Question

. Suppose Adam and Sara are living close to a lake full of mosquitoes, but it is possible to control the mosquitoes by spraying regularly. Suppose Sara's and Adam's preferences are the following: Adam: UAC, yA)-Ya-(15-x)? Sara: Us(x, Ys)ys 1/2 (6 x)2 where x denotes the number of gallons that are sprayed each week, and y, and yB are Adam's and Sara's weekly incomes. Each gallon of spray costs $24 per gallon. What is the efficient provision of this good?

Answer 1

X represents a public good

In case of public good, at efficient provision ,

Summation of Willingness to pay equals to the marginal cost of provision of public good.

X represents a public good In case of public good, at efficient provision, Summation of Willingness to pay equals to the marginal cost of provision of public good. at efficient level of public Good provision rightarrow summationsign M R S_xy = M C_x MC_x = 24 M R S_xy^A = partial differential u/partial differential x/partial differential u/partial differential y_A = + 2(15 - x)/1 M R S_xy^B = partial differential u/partial differential x/partial differential u/partial differential y_B = 2 + 1/2 (6 - x) = 6 - x thus at eq^n: 2(15 - x) + 6 - x = 24 30 - 2x + 6 - x = 24 36 - 24 = 3x x = 12/3 = 4, x = 4 Ans