Question

Suppose there are two people who live on a lake and value a clean shoreline on the lake as follows (assume this is a public good). Person 1 values it at 400, and person 2 values it at 800. Assume that an unclean shoreline gives zero value to each. Cleaning the shoreline will cost 950. Person 1’s income is 700, and person 2’s income is 1500.

Part A: Should the shoreline be cleaned? Why?

Part B: Will it be cleaned if the government is restricted to using a “head tax” (each pays an equal amount) on players 1 and 2 to pay for the clean up?

Part C: Will it be cleaned if the government is restricted to using a proportional tax (each pays the same proportion of her income) on players 1 and 2 to pay for the clean up?

Answer 1

Part A: Yes the shoreline would be cleaned because if we add the two values of Person 1 whose value is 400 and Person 2 whose value is 800, the combined value is coming to (400 + 800) = 1200 whereas cleaning the shoreline would cost 950 which is less than the combined value of the two persons.

Part B: If the government is restricted to using a “head tax” (each pays an equal amount) on players 1 and 2 to pay for the clean up, the shoreline would not be cleaned. Cleaning the shoreline will cost 950. If person 1 and person 2 both need to pay equal amount it means they have to pay (950/2) = 475 each. Since, Person 1 values it at 400 and 475 is greater than 400, person 1 will not pay the amount and hence the shoreline will not be cleaned.

Part C: If the government is restricted to using a proportional tax on players 1 and 2 to pay for the clean up, the shoreline would be cleaned. Say, for example the government says they need to pay 45% of their income for the shoreline to be cleaned. Then, person 1 would have to pay = 45% * 700 = (45/100) * 700 = 315 and person 2 would have to pay = 45% * 1500 = (45/100) * 1500 = 675 and then the total is summing up to (675 + 315) = 990 which is greater than cleaning the cost of shoreline which costs 950.