PUBLIC GOODS & AGGREGATE DEMAND QUESTION

Given:

Two persons' marginal benefits --- MB(a) = 100 - Q; MB(b) = 300 -Q --- for a certain good.

First case: there exists a PRIVATE GOOD.

a): Solve the aggregate demand curve.

NOW: It turns out to be a PUBLIC GOOD.

b): Solve the aggregate demand curve.

c): Image there are no cooperation between a & b. Who is the free rider? And who is the person that provides goods?

UPDATE: We have the MARGINAL PRIVATE COST: MC (Q) = 50 + Q.

d): When a&b act ONLY self interest (hint: no cooperation), what will the quantity be, Q, be in the market?

e): What will be the efficient level?

THEN: b brings another person c, who has the same MB(b) curve (recalled:MB(b) = 300 -Q).

f); What is the new efficient level and the new quantity?

FINALLY: now exits an MARGINAL EXTERNAL COST: MEC (Q) = 70 + Q.

g): What is the new efficient level and the new quantity? (Hint: MSB is same as (f)).

h): What can we noticed the difference between results in (f) and (g)?