1) This question concerns water pollution in a small town. Assume that there is a small town that gets its water from a river that runs through it. Imagine that upriver there are 4 factories that emit some pollution into the river. Each factory emits up to 5 tons of pollution into the river.
Imagine the marginal cost of abatement for each firm is given by the following table.
Table: Marginal Costs of Pollution Abatement
Firm A Firm B Firm C Firm D
First Unit $100 $50 $75 $200
Second Unit $200 $150 $150 $250
Third Unit $400 $300 $400 $300
Fourth Unit $1200 $800 $900 $400
Fifth Unit $2000 $1500 $1700 $650
Each unit of pollution emitted into the water offers the firms a benefit of $1400. Each unit of pollution emitted into the water costs the city $2000.
A) If there was no government intervention in this market and no one held property rights to the river, how much pollution would be emitted into the river. What would be the total benefit to the firms? What would be the total cost to the town? Is this a good outcome?
B) What if the government gave ownership of the river to the town. If negotiation between the town and firms was not allowed, how many tons of pollution would be put into the river? Compared to the situation in A), what would be the total benefit/cost to the town? What would be the total benefit/cost to the firms? Is this a better outcome than part A)?
C) What if instead the property rights were given to the firms, but negotiations between the two groups was allowed. If the town offered the firms $1,900 for each unit of pollution abated, how much pollution would be abated? What would be the benefit to the firms? What would be the benefit/cost to the town? Is this result better or worse than that from part A)?
This question is designed to get you familiar with the concepts of marginal utility. Suppose there are two goods you can consume, Good X and Good Y. Suppose your utility (happiness) from consuming these two goods was given by the following equation:
U = 5X + 2Y
Where U is the measure of your happiness. X is the number of units of good X you consume. Y is the number of units of good Y you consume.
A) What is your marginal utility from consuming good X? What is your marginal utility from consuming good Y?
B) If you had $30 to spend on these two goods, how much of each good would you wish to consume if the prices were:
1. Price X =$2. Price Y=$1.
2. Price X =$5. Price Y=$1.
3. Price X =$10. Price Y=$4.
Now suppose your marginal utility is given by the following equations:
Marginal Utility of X = 120
X
Marginal Utility of Y = 60
Y
C) If you had $30 to spend on these two goods, how much of each good would you wish to consume if the prices were:
1. Price X =$2. Price Y=$1.
2. Price X =$5. Price Y=$1.
3. Price X =$10. Price Y=$4.
D) Why are your answers so different between parts B and C? What is it about how you value these two goods that has changed?