Week 1 A closer look at the representative agent model

Question 1

In Economics what do we use to try and understand the world?

Answer 1

Models

Question 2

What should a model be?

Answer 2

As simple as possible, but no simpler

Question 3

In a one period model, which 3 types of agents exist?

Answer 3

• Households
• Firms
• Governments

Question 4

What does the Competitive Equilibrium depict?

Answer 4

Agents trying to maximise their own welfare

Question 5

What does the Social Planner depict?

Answer 5

Someone whom is trying to maximise social welfare.

Question 6

What is the utility function for households?

Answer 6

U=U(C,L)

Question 7

What is the constraint for households?

Answer 7

C= wN+π-T

Question 8

What do the letters stand for in the equation: C= wN+π-T

Answer 8

• C= Constraint
• w= Wage
• N= Hours worked
• π= Dividends
• T= Taxes

Question 9

What does N+L equal to?

Answer 9

Hours worked + Leisure = 1

Question 10

Are there any Pareto improvements in a Competitive Equilibrium?

Answer 10

No

Question 11

How would we write the Lagrangean for households?

Answer 11

U(C,L) + λ[w(1-L) π-T-C]

Question 12

When differentiating λ[w(1-L) π-T-C] for C, what do we get?

Answer 12

Uc= λ

Question 13

When differentiating λ[w(1-L) π-T-C] for L, what do we get?

Answer 13

Ul= wλ therefore Ul= Ucw

Question 14

What is a firm’s production function?

Answer 14

π = zF(K¯, N) − wN

Question 15

Using the Lagrangean, what is then the first order condition of the firm’s production function?

Answer 15

MPN = w

ie marginal product of labour = wage

Question 16

What is the optimising equation for a firm?

Answer 16

MPN = w

Question 17

In a 1 period model, what is the equation for government?

Answer 17

G=T

Question 18

If we combine the budget constraints (household and

government) with the profit function, what do we get?

Answer 18

Y = C + G

Question 19

What is the aggregate resource constraint?

Answer 19

Y = ZF(K¯, N)

Question 20

What does Z stand for?

Answer 20

Technology

Question 21

In a standard one period representative agents model, what does an increase in Z cause?

Answer 21

•Raises the MPN, increasing labour demand and pushing up the real wage
•If SE > IE, the increasing real wage raises labour supply
•Overall, N goes up (so L must fall)
•As the production function has Z and N rising, output
(GDP) rises
•As G has not risen, the increase in Y corresponds with a one-for-one increase in C

Question 22

When using a competitive equilibrium, would we include externalities such as pollution when solving equilibriums?

Answer 22

No, but social planners would.

Question 23

What does a Social Planner seek to maximise?

Answer 23

The SP aims to maximise U(C, L) subject to:

zF(K¯ , N) = C + G

Question 24

What are then the Social Planners first under conditions using the Lagrangean?

Answer 24

• Uc= λ
• Ul = MPNλ
• Therefore Ul= UcMPN

Question 25

What is the difference between endogenous and exogenous variables?

Answer 25

In an economic model, an exogenous variable is one whose measure is determined outside the model and is imposed on the model, and an exogenous change is a change in an exogenous variable. In contrast, an endogenous variable is a variable whose measure is determined by the model.

Question 26

When will the solving via Social Planner give different results to the Competitive Equilibrium?

Answer 26

When there are frictions in the market, eg impediments that prevent wages and prices being able to adjust to supply and demand.