intermediate macroeconomics

both versions of the aggregate production functions with and without B (cobb douglas)

Y: aggregate output, K: aggregate physical capital (capital stock), L: labour force, A/B: index of productive efficiency

→ divide through by L to get

Y/L=Bk^α

y=Bk^α

what is K^. (fundamental equation)

capital accumulation (in this case without investment)

could be K^. = -δK

growth rate of L

assumed to be proportional to population

MPK =

r + δ

MPL=

w

total gross income equation Y=

Y=C+I+G+NX

no government and a closed economy: Y=

Y=C+I

rewriting S as gross national saving : S=

S=Y-C=I

saving behaviour, definition and equation

S=sY=I

• households save a constant fraction of their income s=S/Y

what are y, k, y^~, k^~

y=Y/L, k=K/L

y^~ = Y/AL , k^~=K/AL

output/capital per worker and output/capital per effective worker respectfully

what is k^.

fundamental equation for cobb douglas

what is gk (not in steady state)

what is k* (from the fundamental equation where k^.=0)

where k* is the steady state capital per worker

graphical representation of the fundamental equation

• k must always converge to k*

solow growth model graph

lines intersect at the steady-state capital per worker

where gk=0

technological growth

A^. / A = g

or ga=g

what is true about gk and gy at the stady state

gk=gy=0

equation for the growth rate of Y (gy) on the balanced growth path

• must always be true at any time t (given our production function)

equation for the growth rate of Y (gy) when the economy has reached the steady state

and n + g is the growth rate of AL, so Y* and K* grow at the same rate as AL

the fundamental equation, relationship betwen y^~ and k^~

check by dividing the production through by AL

if you rewrite K^.=sY-δK

equation for growth rate of k^~ gk^~

←equalising the right hand side of the previous two equations

gk^~ = sy^~/k^~ - (n+g+δ)k^~ = sk^~α - (n+g+δ)k^~

equation for k*^~

k*^~ is the steady state capital per effective worker

k*^~ constant implies that

g*k~ = 0

what happens to g*k at the steady state?

• the growth rate of capital is equal to the growth rate of labour

• at steady state only n or g can raise g*k so only an increase in the growth rate of labour or population growth rate

• population growth rate is zero at the steady state

what is true about k*, y*, K*, Y* (their growth over time)

• all are either constant or growing at rates n or n+g so an economy that has reached the steady-state is one that’s evolving along a balanced growth path (BGP)

capital-output ratio at the steady state

this is constant

steady-state impact of a high s and a low n

if a country starts at the steady state with a saving rate s

• let s increase to s’ : s’>s

• which changes the point at which the red sy^~ line intersects the (n+g+δ) from k(0)^~ to a slightly higher k*^~

• the decrease in n to n’ causes gradient of the blue (n+g+δ)k^~ to rotate clockwise to (n’+g+δ)k^~ to a higher k**^~ point of intersection between the lines

conditional convergence

when an economy’s growth rate is greater the further away it is from its steady state (on the balanced growth path)

• eg. diminishing returns to capital and the more slowly the decline, the slower the convergence rate

if two economies are identical in all aspects except from their initial k(t)^~

economies 1&2 have the same parameter values s, n, g, δ, the same A and same production frunction

if economy 1 starts of with a lower k(t)^~/k(t) then economy 1(poorer) will grow faster than economy 2 (richer)

in this case, there will be convergence of incomes per capita over time as the poorer economy 1 catches up with the richer economy 2

conditional convergence

in a group of similar countries or regions, the poorer should go faster

→ a prediction of the neoclassical growth model

absolute convergence

poor countries should faster than the rich ones

the idea of growth accounting

considering the change of GDP(Y) over an extended period of time and trying to “account for” this change by measuring the change in all the variables of the production function

eg. capital is split into:

• K(physical capital)- value of the capital stock

• H(human capital)- often measured by considering average educational attainment of people 15-65 yrs old

growth accounting example using ; Y=AK^0.5(H)^0.5

H=Lh (stock of aggregate) human capital, L: labour force, h: average human capital per worker

→ taking logs on both sides of the last equation and differentiating with respect to t gives:

gy = ga + 1/2gk +1/2gL + 1/2gh

→ using r.h.s of equation there are 4 sources of GDP growth

• K accumulation

• growth in L (greater population/greater fraction of population in labour force)

• h accumulation (improvement in educational attainment)

• A accumulation (eg. better technology, structural change)

gy, gk, gL(n), gh can all be measured so ga (our g) can therefore be determined as a residual

steady state values of gy, gk, gal

g*y=n+g

gal = ga + gL = g + n

g*y = g

→ where growth rate of output per worker is only determined by g(growth rate of technology) where y=Y/L

2 key elements of government spending

1. expenditure on consumption of goods and services and “public capital” (eg. new hospital)

this is the G of the national income accounts identity equation

1. transfer payments (eg. state pensions, job seeker’s allowance, incapacity benefits, maternity pay)

affects C via its impact on household income

government spending redistributes resources in various ways (over a lifetime, across households, across generations)

over an individual’s lifetime:

• pay taxes (in net terms) when “young” [20s-50s]

• receive benefits (in kind and in cash) when “old”

across households:

• pay high taxes if “on high income”

• receive benefits if “on low income”

across generations:

• introduce a state pension system with no contribution condition

• or make the system more generous

what is sovereign debt

when a national government borrows money by issuing various securities

• can be issued in domestic/foreign currency exposing the issuer to currency risk

• credit ratings assess the likelihood of a country honouring its debt obligations, impacting borrowing terms

• usually through bonds, bills or loans to fund public investment and support the economy

sovereign debt crises manifest themselves in many ways, including

• downgradings by rating agencies

• large increases in the cost of borrowing

• difficulty borrowing in financial markets

• sell-off assets denominated in home currency (a “run on the currency”

general government balance sheet (GIBC)

components are;

• financial assets

• nonfinancial assets

• debt liabilities

• nondebt liabilities

“nondebt” liabilities in the GIBC

public sector/service pensions:

• these rights are legally binding (established by employment contract)

• these rights have already been earned by current and past state employees

• in the uk, this is bigger than “debt”

financial assets in the GIBC

• loans to the private sector

• equity and investment fund shares

nonfinancial assets

• land, buildings

• mineral resources

public sector balance sheet PSBS

GIBC plus public corporation assets and liabilites

components:

• “nondebt” and public corporations liabilities

• assets and public corporation assets

“nondebt” and public corporation liabilities in PSBS

• public sector/ service pensions

• liabilities of state-owned banks

• liabilities of insurance companies

• monetary base (central bank)

assets in the PSBS

• land, buildings, mineral resources

• loans to the private sector

• liabilities of state-owned banks

• liabilities of insurance companies

• equity & investment fund shares

• sovereign debt held by the bank

intertemporal public sector balance sheet (IPSBS)

essentially, adding the present value of future spending and revenues to the PSBS

components:

• financial assets

• nonfinancial assets

• public corporation assets

• future revenues

• debt

• nondebt

• public corporation liabilities

• future spending

future spending in the (ISPSBS)

• state pension spending

• health (NHS) spending

• long-term care spending

• education spending

future revenues in the IPSBS

• taxation

• profits from state-owned corporations

• returns from other state-held assets

• seigniorage (by central bank)

what determines a solvent government

a solvent government must have IPSBS with an assets/inflows side at least as big as the liabilities/outflows side

what a non-solvent government looks like

future revenues < future spending

what a solvent government looks like

future revenues ≥ future spending