Representative Agent Model: One-Period Model

Question 1

A representative agent model consists of what 3 agents and recalls the assumptions of what type of period model?

Answer 1

3 agents: households, firms, and government.

Recalls the assumptions made by the One-Period Model. Thus assumes flexible pricing and perfect competition

Question 2

What 2 ways can we solve a model?

Answer 2

Competitive Equilibrium (CE) and Social Planner (SP)

Question 3

Given households utility and constraint function, solve for the household lagrangian:

Answer 3

𝓛 = U(C,L)+𝓛 [w(1-L)+π-T-C]
FOC: Uc=𝓛
UL=w𝓛 thus: UL=Ucw

Question 4

Firms aim to maximise profits of:

Answer 4

π=zF(K,N)-wN
FOC: MPN=w
Note* the marginal benefit of MPN is the extra output each additional employee creates, while the marginal cost is the extra wage incurred by an additional employee.

Also worth noting how zF(K,N) is simply the production (Y). We can therefore simplify the firms’ profit function to π=Y-wN.

Question 5

What are the effects of increased technology (positive technological shock)?

Answer 5

Initially, z increases (since Y=zF) we can assume this has a positive effect on output. This is clarified fully later. Increase to z increases MPN - labour demand (Nd) increases - thus pushing up the real wage price (w) (since MPN=w). The increase to w and the availability of more vacancies influences employed to work more labour hours and unemployed to fill vacancies thus labour supplied (Ns) increases. Since N+L=1, an increase to Ns=increase to N, meaning leisure (L) must fall. Increased Ns and Z implies output (Y) must increase. Since there is 0 effect to G, and since (Y=C+G) Y and C have a 1:1 effect.

Note* z has a direct effect upon consumption and output, but has no direct effect on employment.

Question 6

What is the aggregate resource constraint?

Answer 6

Y=C+G

Question 7

In the one-period model, what is the government’s constraint?

Answer 7

G=T. Government expenditure is equal to tax revenue.