Term 2 week 5 RBC

Question 1

What is the relationship between output and consumption

Answer 1

Pro-cyclical with output

Consumption is slightly lessvolatile than output

Question 2

What is the relationship between output and investment

Answer 2

pro-cyclical

More volatile than output

Question 3

What is the relationship between output and capital?

Answer 3

-a-cyclical

-Less volatile than output

Question 4

What is the relationship between output and hours per worker?

Answer 4

-Pro cyclical

-more volatile than output

Question 5

What is the realtionship between output and real wage

Answer 5

-Acyclical

-less volatile than output

Question 6

What is the relationship between output and TFP?

Answer 6

-Procyclical

-moderately less volatile than output

Question 7

What are business cycles

Why do they matter?

Answer 7

Short-term alterations from trend growth

They are a source of uncertainty and affect welfare

Question 8

What is RBC model and what does it explain and what is the set up?

Answer 8

-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)

Question 9

What is RBC theory?

Question 10

What is the setup of household in RBC model?

Answer 10

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)

Question 11

How can we write expected lifetime utility function?

What transformation is done for this through an assumption in RBC model

Answer 11

E0 sum of Beta^t[u(ct) + v(1-ht)]

• Households are said to have perfect expectations so expectation operator can be removed.

Question 12

What does the Beta t discount factor represent

Answer 12

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

Question 13

What is the budget constraint for households in RBC model

Answer 13

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

Question 14

How do you set up lagrange in RBC model?

Question 15

What is the firm’s set up in the RBC model?

Answer 15

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

Question 16

What is the maximisation problem for a household in the infinite periods for RBC model

How can we solve it

Answer 16

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

Question 17

How can you interpret the labour supply condition from the RBC model F.OC

Answer 17

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.

Question 18

What is the Euler equation and how can it be interpreted

Answer 18

This is the consumption path

u’(ct) = beta^t[1+rt-dep)u’(ct)]

Marginal cost of giving up one unit of consumption today

Question 19

How do you solve the RBC model by hand?

Answer 19

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.