Real Business Cycles

Question 1

What is a:

• Recession
• Depression
• Stagflation

Answer 1

*Recession: (simple definition) GDP decline for two consecutive quarters.

*Depression: A more severe and prolonged economics recession

*Stagflation: Low economic growth (may or may not be recession) and high inflation

Question 2

Rate non-cyclical, cyclical or very cyclical

• Consumption (total)
• Inventories
• Investments
• Non-durable goods -Services

Answer 2

*Consumption: cyclical (moves with GDP, but a little bit less)

*Investments: Very cyclical

*Non-durable goods: Very cyclical

*Services: non-cyclical (but still a little bit).

Question 3

Imagine a cross correlation table with employment and Industrial production. Industrial production is underlying. Some weakly negative dots in before 0, strong positive dots after 0. Highest positive dot 1 month after. What does this tell you?

Answer 3

Employment one month after measurement of IP-index is strongly correlated with IP-index. -Employment is a lagging indicator of IP. (IP is proxy for GDP).

Question 4

A central Business cycle feature is the co-movement of employment and GDP. Most economists believe demand for labour is the most important driver. Why?

Answer 4

Productivity shocks.?

Question 5

A central Business cycle feature is the co-movement of employment and GDP. Most economists believe demand for labour is the most important driver. Why?

Answer 5

Productivity shocks.?.. Not sure about this one.

Question 6

What are the main assumptions of the RBC model?

Answer 6

!Not completed!

Question 7

Definition of General Equilibrium

Answer 7

Given prices and exogenous shocks

1. Households maximise utility (s.t budget constraints). 2. Firms maximize profits
2. Prices clear the market.

Labour supply = labour demand

Goods produced = goods consumed

Question 8

State the household optimisation problem in RBC:

What is a: 1 - l

(l is small L)

Answer 8

Max u(c,l)

s.t. c=w(1 - l) + d

1-l = n

Question 9

State the Firm maximisation function in RBC.

What is z?

Answer 9

max d=zn-wn

z is total factor productivity

Question 10

Does the invisible hand hold for the simple RBC model?

Answer 10

Yes!

Any competitive equilibrium leads to a Pareto efficient allocation of resources.

Question 11

If the household utility function is u(c,l) = ln(c) + ln(l), what is the marginal rate of substitution between the goods?

Answer 11

Take partial derivatives of c and l to find the marginal utilities

MU(c)= 1/c

MU(l) = 1/l

MU(l) / MU(c) = c/l

Question 12

In the simple RBC model (not extended to labour market) what three “facts” clearly differentiates it from the data. Or, what is “missing” from the model.

Hint 1. Think real world vs model.

Hint 2. Why do we extend the RBC model with regards to the labour market? What is it that we seek to incorporate?

Answer 12

*Some are unemployed

*For most people, working or not working is a discrete choice (yes or no)

*We see large flows of workers moving in and out of employment at the same time.

Question 13

If households have the following optimization problem, what is the labour supply function?

Max u = ln(c) + vl v >= 0

s.t

c = wn + a

Which variable is discrete?

Answer 13

Remember chain rule, and substitute constraint into max.

FOC: v ( wn + a ) = w

Gives:

n= 1/v - a/w

n is discrete. 1 or 0.

Question 14

W.r.t RBC with extended labour market.

Given the household optimization problem:

max V(n) = ln(wn+a) + v( 1 - n)

1. What is the payoff if you choose not to work?
2. What is the payoff if you choose to work?
3. Using w on the x axis and utility on the y axis, draw the two functions you find in 1 and 2.
4. What is the intersect between the two?

Answer 14

n is either 1 or 0.

1. V(1) = ln(w+a)
2. V(0) = ln(a) + v
3. 1 is a concave curve, 2 is a straight line.
4. The reservation wage.

Question 15

Consider a person with a concave utility function who is considering whether to search for work or not. If she succeeds in finding a job, she will have a wealth of 6. If does not succeed she has a wealth of 1. Put utility on the y-axis and wealth on the x-axis.

1. Draw the concave utility function (disregard math).
2. What is the expected payoff of a job search (use math).
3. What is the Certainty equivalent of the search (approximate without math, use graph).
4. Let’s say the person currently has a job paying 3 wealth, and the certainty equivalent you approximated is 2.35. Will she search for a job? If she had a linear (risk-neutral utility function), what is the Certain equivalent? Would she search for a job then?
5. Let’s say she is currently unemployed (1 wealth). Will she search for a job?
6. What does this explain with regards to unemployment in the neoclassical BC model?

Answer 15

1. See pic. A concave utility function implies risk aversion.
2. 0.5*6 + 0.5* 1 = 3.5 wealth.
3. Any answer below 3.5 is considered correct since you don’t use math. In our example, the CE is 2.35.
4. If she has a job with wealth 3, it is higher than the CE of 2.35. She will not search for a job since she is risk-averse. If she as not risk awerse, her CE would be 3.5 and she would search for a job.
5. Yes. CE>1
6. Most ppl are risk averse, therefore there is a rigidity in the job market. Can explain some unemployment and can also explain why not everyone works where they get the highest pay.

Question 16

With regards to the labour market:

1. What is meant by “seperation”
2. What is meant by “accession”?
3. In period 1 there was 20% unemployment. Moving to t=2, there was 10% separation and 25% accession. What was unemployment in period 2?
4. What was the percentage-point change in unemployment? In percentage?

Answer 16

1. Fraction of employees who lose their job
2. Fraction of unemployed who find jobs
3. Percentage of total labour force who lost jobs: 0.8*0.1 = 8%

Percentage of total labour force who got jobs= 0.2*0.25 = 5%

• > 3% increase in unemployment. Unemployment period 2: 20%+3% = 23%
  4. Percentage point increase: 23-20=3%. Percentage increase of 3/20=15%

Question 17

Draw the (frictionless/neoclassical) labour market.

Answer 17

Question 18

Draw supply/demand labour market.

Introduce minimum wage.

Show the unemployment caused by the minimum wage and deadweight loss.

Answer 18

• The reduction in employment is F to C.
• Excess labour supply (also designated a unemployment) is A to B.
• Deadweight loss is DAC.

Question 19

A central trade-off in the labour market is “protection” vs “flexibility”.

1. List 3 policies that if, implemented are protective and when removed promote flexibility in the labour market.
2. With regards to skills, what is a severe implication of long time unemployment.

Answer 19

* Fixed term contracts

* Overtime pay

* Dismissal (fore employee) laws

* Collective bargaining (allowing unions to bargain)

3. Skills deteriorate. The productivity of labour decreases.

Question 20

Do high levels of employment always equal economic welfare?

What should economic welfare be evaluated on?

Answer 20

Economic welfare should be evaluated on the basis of broadly defined consumption; not on how individuals choose to allocate their time across competing activities. There is no a priori reason to believe that high levels of employment necessarily correspond to high levels of social welfare.

Question 21

y = zF(k, n).

F(k, n) = kˆ1−θ * nˆθ

1. If teta is one and the rest of the expression is static. What ‘form’ does the increase in n look like?
2. Derive the marginal product of labour
3. Write the profit maximization problem of the firm, given the production function over.
4. Find the FOC. What is the marginal product of labour equal to?
5. Find the labour demand function
6. Do firms earn profits? Use math and findings from above.

Answer 21

1. It follows a linear trend.
2. Take partial derivative of n: θz(k^1−θ * n^θ−1 ) - k=1 -> θzn^θ−1
3. Max n, Π= zn^θ - wn
4. FOC: θzn^θ−1 − w = 0. MPL=w
5. nD = ( w/θz )^1/θ−1 => ( θz/w )^1−θ
6. Yes. Π = zn^θ − θzn^θ−1n -> Π = (1 − θ)zn. So if teta>1, you get profits.

Question 22

A person has the utility function and makes a discrete choice to working or not:

u= c + 1/2*l

Using FOC, find the reservation wage

(l is leisure)

Answer 22

u= c + 1/2l

c= wn + Π

l = 1-n

u = wn + Π + ½*(1-n)

FOC: w - ½n = 0

w = ½n

If work is to be profitable (n=1), w > ½ * 1

Question 23

You have the production function

y= z(k^1−θ n^θ)

-> θ=0.5 and the model is static.

Utility function (households)

u=c+0.5*ln(l) (l=leisure)

1. Find labour supply and labour demand
2. Derive the equilibrium wage
   * Hint, for question 2, you will not get a pure number answer. Z will still be in there. Use ABC formula.*

Answer 23

Some side steps.

• y=zn^θ
• Profits = zn^θ-wn
• Household utility: u=wn+Π+0.5(1-n)

You need to take FOC for both demand and supply derivations.

1. n^D= (1/4) * (z/w)² , n^s= 1 - (1 / 2w)
2. Equation the two gives: w² - (1/2)*w - (1/4) * z²

z is just a constant.

With ABC (take only positive values): w = (1/4) + ( ((0.5² + 0.5z²)^½ ) / 2)

Question 24

Rate each of the following businesses as not cyclical, cyclical, or very cyclical.

(a) Home appliance producers and retailers
(b) Grocery stores
(c) Family practice medicine
(d) Plastic surgery

Answer 24

1. Home appliance producers and retailers: Durable good, very cyclical.
2. Grocery stores: Nondurable goods, moderately cyclical.
3. Family practice medicine: Service, not very cyclical.

4 Plastic surgery: Luxury, likely to be very cyclical.

Question 25

Which of the following companies do you think has the most cyclical production? Explain.

a. Walmart
b. Tesla
c. American Apparel (clothes)

Answer 25

Answer: Tesla, because it produces cars, which is a durable good

Answer 26

1) generally transform series in levels to ease comparability and reduce

numerical problems; variables that are rates or shares are usually not transformed.

(2) taking natural logs transforms multiplicative/exponential relations to log-linear.
(3) changes in logged variables are approx. growth rate of variables. (4) partial

derivative d ln(y) / d ln(x) can be interpreted as elasticity (see tricks with natural logs).

Question 27

Explain the differences between endogenous and exogenous variables.

In the RBC model, which variable is exogenous?

Answer 27

Endogenous variables are determined outside the model (chosen

by nature). Endogenous variables are determined by the participants of the model.

The only exogenous variable in simple RBC is z. Given by technology shocks in the economy.

Question 28

Consider a model economy populated by a representative household with preferences u(c, l) = c + λ ln(l); so that MRS(c, l) = λ/l. There is also a representative firm with technology y = zn^1/2 ; so that MPL(n, z) = (1/2)zn^−1/2 .

Solve for the competitive equilibrium allocation and real wage rate as a function of z and other parameters. How does this economy respond to exogenous changes in z?

• > Most important is n-supply = n-demand
• > Also find y supply and y demand (c demand)

Answer 28

y-demand = w-lambda+profits (substitute l demand = lambda/w into c constraint)

y-supply = (z²/2w) (plug labour demand function into production function)

For reference, see Adalfatto pages 60 and 61.