Defining a Competitive Equilibrium for a two Period Model

Question

Consider an economy that lasts for two periods populated by a representative consumer/worker, a representative firm, and a government. After these two periods, the economy ends.

The question asks me to - Define a competitive equilibrium for this economy. - Show the demand and supply curve in a diagram with variables (r, Y ). - Show the effect of an increase in the current capital stock K. - Compare the equilibrium path with the case in which workers have a preference shock that reduces the disutility from work h − l in period one. Preferences are back to normal in period 2.

My Problems I am so confused: what are the steps to defining a competitive equilibrium? Do I just rewrite what competitive equilibrium is from the lecture notes, or do I have to define one from the problem above?

Also, there are a lot of variables with no numbers. I am very confused to how to approach a question with no numbers.

Answer 1

A competitive equilibrium is specific to the economy you're modeling. Your economy has three markets:

• Capital market for $K$
• Labor market for $L$
• Goods market for $Y$

Furthermore, there are several optimization problems / budget identities that have to hold.

• The household has a consumption/savings and a leisure/labor decision
• The firm has a labor and a capital choice
• You need to ensure that the government's budget constraint holds.

In a competitive equilibrium, you need to clear all the markets, and any quantity that is chosen, needs to be done so optimally, given everything that's happening in your economy. Here, you have two periods which need to be in equilibrium at the same time. If I were grading your homework, I would expect you to write the above for minimum points. You should then show what the conditions/equations are for each of the bullet points.

Example: Multi-Period Non-Equilibrium

For example, the household will chose savings in period 1, given what he expects to do with those savings in period 2. If you'd expect him to do something stupid with the savings in period 2 (say, throw them away), then it would be optimal to save nothing at all. In this case, you would be at an equilibrium in period 1. However, your choices for period 2 would be non-optimal, hence we do not have a 2-period equilibrium.