1. Marek Kapicka Lecture 2 Basic Intertemporal Model
Econ 208
Marek Kapicka
Lecture 2
Basic Intertemporal Model

2. Where are we? 1) A Basic Intertemporal Model A) Consumer Optimization
B) Market Clearing
C) Adding capital stock
D) Welfare Theorems
E) Infinite horizon

3. Consumer’s optimization
Consumers maximize utility subject to budget constraints
Lagrangean

4. Consumer’s optimization
First order conditions
Euler Equation

5. A) Consumer’s optimization
Log utility:
Solution:

6. Where are we? A Basic Intertemporal Model A) Consumer Optimization
B) Market Equilibrium
C) Adding capital stock
D) Welfare Theorems
E) Infinite horizon

7. B) Market Equilibrium Suppose that there is N identical agents
Market clearing condition is
Log utility:

8. Where are we? A Basic Intertemporal Model A) Consumer Optimization
B) Market Clearing
C) Adding capital stock
D) Welfare Theorems
E) Infinite horizon

9. C) Adding Capital Stock
Shortcomings of the previous model
Production is not determined within the model
Solution: Introduce production
There is a firm producing output using capital stock it owns
Consumers own the firm, get the profits

10. C) Adding Capital Stock Firm’s Problem
Production function
Capital changes according to
Initial capital stock K1 given
Capital stock K3 can be sold at the end of period 2

11. C) Adding Capital Stock Firm’s Problem
Profits
Maximize the present value of profits
In the optimum:

12. C) Adding Capital Stock Consumer’s problem revisited
Budget Constraints:
B1 are savings from period 1 to period 2
r is the interest rate

13. C) Adding Capital Stock Market Equilibrium
Market Clearing
Properties of Equilibrium:

14. Where are we? A Basic Intertemporal Model A) Consumer Optimization
B) Market Clearing
C) Adding capital stock
D) Welfare Theorems
E) Infinite horizon

15. D) Efficiency of Equilibrium Pareto Efficiency
Thought experiment: How to choose consumption and investment if one doesn’t need to obey the markets
The only constraints are the resource constraints
This is the best one can possibly do!
Will the solution coincide with the market solution?

16. D) Efficiency of Equilibrium Pareto Efficiency
Pareto Efficient Allocation satisfies
Properties of Pareto Optimum:

17. D) Efficiency of Equilibrium Welfare Theorems
The allocation is the same as in the competitive equilibrium
The equilibrium allocation is (Pareto) efficient
Practical advantages of this result:
Solving for Pareto Optimum is easier
How to figure out what the prices must be?

18. Where are we? A Basic Intertemporal Model A) Consumer Optimization
B) Market Clearing
C) Adding capital stock
D) Welfare Theorems
E) Infinite horizon

19. E) Infinite Horizon Shortcomings of the previous model:
2 periods are arbitrary
Solution: Infinite number of periods
Solve the Pareto Problem

20. E) Infinite Horizon Euler Equation again and Steady State
Consumption satisfies:
Steady State: