Suppose that there are two agents in the economy, and two goods: (m)oney and mosquito (c)ontrol. Mosquito control is a positive externalize: in fact, each player enjoys the total amount of mosquito control bought by the players. More specifically, assume that the utilities of the players are:
u1 (m1;c1;c2) = m1 +12(pc1 +c2)^0.5
u2(m2;c2;c1) = m2+12 (c1+c2)^0.5
where mi is the quantity of money "consumed" by player i and ci is the amount of mosquito control purchased by player i. Suppose also that initially each player has 30 units of money and no mosquito control, m1 = m2 = 30; c1 = c2 = 0. Also, there is a single Örm in the economy that can produce mosquito control from money using the technology
Fc(m)=0.5m
a) Think about the market game in the economy, in which each consumer maximizes his utility, given the prices (and given the choices of the other player). Arguing as in the class, one instance of market prices would be Pm = 1 and Pc = 2. Find the equilibrium allocation in this economy.
b) Suppose now that a social planner wants to maximize the sum of the utilities of both players. What allocation would he choose?
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The problem is im not able to find out the solution since there is the externalize inside no idea how to get rid off.
I got the
1)Direct MU+externalize=MU labor
2) direct MU lesiure by 1 = MU conof 2
3) MU labor for 2 = MU con for 2
then why direct MU cons1 =direct MU con 2?
Also in question B , I don't get how will he choose the allocation would he chose ? is that mean PE allocation or another point?
thank you so much
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