Lucy and Melvin share an apartment. They spend some of their income on private goods like food and clothing that they consume separately and some of their income on public goods like the refrigerator, the household heating, and the rent, which they share. Lucy’s utility function is 2XL + G and Melvin’s utility function is XMG, where XL and XM are the amounts of money spent on private goods for Lucy and for Melvin and where G is the amount of money that they spend on public goods.Let Y be the total amount they can spend.
a) What is the absolute value of Lucy’s marginal rate of substitution between public and private goods? What is the absolute value of Melvin’s?
B) Write an equation that expresses the condition for provision of the Pareto efficient quantity of the public good.