Suppose That Two Individuals,Jon and David,form a Community and Would

question 20

Essay

Suppose that two individuals,Jon and David,form a community and would like to construct a communal fort that would protect them from attacks.They both consume good X,a private good,and the protection of the fort,P.One unit of good X costs 1 unit of currency,and one unit of P costs 2 units of currency.Both Jon and David have an income of 100 and a utility function of the form:
U = log(X_i)+ 2 × log(P_J + P_D)
The budget constraint for each is given by:
X_i + 2 × P_i = 100
(a)Find the amount of protection Jon will provide as a function of how much David provides,and explain why the relationship is the way it is.
(b)How much protection P will be privately provided in this case?
(c)Explain the economic intuition behind this amount,and compare it to the socially optimal amount without solving for the socially optimal amount.

---

Definitions:

Semilunar Valves

Heart valves located at the bases of the large arteries that leave the heart; they prevent blood from flowing back into the heart.

AV Valves

The atrioventricular valves, consisting of the tricuspid and mitral valves, regulate blood flow from the atria to the ventricles in the heart.

Left Ventricle

The chamber of the heart that receives oxygen-rich blood from the left atrium and pumps it out to the body through the aorta.

Ventricular Systole

Ventricular systole is the phase of the cardiac cycle during which the ventricles contract, pumping blood out of the heart and into the circulatory system.