Question

Imagine we have a society of two citizens, A and B, who can own (and consume) two types of goods and services: private(X) and public(Y). Their utility functions are as follow: U^(XA, Y) = 2lnxa + InY UB (X,Y) = Inxg + 2lny Where xi is the level of the private good for citizen i and Y refers to the public good level. The production possibility frontier is: Y + X = 100, where X = Xxi. If the monetary endowment (wealth) of the citizens are 14 = $90,1 = $30 and the public good costs(MC) $5, answer the following questions: a. What are the market (collective) demand functions for X and Y? b. What is the optimal level of Public Good provision? c. What is the price of X and what are the Lindhal prices for the public good?

Answer 1

Person A: 2 (2) . uc4x: и* = 2м 4 + m X Budget: 90= Px XA + QT Equilibrium: Muka . Mura . ох, 24x - Pz 34 From budget : 90 = 224 +2Y :. «ү = 30 . 60 Person в: нам: 8 . w @ + 2 X Budget : 30 = Pa RB + BY Equilibrium: Muro Pro а . w, px = Px, № . from budget : 30 = Pq xo + 2 P2 XB : 30 = 10, = 20

market demand for 8: Rat Ro :.* at leve op For pucelic good: de 30 , B = 20 .::MBLY) = 50 -> demand for Y Now; . A+B=.5. Y = 10 x = 90 : Pe = ha :. 2 3 Lindha ::$: 20 flindhal price