Term 2 week 5 RBC Flashcards
What is the relationship between output and consumption
Pro-cyclical with output
Consumption is slightly lessvolatile than output
What is the relationship between output and investment
pro-cyclical
More volatile than output
What is the relationship between output and capital?
-a-cyclical
-Less volatile than output
What is the relationship between output and hours per worker?
-Pro cyclical
-more volatile than output
What is the realtionship between output and real wage
-Acyclical
-less volatile than output
What is the relationship between output and TFP?
-Procyclical
-moderately less volatile than output
What are business cycles
Why do they matter?
Short-term alterations from trend growth
They are a source of uncertainty and affect welfare
What is RBC model and what does it explain and what is the set up?
-RBC model explains causes of business cycle
Frictionless model, all markets are competitve
Exogenous TFP shocks, drive the economy
These are real shocks and impact the supply side of the economy
Fluctuations are efficient responses to shocks (no role for policy)
What is RBC theory?
What is the setup of household in RBC model?
Inifintely lived agent
They decide, consumption, savings and labour
Faces a dynamic problem as savings today impact future consumption
They can work ht or have leisure lt
lt = 1- ht
They like leisure and do not like work
The utility function = u(ct) + v(1-ht)
How can we write expected lifetime utility function?
What transformation is done for this through an assumption in RBC model
E0 sum of Beta^t[u(ct) + v(1-ht)]
- Households are said to have perfect expectations so expectation operator can be removed.
What does the Beta t discount factor represent
patience parameter
The higher the level of beta, you care about the future just as much as the present
A lower value of beta suggests you do not care about the future
What is the budget constraint for households in RBC model
Expenditures = resoruces
Ct + Kt+1 = (1+rt-dep)Kt + wt.ht
Ct is value of consumption
Kt+1 is expenditure on investment
Kt(1+rt-dep) is gross return on capital
wt.ht is income from wages
How do you set up lagrange in RBC model?
What is the firm’s set up in the RBC model?
Yt = At . F(kt,ht)
They then maximise profits so
Max At . F(kt,ht) - wt. ht + rt. kt
Diff W.R.T to kt and ht and you get
MCK = MPK
MCH = MPH
What is the maximisation problem for a household in the infinite periods for RBC model
How can we solve it
Max lifetime utility in all t , ct, ht and kt+1 S.T B.C in all time t
u’(ct) = lamdat
v’(1-ht) = lamdat . wt
lamdat = lamdat+1 . Beta(1+rt+1-depreciation)
Combine 1 and 2
Yields intertemporal optimality condition for labour supply (1)
Yields Euler equation (2)
Using BC (3)
Using 1,2 ,3 we can solve
How can you interpret the labour supply condition from the RBC model F.OC
v’(1-ht) = u’(ct) .wt
Marginal cost of working an extra hour = marginal utility of working an extra hour consumption x wage
This also yields substition effect as if w increases you want to increase ht
However, then income effect as if wage increases you will decrease wage.
What is the Euler equation and how can it be interpreted
This is the consumption path
u’(ct) = beta^t[1+rt-dep)u’(ct)]
Marginal cost of giving up one unit of consumption today
How do you solve the RBC model by hand?
You list out all the parts of the inifinite problem but are only interested in ct, ht and Kt+1 but then you must take derivative only for this.
