macro exam 2

lessons of growth theory help us (3)

understand why poor countries are poor, design policies that can help them grow, and learn how our own growth rate is affected by shocks and our government’s policies

what benchmark is used against which most recent growth theories are compared - and what does it do

the Solow model looks at the determinants of economic growth and the standard of living in the long run

K in the solow growth model

not fixed - investment causes it to grow and depreciation causes it to shrink

L in the Solow growth model

not fixed - population growth causes it to grow

output per worker

y = Y/L

capital per worker

k = K/L

consumption function

c = (1-s)y

savings per worker

y - c

y - (1-s)y

= sy

investment

i = y-c = sy

output per worker is y= $80,000, and the savings rate is s=0.20. what is investment per worker

$16,000

Using y= $80,000 and s= 0.20, what is consumption per worker

$64,000

basic idea of capital accumulation

investment increases the capital stock, depreciation reduces it

change in capital stock formula

investment - depreciation

sf(k) (investment per worker) - depreciation

at the current capital stock, sf(k) = 24 and depreciation =30. what happens to capital per worker

change in capital per worker is -6, so k falls

steady state capital stock

change in capital = sf(k) - depreciation

what do catch up growth trends follow (ex)

low initial capital (low starting capital leads to higher marginal product leading to transition growth)

what happens when there is an increase in the savings rate

investment rises, causing k to grow toward a new steady state (higher s → higher k* → higher y*)

the solow model predicts that…

countries with higher rates of saving and investment will have higher levels of capital and income per worker in the long run

in the basic Solow model, an increase in the savings rate causes

a higher steady state level of output per worker, but no change in its long-run growth rate

how do we know which is the “best” steady state

it will have the highest possible consumption per person

c* = (1-s)f(k*)

how do we find the golden rule level of capital

on a graph, look at where the gap between f(k*) and depreciationk* is the biggest (MPK = depreciation)

how do we transition to the golden rule steady state when we start with too much capital

we need to decrease the savings rate so consumption immediately increases while investment immediately decreases and capital / output per worker gradually decreases

how do we transition to the golden rule steady state when we start with too little capital

we need to increase the savings rate so consumption immediately decreases while investment immediately increases and capital / output per worker gradually increases

at the golden rule steady state, which condition holds in the basic Solow model

MPK = depreciation

population growth

n = change in L / L

break even investment

(depreciation + n)k

motion of capital

sf(k) - (depreciation + n)k

or actual investment - breakeven investment

prediction of population growth rates in Solow model

countries with higher population growth rates will have lower levels of capital and income per worker in the long run

golden rule capital stock with population growth

MPK - depreciation = n

In the Solow model without technological progress, a higher population-growth rate n leads to

lower steady-state k and y per worker, with no change in their long-run growth rates

Malthus perspective on population growth

predicts population growth will outstrip the Earth’s ability to produce food, leading to impoverishment of humanity

Kremerian perspective on population growth

predicts that population growth contributes to economic growth

GDP per capita growth

real GDP growth - population growth

real GDP grows by 3% while population growth grows by 1%. approximately how fast does real GDP per person grow

2%

the solow growth model shows that in the long run a country’s standard of living depends

positively on its savings rate

negatively on its population growth rate

an increase in the savings rate leads to

higher output in the long run, faster growth temporarily but not faster steady-state growth

the solow growth model shows that a higher rate of population growth leads to

lower steady state level of capital per worker and output per worker

suppose an economy has production function f(k)= k^1/2, saving rate s=0.20, and a depreciation rate of 0.05. what is the steady state level of capital per worker (k*)

k* = 16

Which of the following best describes the nature of the Golden rule level of capital (k*gold) in the Solow model without technological progress

Specific steady state maximizing consumption per worker across possible savings rates

An economy starts in steady state with capital below Golden Rule (k* < k*gold). If policymakers raise saving rate s to reach Golden rule, what happens to consumption?

consumption drops initially, then gradually rises to a higher steady state level than before

An economy starts with capital above Golden Rule (k* > k*gold). if policymakers lower saving rate s to reach Golden Rule, what happens to consumption over time

consumption increases immediately and remains strictly higher at all times

in the solow model with depreciation rate and population growth rate, which condition characterizes the Golden Rule level of capital stock (k*gold)

MPK = depreciation + n

In the solow model with population growth rate and no technological progress (g=0), what are the steady-state growth rates of output per worker (y), total output (Y), and total capital (K)

y grows at rate 0 ; Y grows at rate n ; K grows at rate n

technological progress in the solow model

g = change in labor efficiency (E) / E

number of effective workers

L x E

increases in labor efficiency have the same effect on output as increases in the labor force

technological progress in the solow model

(depreciation + n + g)k = breakeven investment

capital per effective worker (symbol and steady state growth rate)

k = K / (L x E)

0

output per effective worker (symbol and steady state growth rate)

y = Y / (L x E)

0

output per worker (symbol and steady state growth rate)

(Y/L) = y x E

g

total output (symbol and steady state growth rate)

Y = y x E x l

n + g

population grows at n=2% per year, and labor efficiency grows at g=3% per year. in the steady state, how fast does total output Y grow

5%

the golden rule with technological progress

MPK - depreciation = n + g

suppose output per effective worker is y= square root of k. which savings rate leads to the golden rule steady state

50%

solow growth predicts conditional convergence:

countries converge to their own steady states, which are determined by saving, population growth, and education

countries A and B have the same savings rate, population growth, technology growth, and education. country A begins with less capital per worker. what does the Solow model predict

A grows faster while approaching the common steady state

differences in income per capita among countries can be due to differences in

capital (physical or human) per worker and the efficiency of production (the height of the production function)

possible explanations for the correlation between capital per worker and production efficiency

production efficiency encourages capital accumulation, capital accumulation has externalities that raise efficiency, a third unknown variable causes capital accumulation and efficiency to be higher in some countries than others

if (MPK - depreciation) > (n+g)

US economy is below the golden rule steady state and should increase s

if (MPK - depreciation) < (n+g)

US economy is above the golden rule steady state and should reduce s

to estimate (MPK - depreciation), what 3 facts should we use

1) k = 2.5y

2) depreciation of capital = 0.1y

3) MPK x k = 0.3y

suppose MPK - depreciation = 7% and n+g = 4%. what does the golden rule criterion imply

the economy is below the golden rule, increase saving

policy issues: how to increase the savings rate

reduce the government budget deficit or increase the budget surplus by increasing incentives for private savings (reduce capital tax, replace federal income tax with consumption tax, or expand tax incentives)

policy issues: allocating the economys investment

1) equalize tax treatment

2) industrial policy (gov should encourage investment in capital of certain types that private investors dont consider)

policy issues: encouraging technological progress

patent laws, tax incentives for R&D, grants to fund basic research at universities, industrial policy

key results from Solow model with tech progress

steady state growth rate of income per person depends solely on the exogenous rate of tech progress, the US has much less capital than the golden rule steady state

ways to increase the saving rate

increase public saving (reduce budget deficit), tax incentives for private saving

productivity slowdown

early 1970: productivity growth fell in the US and other countries

mid 1990: productivity growth increased, probably because of advances in information technology

late 2000: growth fell again because of global financial crisis and recession

empirical studies

solow model explains balanced growth (conditional convergence), cross country variation in living standards is due to differences in capital accumulation and in production efficiency

GDP and consumption volatility

consumption fluctuates less than GDP

GDP, consumption, and investment

investment fluctuates more than GDP or consumption

which series typically shows the largest percentage fluctuations over the business cycle

real investment

facts about the business cycle (4)

real GDP grew by about 3.1% per year, consumption is less volatile than investment when moving with GDP, unemployment tends to rise during recession and fall during expansion, Okun’s law describes the negative relationship between output growth and changes in unemployment

suppose Okun’s law is approximated by: GDP growth (%) = 3-2 x change in unemployment

if annual average unemployment rises from 5 to 6%, what GDP growth does this relationship predict

+1%

the leading economic index falls while the coincident economic index rises. which interpretation best fits these signals

current activity is expanding, while the outlook is weakening

sentiment-driven fluctuations

sentiment often weakens before or during a recession

firms face greater uncertainty and postpone investment. productive capacity remains unchanged. how would we represent this in the AD-AS model

aggregate demand shifts left

time horizons in macroeconomics

long run; prices adjust to changes in supply and demand

short run: many prices remain fixed or adjust slowly

classical macroeconomics: a recap (4)

• in the long run, capital, labor, and technology determine output

• changes in demand affect the price level without changing natural output in this model

• the classical model assumes complete price flexibility

• this framework describes the long run

policy changes when prices are sticky

• fiscal policy changes demand through government purchases and taxes

  • monetary policy changes demand through the money spply

the quantity equation

M x V = P x T

what represents a movement along an existing AD curve, rather than a shift of that curve

a higher price level reduces output demanded, with money and velocity fixed

if all prices are fixed at a predetermined level, what shape does SRAS have when output is on the horizontal axis and the price level is on the vertical axis

horizontal

using MV = PY, suppose the money supply increases by 10%. velocity remains constant, and the price level is fixed in the short run. what happens?

output rises by 10%, and the price level remains unchanged

the money supply rises permanently. velocity and natural output stays fixed. what does this model predict

output rises in the short run. only the price level is higher in the long run

the economy starts at natural output. money permanently rises by 10%. velocity and natural output stay unchanged. after prices fully adjust, what happens

output remains unchanged, and the price level rises by 10%

in a negative demand shock

AD shifts left, output falls in the short run, and output returns to Ybar

velocity falls by 20%. by how much must the central bank change the money supply to keep nominal spending, MV, unchanged

increase it by 25%

a temporary oil-price shock raises production costs without changing natural output. aggregate demand remains unchanged. what foes the model predict in the short run

a higher price level and lower output

stabilization policy

aims to reduce the severity of short-run economic fluctuations - policy must balance the effects on output and the price level

a supply shock: output falls

shifts SRAS up, the price level is higher and output is below Y bar

how to accomodate a supply shock

the central bank shifts AD to the right

output returns to Ybar at C, while the price level remains higher

an oil shock raises production costs. the central bank expands demand enough to restore natural output. what happens to the price level

it remains above its initial level

in the long run:

prices are flexible. output and employment return to their natural levels in the model

in the short run..

prices are sticky. shocks can move output and employment away from their natural levels

the curves in AD - AD model

AD slopes downward for given money supply and velocity, LRAS is vertical because factor supplies and technology determine natural output, SRAS is horizontal in this chapter’s simplified model because the price level is fixed

shocks and policy summary

demand and supply shocks cause short run fluctuations in output and employment, monetary policy can help stabilize output, after an adverse supply shock stabilizing output involves accepting a higher price level in this model