The next 3 questions form a package, the concept is negative externalities and finding the equilibrium and Pareto efficiency in the Edgeworth box. Eveline and Victor share a flat. They both love eating healthy and cook at home many times. The parents of both of them are farmers and always give them some food to take to the city. Evelines parents give her 12kg cabbages and 8 kg meat per month, while Victors parents give him only 14 kg meat. Endowments for Eveline is (12, 8) and for Victor is (0, 8).

Eveline loves eating cooked cabbage while Victor rather eats it raw in salads. Victor hates the smell produced during the cooking of cabbage. As a matter of fact, Victor feels truly embarrassed when he brings friends and Eveline has cooked cabbage; every single time she does, he goes all over the flat, ventilating the house and spraying room freshener.

Evelines utility from meat (m) and cabbage (c) is given by u_E(m_E,c_E) = c_E^1/2m_E^1/2,

while Victors utility is given by u_V (m_V ,c_V ;c_E) = c_V^1/4m_V^3/4c_E^1/4

As the utility function for Victor clearly shows, Evelines consumption of cabbage clearly represents a disutility for him. We then say that Evelines consumption of cabbage causes a negative externality on Victor. Let us normalize the price of cabbage to p_c = 1.

1. Derive the competitive equilibrium of the economy formed by Eveline and Victor. The competitive equilibrium price ratio p_m is equal to:

A. 1/5 B. 3/5 C. 4/5 D. 2/5

2. Derive the market allocation corresponding to the competitive equilibrium of the economy formed by Eveline and Victor.

Report your answer for the pairs (c_E , m_E) and (c_V , m_V)

3. Derive the equation that describes the Pareto set.

A. m_E= 88/(16c_E)

B. m_E= 22/(6c_E)

C. m_E= 44/(16c_E)

D. m_E= 18/(12c_E)