Suppose the utility functions of two roommates are given by ui = 2x G U2 = zxzG where xi and x2 denotes the consumption of the private good for person 1 and 2, respectively, and G denotes the public good

Answer: D

Budget line equation for person1:

x1 + 2G = 80

Therefore, slope = -1/2 =-0.5

Utility function u1=½x1²G

Marginal rate of substitution (MRS) is given by

MRS = - MU_x1/MU_G

= - x1G/(½x1²)

= - 2G/x1

At optimal conditions, MRS = Slope

=> -2G/x1 = -0.5

=> x1 = 4G

Substituting this value in budget eqn. We get,

4G + 2G = 80

=> G = 13.33. Therefore G for person 1 is 13.33

As the budget and utility functions are similar for person 2 as well, the value of G for them remains the same. So, G for person 2 is 13.33.

Hence, efficient quantity of public good G = 13.33 + 13.33

= 26.66