macro final

credible reserve bank

will get the inflation rate to equal to expected inflation rate

what happens to variables at the steady state

they all go to their natural or expected values

Fisher relation

nominal interest = real interest + inflation

Phillips curve formula

inflation_t = (1 − expec)base inflation + expec*prev inflation + (m + z) − unemp

what does the phillips curve state

negative relationship between the employment and the inflation rate, increasing unemployment lowers inflation

okuns law

positive relationship between output and employment

output gap

difference between acutal and nautral output

natural rate of employment

employment rate resulting when inflation is at expected rate

fisher relation

i = r+ inflation

credible reserve bank

makes inflation equal to the target rate

steady state

all variables reach their natural or target rates

what is the taylor rule

gives a value that the interest rate should be set to, given the inflation and unemployment statistics

original phillips curve formula

inflation = baseline inflation + (m+z) - alpha unemployment

original phillips curve

inflation is only effected by unemployment, expectations have no effect

modified phillips curve formula

inflation = last year inflation + (m+z) + alpha unemployment

modifed phillips curve

inflation is based on last years inflation and unemployment, showing that expectations around the inflation rate effect the rate

natural rate of unemployment

resulting unemployment when inflation = expected inflation

what does m + z mean in phillips curve

markup + any other factors effecting wages

conditions needed for steady state captial

savings time income is equal to depreciation times capital

determing wage forumula

wage = expected price times function of unemployment and catchall

natural rate of unemployment formula

real wage from wage setting is the same as the wage created by price settings

wage setting equasion

W/P = 1/(1+m)

how does output per worker change in the steady state with technological growth

it stays constant at the steady state

effective labour / worker

worker who has productive technology

how does output per effective worker change at the steady state

increases due to exogenous tech growth

what effects the change in output at the steady state with technology growth

growth of population and technology progress

how does captial and output change at the tech growth steady state

has an increase over time due to technology growth

what determines the level of capital needed to be produced

depreciation of capital and growth of population and tech

why is technology growth the most important for growth in solow model

because it causes a rise in output per worker, so overall output grows

what causes growth in capital and input at the steady state

growth of technology and population

why does output grow over time at the steady state

because of technology growth causing more efficient workers and higher output increasing workers

why does capital grow over time in the steady state

population growth create more workers who need capital, and growing tech means that more capital is needed to take advantage of new tech

how does labour number grow at steady state

grows with population growth

golden rule of savings

savings rate should maximise the consumption with the given level of capital

what happens to the growth of output when savings rate changes

momentary growth or shrinkage until it reaches the point assosiated with the new steady state, where it is constant

golden rule of capital

the level of capital that is maintainted at the golden level of savings

consumption per worker

c=(1-s) y

steady state condition

sy = depreciation * k

deriving the golden rule savings rate

find consumption per worker, substitute this into the steady state condition, and solve for consumption as a function of these, then differentate to give the maximum