Answer to Question #112250 in Microeconomics for Rakesh Govindaram

Question

Q. Ardashir (A), Bashir (B) and Diana (D) have utility functions defined over chocolates (‘c’), a private good, and music (‘M’), a public good. Their utility functions are defined by ui = ci.M , i= A,B and D. Chocolates (c) cost Re.1 each and music (M) costs Rs.10 an hour. The wealth (in Rs.) of agents A,B and D is Rs.30,Rs.50 and Rs.20 respectively.
(i)Set out the Lagrangian to calculate the Pareto optimal quantity of music consumed. (3)
(ii)Confirm your calculations by writing out the Samuelson-Lindahl condition for the Pareto optimal consumption of music .Would the Pareto optimal consumption of music change if each

Answer 1

utility functions are defined by ui = ci.M ,

i= A,B and D. Chocolates (c) cost Re.1 each

music (M) costs Rs.10 an hour.

The wealth (in Rs.) of agents A,B and D is Rs.30,Rs.50 and Rs.20 respectively.