Question

Consider the following provision of public good problem:

Citizen 1 initial budget: w1 = 80,000 $

Citizen 2 initial budget: w2 = 60,000 $

Cost of public good: C = 40,000

Citizen 1 Utility Function: U1(x1,g) = 3(x1) + 90,000g

Citizen 2 Utility Function: U2(x2, g) = 2(x2) + 60,000g

Notation: xi is the budget that citizen i spends on goods other than the public good; g is a public good indicator variable which takes on the value 1 when the public good is provided and zero otherwise.

Given this information, the level of utility of citizen 2 when 1 pays and 2 free-rides will be

Answer 1

$Soln,$

Citizen 1 initial budget $W1=\$80000$

Citizen 2 initial budget $W2=\$60000$

Cost of public good C $=40000$

Citizen 1=$U1(x1,g)=3(x1)+90000g$

Citizen 2$=U2(x2,g)=2(x2)+60000g$

g is a public good indicator variable that is 1 when its value is provided and zero when otherwise not provided.

$g=1$

initial budget - cost of public good C.

$\$60000-\$40000=\$20000$

$x2=\$20000$ ;Budget that citizen 2 spends on goods other than public goods.

Citizen 2 utility function, $=U2(x2,g)=2(x2,)+60000g$

$=U2(\$20000,1)=2(\$20000)+60000(1)$

$=U2=\$40000+\$60000$

Citizen 2 utility level.$=100000$