ECON 433: Public Goods, Common Resources, and Externalities Problem Set 1. This problem is meant to illustrate the free rider problem quantitatively. Frank, Matt, and Andre live in the same neighborhood. The neighborhood is raising money to plant trees in the park. It costs $5 to sponsor a tree. Frank, Matt, and Andre derive benefits based on the number of trees sponsored, according to the schedule shown below. Individual Benefit (Total) Social Social Marginal Benefit per Individual Marginal Marginal Benefit Cost Social # Tree Frank Matt Andre [Total [Total) Frank Matt Andre Cost Benefit $10 $10 $10 $30 $5 $10 $10 $10 $30 $19 $19 $9 $9 $9 $27 $27 $27 O U D W N $34 $34 540 $40 $40 $45 $45 $45 7 549 $49 $49 8 $52 $52 $52 LD $54 $54 $54 10 $55 $55 $55 a) Fill out the rest of the table. b) What number of trees maximizes the net social benefit? (Social benefit - social cost) c) If the costs are to be split evenly, how many trees should each person sponsor in order to get the total number of trees from part b? d) Suppose Frank and Matt are doing their part and sponsoring 3 trees each. Andre hasn't yet decided how many trees to sponsor. If he decides to sponsor 1 tree (the 7"h tree in total), what is Andre's marginal benefit from doing so? What is his marginal cost? Would Andre choose to sponsor the 7" tree? 2) Because Frank and Matt are already sponsoring 6 trees in total, Andre decides not to sponsor any trees. What would we call Andre? Is the number of trees that ended up being sponsored more or less than the socially optimal number of trees