Intermediate Microeconomics · free preview
The Two Welfare Theorems
The first welfare theorem states competitive equilibria are Pareto efficient, the worked equilibrium (25, 25) sitting exactly on the utility frontier, needing price-taking, markets, and no externalities, the second theorem that any efficient point, the equal-utility (16, 36) say, is reachable by lump-sum transfers then trade, efficiency and distribution separated.
1. The utility frontier
The utility frontier
2. The first theorem
The first theorem
3. The second theorem
The second theorem
4. Reading the theorems together
Reading the theorems together
5. The first theorem's statement
What exactly does the first welfare theorem assert?
6. The failure checklist
Which condition's failure corresponds to a Pigouvian tax?
7. The second theorem's statement
What does the second welfare theorem allow a planner to do?
8. The lump-sum catch
Why does the second theorem not simply endorse income taxation for redistribution?
9. Frontier utilities at t of 4
On the diagonal contract curve at t of 4, compute uA as 4 squared and write the number.
10. B's paired utility
At the same point, compute uB as 10 minus 4, squared, and write the number.
11. A point below the middle
At t of 3 on the frontier, what are uA and uB?
12. The frontier's endpoint
What allocation sits at t of 10 on the contract curve?
13. The theorem's check
How does the first welfare theorem apply to this economy's equilibrium at (5,5)?
14. Engineering a chosen efficiency
How could a planner implement the t of 4 allocation, uA 16 and uB 36?
15. A's utility at t of 3
On the frontier at t of 3, compute uA as 3 squared, and write the number.
16. The utility sum at t of 4
At t of 4 the utilities are 16 and 36. Compute their sum, and write the number.
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