Applied Economics 3611

Environmental and Natural Resource Economics

Questions set #1

Preparation for quiz #1

1. Suppose annual inverse demand and inverse supply for electricity are given by the following equations, where \(Q\) is gigawatt-hours of electricity:

\[D(Q) = 24 - \frac{Q}{10} \quad \text{and} \quad S(Q) = 3 + \frac{Q}{60}.\]

  1. In a diagram with \(Q\) on the horizontal and \(P\) on the vertical axis, draw the demand and supply curves. Compute the equilibrium quantity and price of electricity and indicate the equilibrium on the graph. Be sure to indicate the value of the vertical intercepts of the two lines. Label all of the items in your diagram, especially demand, supply, \(Q^*\), and \(P^*\).

  2. Calculate consumer and producer surplus at the equilibrium outcome from part a. Show your work. Indicate CS and PS on your diagram. (Recall that consumer surplus, for example, is the area under the demand curve and above the equilibrium price line.)

  3. Suppose the government chooses to impose a tax of \(t = 3.5\) on each unit of electricity, to be collected by producers. Compute the new equilibrium quantity and price of electricity. How much tax revenue is collected? What is the deadweight loss associated with the tax?

2. Suppose that your demand for time spent in the Boundary Waters Canoe Area Wilderness each year is given by the inverse demand function \(D(Q) = 200 - 25Q\). The constant marginal cost of a day spent in the BWCA is $50.

  1. How many days do you choose to spend in the BWCA? What is your consumer surplus?

  2. Suppose the government decides to remove the ban on boat motors in parts of the BWCA, which causes your demand function to shift down to \(P = 150 - 25Q\). How many days do you choose to spend in the BWCA now? By how much did your consumer surplus fall? By how much did your expenditure on BWCA trips fall?

3. Suppose annual inverse demand and inverse supply for milk are given by the following equations, where \(Q\) is millions of gallons of milk:

\[D(Q) = 8 - \frac{Q}{10} \quad \text{and} \quad S(Q) = \frac{Q}{30}.\]

  1. Draw the demand and supply curves. Compute the equilibrium quantity and price of milk and indicate the equilibrium on the graph. Be sure to indicate the value of the vertical intercepts (one will be zero) of the two lines. Label all of the items in your diagram, especially demand, supply, \(Q^*\), and \(P^*\).

  2. Calculate consumer and producer surplus at the equilibrium outcome from part a. Show your work. Indicate CS and PS on your diagram. (Recall that consumer surplus, for example, is the area under the demand curve and above the equilibrium price line.)

  3. Suppose the government, wishing to reduce the amount of milk consumed, chooses to impose a tax of \(t = 2\) on each gallon of milk, to be collected by producers. Write down the new supply curve, with the tax. Add this curve to your diagram, and label it clearly.

  4. Compute the new equilibrium quantity and price of milk. How much tax revenue is collected? Compute the new consumer surplus after the tax.