rate gA

Because output, capital, & effective labor grow at gA + gN in steady state = state  of balanced growth.

Two scenarios in which a country might see fast growth rates:

∙ country might be experiencing steady state growth in output per worker (high technology growth

∙ Country has temporarily fast growth due to capital accumulation, transitions  steady states.

If growth of output in excess tech. growth, the economy is in transition between  steady states

If the growth of output = growth of technology we are on a balanced growth path Growth rate of technology, gA = (1/ 1- α) [gY − (αgK + (1 − α) gN)]

Technological Progress, Output and Unemployment in the Short Run ∙ No longer assume that the entire population works

∙ the AS and AD relations now depend on technology

∙ An increase in A unambiguously shifts the AS curve down

∙ If tech. creates a major invention, might lead increase consumer confidence.  shift AD right.

∙ If tech. makes inventions more efficient, might decrease consumer sentiment. shift AD left.

∙ Output growth tends to exceed productivity growth, expect technology  increases employment.

Medium Run

∙ Converge back to the natural rate of unemployment.

Technological unemployment -argues that technological progress leads to  increases in unemployment

A more plausible argument of technological unemployment is that: ∙ unusually high technological progress is associated with higher natural rate of unemployment

∙ unusually low technological progress is associated with a lower natural rate of unemployed

AF(u, z) =A/ 1 + m → F(u, z) = 1/ 1 + m

∙ The natural rate of unemployment is independent of technology

Implications:

1. The natural rate of unemployment should not depend on the level of  productivity

2. The natural rate of unemployment should not depend on the rate of  productivity growth

∙ In short run, there is no relation between movements in productivity growth & unemployment

∙ In the medium run, if there is a relation, it is an inverse relation. ∙ Fears of tech. unemployment come from structural change of economy due  to tech. progress.

∙ Structural change may mean that some workers’ skills will no longer be in  demand

Wage Inequality

Over the last 25 years, the U.S. has experienced a large increase in wage. Much of this increase in inequality may be due technological change. ∙ Skill-biased tech. change leads to larger returns to skill, new tech. requires educated workers

∙ There’s no reason to believe that the trends in relative demand are going to  continue forever

the top share 1% is cyclical: it goes down in recessions

We see increasing inequality from the 1970’s onward.

after the mid-1990’s inequality seems to be increasing much more slowly. Since 1990, some states have become more unequal, others, like New York, are  actually more equal.

∙ Inequality might lead to lower growth rates over time.

∙ Inequality might lead to increased indebtedness, making financial crises more likely

∙ Inequality can lead to political polarization.

Econ 313 Study guide

Output

● The most common measure of output is Real Gross Domestic Product. ● We also often are interested in Real GDP per person (per capita)

Unemployment

● : the proportion of people in the labor force who don’t have a job but are actively looking for one.

Inflation

● Inflation measures how much prices are increasing over time

● ”hyperinflation” extremely high inflation rates

GDP

● value of final goods and services produced in the economy.

● GDP is also equivalent to the total income (wages, profits, etc) in the economy. ● Value added is simply the final good sales price less the cost of intermediate goods.

Y = C + I + G + (X − IM) GDP is the sum of Consumption, Investment, Government Spending, and net exports.

C = consumption I= Investment G=govt spending (X­IM) = exports ­imports

Y Real GDP ­ constant base year prices (better measure) \$Y Nominal­ Price adjusts each year

Employment, Labor force, Working Pop

Population =P Labor force =L unemployes =U Employed=E NILf= Not in labor force

UR= Unemployment rate LFPR= Labor force participation rate

P= L+NILF L= U+E UR=U/L LFPR= L/P

discouraged workers­unemployed people dropping out of the labor force.

The GDP deflator is the ratio of nominal to real GDP: Pt = \$Yt/ Yt .

The CPI is the price of the ”CPI basket” in current dollars. Inflation is the percent change in these price indices: π =( P−P*)/( P*) P*= last year

Okun’s law​­ I the relationship between output growth and the change in the unemployment rate is negative, linear, and has a slope of about −0.5.

Phillips curve​­ that there is a tradeoff between unemployment and inflation (at least in the short run).

Together, these relations point to the central lesson of economics: we want high growth, low inflation and low unemployment, but it might be impossible to accomplish all three.

Investment

● Residential investment is all purchases of new homes and apartments by households. I

● Non­residential investment is all purchases of plants, machinery, equipment, software and intellectual property by firms I

● Inventory investment is all final goods and services produced by firms in one year but kept “in inventory” for future years.

Assumptions

● All firms produce a single good, which is used for investment and consumption. I ● Firms are price­takers and are willing to supply any amount of the good at the market price p. I

● The price of goods is fixed in the short run. I

● The economy is closed, so that X = IM = 0.

● Z ≡ C + I + G. is demand equation

Consumption

● The most important determinant of consumption is disposable income (YD) ● C = Co +C1 YD

● c1 is the marginal propensity to consume (MPC).

● c0­ autonomous consumption the portion of consumption which doesn’t vary with income

● C = c0 + c1 (Y − T) with taxes included

Equilibriums

● Y (Output/GDP) = 1 /(1 − c1 ) * (c0 − c1T + I+ G)

● multiplier(x term) autonomous spending(intercept term)

● know how to interpret changes

● Production is determined by demand, production is equal to income and demand is determined by income.

● The multiplier is the central mechanism by which changes spending affect output.

Investment & savings

● Private savings is S = YD − C

MOney demand

● people can hold their wealth either in money or in bonds.

● Money is a liquid asset that can be used to buy goods and services.

● Money is composed of: I

○ currency, which is provided by the government I

○ checkable deposits, which are provided by the financial sector.

● Bonds are illiquid assets that provide some return, but cannot be used for transactions.

Demand for \$

● If the interest rate is higher, households might be more likely to hold bonds ● How responsive the demand for money is to the interest rate is summarized by the liquidity function: L (i).

● We assume the level of transactions is equal to total (nominal) income. ● We can then summarize the relationship between the demand for money Md and the interest rate as Md = \$YL (i)

● L (i) represents a negative relationship between interest rates and money demand ● . As interest rates rise, households hold more bonds and less money. ● The demand for money increases with aggregate income

\$ supply and equilibrium

● In equilibrium, the supply of money equals money demand, so that M = \$YL (i)

Market operations

● n expansionary monetary policy, it buys bonds from banks and creates new money ● n contractionary monetary policy, it sells bonds, and destroys the money used to purchase them

Bond Prices

● interest rates (also called bond yields) can be calculated based on prices. ● Consider a bond that pays \$100 for sure in 1 year. If you were to pay \$PB for the bond today, then the rate of return is i = (100 − \$PB) /\$PB

● if we have an interest rate, we can figure the bond price from it: \$PB = 100 /(1 + i) ● Buy bonds and decrease rates sell bond and increase rate

Banks

● financial intermediaries, pool deposits from a large number of consumers and buy assets (make loans) I

● Not all financial intermediaries are banks, (e.g. mutual funds)

● Banks’ assets consist of loans and bonds. We assume that banks also hold some liquid assets as reserves.

● central bank money­ household currency and reserves of banks

Reserves

● e amount of cash that depositors withdraw might not be equal to the amount that depositors deposit

● required reserve ratios in order to prevent bank runs.

● .Money supply is now currency held by households and reserves held by banks ● Money demand is now the demand for reserves plus the demand for currency Demand for currency

● CUd = cMd D d = (1 − c) Md

Demand for reserves

● R d = θ (1 − c) Md θ= required reserves ratio

Demand for central bank \$

● H d = (c + θ (1 − c)) \$YL (i)

● H s = H d ⇒ H = (c + θ (1 − c)) \$YL (i) equilibrium

Money Multiplier

● Equilibrium: 1/ (c+θ(1−c)) H = \$YL (i)

● money multiplier can be thought of as the change in money supply due to successive purchases of bonds by banks.

ISLM model

● I the IS relation (which describes goods market equilibrium)

● LM relation (which describes money market equilibrium).

● describes how the money market and the goods market interact

IS: Goods Market Equilibrium

● loosen this assumption by allowing investment to depend on both output and the interest rate.

● assume that Investment now depends on two factors: the level of sales (i.e. output), and the interest rate.

● Y = C (Y − T) + I (Y , i) + G

● As before increases in output will increase investment and consumption and hence demand

● increases in the interest rate will lead to decreased investment, which will shift the goods market equilibrium curve downward

● Any change to autonomous spending will result in a shift of the IS Curve. ● Any change in autonomous spending that would shift the goods market equilibrium down will shift the IS curve back

LM relation

● M/ P = YL (i)

● Any change in interest rates or income is exhibited as a movement along the LM curve ● a change in any other variable will shift the LM curve.

Together

● the IS relation ­ which tells us how interest rates affect output IN the ● LM relation ­ which tells us how output affects interest rates.

● overall (general) equilibrium in the economy occurs goods market and the money market are in equilibrium simultaneously.

● Any point on the IS curve is an equilibrium in the goods market; Any point on the LM curve is an equilibrium in the money market

Fiscal Policy

● There are two policies that policymakers can use in the IS­LM model: I ● policymakers can change taxes and spending (fiscal policy) I Or they can change the money supply (monetary policy)

● both new equilibrium interest rate and equilibrium output are lower after fiscal contraction.

● Reducing the deficit will result in both lower output and lower interest rates ● Taxes do not affect the money market equilibrium directly, but they do affect the goods market through consumption.

Monetary policy

● We refer to an increase in the money supply as expansionary monetary policy (or a monetary expansion)

● A decrease in money supply is contractionary monetary policy (or monetary tightening).

● an increase in the money supply ­The equilibrium output in the IS­LM model is higher, and equilibrium interest rates are lower.

● Disposable income increases, so consumption and investment increases ● Since the interest rate falls and output is higher, investment increases as well. Policy mix

● monetary & fiscal authorities coordinate simultaneously using fiscal and monetary policy

● best way for deficit reduction; central bank expand \$ supply, fiscal reduce deficit Liquidity trap

● we have been assuming that the equilibrium interest rate is strictly positive. ● Near­zero interest rates and sluggish growth are rare.

● led to a large spike in the risk premium

● ”risky” bonds, lead to an increase in borrowing costs for firms, leading to to decrease in investment

● also led to a decrease in consumer confidence, leading to consumption decrease ● At an interest rate of zero, however, households are indifferentbetween purchasing bonds and holding money, since both have the same return.

● Graphically, the money demand curve becomes horizontal at an interest rate of zero. ● This is the liquidity trap ­ the central bank can increase liquid assets (liquidity) only so far before interest rates run into the ZLB and the Central bank loses its ability to increase output.

● fiscal policy is still effective at the zero lower bound.

● Additionally, central banks may be able to engage in ”unconventional monetary policy”.

Midterm 2

Econ 313

Labor market

● The unemployment rate is U /LF

● LFPR is (U+E)/P , and employment

● population ratio is E/P

● The household survey is designed to measure the unemployment rate ● The Establishment survey is designed to track employment (the number of jobs)

● If fewer hires, the chance of an unemployed worker finding a job falls ● If firms layoff workers, the employed experience a higher risk of losing their jobs

Wages

We now consider how wages are determined. This could be done in a

number of different ways:

● I Collective Bargaining is common for unionized jobs

● I Employers will often post wages (they set the wage, workers can take it or leave it) ● I If workers have scarce skills, they will often be able to negotiate for higher wages

The bargaining power of a worker depends on:

● How costly it is for the rm to replace a worker

● Required job skills

● How difficult it is for a worker to nd another job

● Labor market conditions

W = Pe F (u; z)

(­, +)

W denotes aggregate nominal wage

Pe denotes the expected price level

u denotes the unemployment rate (inversely related to wages)

z denotes all other variables that are positively correlated with wages

We can use this to establish a relationship between real wages and the markup over marginal cost, called the price­setting relation W/P=1/(1+m)

● At the natural rate of unemployment, we get the natural level of employment ● Nn = L(1 ­un) Yn = L(1 ­ un)

● Rearranging this equation, one can show that un = 1 ­ Yn/L Aggr Supply

● aggregate supply relation captures the effects of output on the price level, ● P = Pe(1 + m)F (1­Y/L, Z)

● This gives us a relation between the price level P, the expected price level Pe and output.

● the price level also depends on the markup m, the size of the labor force L and the catchall z, which includes, e.g. unemployment benets. Aggr Demand

● The aggregate demand relation captures the effect of the pricelevel on equilibrium output in the goods and money markets.

● Y = Y (M/P, G, T )

We can think of two equilibria then ­ a short run equilibrium, where

Pe is fixed, and a medium run equilibria where Pe is flexible.

short run, Pe isn't equal to the true price Medium run, wage setters revise expectations In the short run,

● I Output can be above or below the natural level of output

● I Changes in any of the variables that enter the AS or AD relation lead to changes in output and to changes in the price level

In the medium run,

● I Output returns to the natural level of output

● I This adjustment works through changes in the price level

● I When output is above the natural level of output, the price level increases which decreases demand and output

Monetary policy

● In the short run, expansionary monetary policy decreases interest ratesand increases output. It also slightly increases prices.

● I As time goes on, however, wage setters adjust their price expectations.If monetary policy pushed output past its natural rate, then the AS curve will shift up as price expectations catch up with real prices.

● I In the medium run, output cannot be pushed above its natural rate. Infact, the only medium run effect is an increase in prices.

Deficit reduction Philpis Curve

Let π denote the inflation rate and πe denote the expected inflationrate. Then with some annoying algebra, one can show that

● π = πe + (m + z) − αu

Substituting πe = 0 into Equation (2) yields

● πt = (m + z) − αut

wage­price spiral:

1. Low unemployment leads to higher nominal wages

2. This leads firms to increase prices and a higher price level

3. An increase in the price level leads workers to ask for higher wages nexttime wages are set 4. The higher nominal wage leads to further increases in the price level,etc.

● that before about 1960,inflation was more likely tooscillate around 0. ● After 1960, inflation is bothconsistently positive and morepersistent

πt = θπt− 1 + (m + z) − αut

If θ = 0, then we just have the original Phillips Curve.

If 0 < θ < 1, then inflation depends on last periods inflation, but on aless than one for one basis.

For θ = 1:

As the value of θ increased from0 to 1, the original Phillips curverelationship disappeared. This relation is often called the expectations augmented Phillips curve.

πt − πt− 1 = −α(ut − un)

● When unemployment is above its natural rate, inflation is decreasing;when unemployment is below its natural rate, inflation is increasing.

● At ut = un, inflation isn’t changing.

● Hence another name for the natural rate of unemployment is oftenthe NAIRU ­ the non­accelerating inflation rate of unemployment.

since 1970 in the U.S., the average rateof unemployment required to keep inflation constant has been equalto 6%.

Neutrality of Money

If unemployment is at it’s natural level, then the aggregate demandrelation becomes Yn = Y(M/P, G, T)

● Let gM be the growth rate of money. Assume that π, the growth rate of prices (inflation) is above zero. Then ∆M P= 0 → π = gM

● In the medium run, the rate of inflation is determined by the rate of money growth

Nothing about the Phillips curve relationship we’ve studied requires itto be constant over time, nor across different countries.

he natural rate of unemployment depends on factors that affectwages (z), firms’ markups over marginal cost (m), and the response of

inflation to unemploymentThere’s no reason these are the same across countries.

Lucas Critique​: estimates of relationships from past data may notaccurately predict future outcomes if people’s expectations change

Wage Indexation: a provision thatautomatically adjusts wages for inflation ● This leads to a stronger response of inflation to unemployment

the PhillipsCurve relation breaks downwhen there is deflation.

Expectations

Nominla vs Interest rate

real interest rates

● Real interest rates are expressed in terms of units of goods

● if we borrow 1 unit of goods at a real interest rate ofr = 0.05, we agree to pay back 1 +r= 1. 05 units of goods in the future.

● nominal interest rates are real interest rates adjust for expected ination

1 +r=(1 +i) /(1 +et+1)

R = i­ π t+1

investment will depend on the real interest rate

r=i­ π^e

The interest rate that central banks can affect is the nominal interest rateI The interest rate that affects output is the real interest rateI

So the effectiveness of monetary policy depends on how changes in the nominal interest rate translate into changes in the real interest rate.

Discounted present values

● the value ofnunits of goods next year in terms of today'sconsumption is n/(1+r)

● the present value of consuming n units in two periods

1/(1+rt)(1+rt+1) * n

● The expected discounted present value of a flow of consumption is V=zt+1/(1 +rt) zet+1+ 1/(1 +rt) (1 +ret+1) zet+2

households care only about consumption ofgoods,so they discount by the real interest rate: V(YeL­TeL) =1/(1 +ret) (Yet+­Tet) +1/ (1 +ret)(1 +ret1)+ (Yet2 ­Tet2)….

assume that consumption depends on both current disposable income, as well as the discounted present value of future disposable income:

C=C(Yt­Tt, V(YeL­TeL))

Econ 313 post midterm 2

Long run growth

∙ Our measure of the standard of living in a country is then output per person  not total output.

Across counties: Exchange rates vary a lot over time and this variation does not re  exchanges in the standard of living in a country

∙ Wide exchange rate swings are quite common

∙ Exchange rates only tell us about the relative price of tradable goods.

Cost of living - the price of tradable and non-tradable goods and services - varies  across countries

We can do this by calculating GDP using a common set of prices for all countries -  including non-tradable goods - purchasing power parity

Convergence: the further away from the “steady state” a country is, the faster its  growth rates.

∙ Its hard to make general statements, but Asian countries exhibited  convergence & not African countries

∙ As China begins to catch up to richer countries like the US and the EU, it will  almost surely see its growth rates decline

Solow Model

two main determinants of growth –

1. capital accumulation,

2. technological progress.

aggregate production function: Y= F(K,N)

∙ Capital is the total amount of physical plants, machinery and software used in production

∙ Labor is the number of workers employed by firms.

Assume

∙ constant returns to scale (CRTS): if we double both the number of workers  and the amount of capital in the economy, output will double:

∙ diminishing returns to capital Each additional unit of capital we add to the  economy produces a smaller increase in output (production function is  concave)

Y/N is output per worker or average output; K/N is the capital-labor ratio

Growth in Solow Model

∙ Increases in capital per worker – capital accumulation

∙ Improvements in the state of technology – technological progress

∙ Capital accumulation by itself cannot sustain growth permanently (decreeing  returns)

Assumption 1: size of the population is constant, and all people work (so that N is  constant)

Assumption 2: There is no technological progress

Assumption 3: The economy is closed

Assumption 4: Public saving is equal to zero

Assumption 5: Private saving is proportional to income

absent any investment, capital depreciates (wears out) at a fixed rate δ. (Kt+1/N) – (Kt/N) = sf( Kt/N) – δ( Kt/N)

The change in capital per worker from year to year depends on:  ∙ Investment per worker in the previous period, sf (Kt/N)

∙ Deprecation per worker in the previous period, δ(Kt/N)

State which output per worker & capital per worker are not changing =steady  state the economy

∙ Y*/N = f (K*/N)

How does the saving rate affect the growth rate of output per worker? 1. The saving rate has no effect the long run growth rate of output per worker,  which is zero.

2. The saving rate determines the steady state level of output per worker in the  long run

3. increase in the saving rate leads to higher growth of output per worker for a  time, not forever

Saving Rate & consumption

Governments can affect the saving rate through policy

∙ directly: Public saving is affected by government spending adjustments ∙ indirectly: Private saving is affected by changes in taxes

What should the saving rate be?

∙ If the saving rate is zero (and always has been) there is no capital  accumulation and hence no output. This in turn implies that consumption is  zero.

∙ If the saving rate is one, people save all their income - capital accumulation  and hence output is very high, but consumption is zero

∙ There must be some value of the saving rate between zero and one that  maximizes the steady-state level of consumption; this is golden rule  savings rate

Technology

∙ lead to more output for a given quantity of inputs

∙ lead to a larger variety of product

State of Technology - how much output can be produced from given capital and  labor at any time.

∙ AN is called effective labor (or sometimes “effective worker”) ∙ When add in technology, interested in output per effective worker, capital per effective worker

Y/AN = f (K/AN)

Including assumption that public saving is zero= Y/AN = sf (K/AN)

Let δ be the depreciation rate of capital

gA be the rate of technological progress

gN be the population growth rate

Assume the population is composed of workers, population growth rate same as the growth rate of the labor force- the growth rate of effective labor is gA + gN

capital accumulation per effective worker (t are time subscripts)   (Kt1/ At1 Nt1) – (Kt / At Nt) = sf (Kt/ At Nt ) – (δ +ga +gn ) (Kt/ At Nt) ∙ graphically this parallels the Solow growth model graph from the previous  chapter

∙ in a steady state, output per effective worker does not grow at all ∙ output per worker grows at rate gA

Because output, capital, & effective labor grow at gA + gN in steady state = state  of balanced growth.

Two scenarios in which a country might see fast growth rates:

∙ country might be experiencing steady state growth in output per worker (high technology growth

∙ Country has temporarily fast growth due to capital accumulation, transitions  steady states.

If growth of output in excess tech. growth, the economy is in transition between  steady states

If the growth of output = growth of technology we are on a balanced growth path Growth rate of technology, gA = (1/ 1- α) [gY − (αgK + (1 − α) gN)]

Technological Progress, Output and Unemployment in the Short Run ∙ No longer assume that the entire population works

∙ the AS and AD relations now depend on technology

∙ An increase in A unambiguously shifts the AS curve down

∙ If tech. creates a major invention, might lead increase consumer confidence.  shift AD right.

∙ If tech. makes inventions more efficient, might decrease consumer sentiment. shift AD left.

∙ Output growth tends to exceed productivity growth, expect technology  increases employment.

Medium Run

∙ Converge back to the natural rate of unemployment.

Technological unemployment -argues that technological progress leads to  increases in unemployment

A more plausible argument of technological unemployment is that: ∙ unusually high technological progress is associated with higher natural rate of unemployment

∙ unusually low technological progress is associated with a lower natural rate of unemployed

AF(u, z) =A/ 1 + m → F(u, z) = 1/ 1 + m

∙ The natural rate of unemployment is independent of technology

Implications:

1. The natural rate of unemployment should not depend on the level of  productivity

2. The natural rate of unemployment should not depend on the rate of  productivity growth

∙ In short run, there is no relation between movements in productivity growth & unemployment

∙ In the medium run, if there is a relation, it is an inverse relation. ∙ Fears of tech. unemployment come from structural change of economy due  to tech. progress.

∙ Structural change may mean that some workers’ skills will no longer be in  demand

Wage Inequality

Over the last 25 years, the U.S. has experienced a large increase in wage. Much of this increase in inequality may be due technological change. ∙ Skill-biased tech. change leads to larger returns to skill, new tech. requires educated workers

∙ There’s no reason to believe that the trends in relative demand are going to  continue forever

the top share 1% is cyclical: it goes down in recessions

We see increasing inequality from the 1970’s onward.

after the mid-1990’s inequality seems to be increasing much more slowly. Since 1990, some states have become more unequal, others, like New York, are  actually more equal.

∙ Inequality might lead to lower growth rates over time.

∙ Inequality might lead to increased indebtedness, making financial crises more likely

∙ Inequality can lead to political polarization.

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