Question 1: Externalities & Common Resources

a. Consider the below information for a demerit good and calculate the size of the Pigouvian tax required to internalise the negative externality associated with the production of this good.

: = 75 8

: = 20 + 4

: = 27 + 4Q

b. Consider a local market for house insulation, which is associated with positive health outcomes. Currently, 35 homes are insulated. The local council wishes to increase this number to 50 homes. What is the minimum sized Pigouvian subsidy that will achieve this policy goal?

: = 260 2

: = 120 + 2Q

c. How much is it likely to cost the local council to subsidise the additional homes to be insulated?

question 2: Monopoly

a .A monopoly's demand function is given by: ; = 200 3. Its costs are given by: = 20 + 2. Specify the firm's total revenue (R), marginal revenue (MR), and marginal cost (MC) functions

b. Based on (a) calculate the quantity and price the firm should set to maximise the firm's profit. Compute the firm's profit.

c. The profit function for a second monopoly is given by: = 2400 2 2 20000. Calculate the firm's fixed costs.

d. Using the profit function in (c) calculate the firms profit if it firm produces 250 units.

e. Using the profit function in (c) calculate the quantity of units this firm should produce to maximise profit. Compute the firm's profit.

Question 3: Government

a. The three individual willingness to pay functions for a public good are given by: 1; = 25 0.5, 2; = 17 & 3; = 12 1.5. Specify the total willingness to pay function (W) for this public good. Then, given: = 3 , calculate the optimal quantity of this public good the government should provide?

b. Assume you work for one of three firms that have submitted applications to the city council to operate a local amenity for the upcoming year. The annual running cost is given as: = 1000 while the market demand curve for this amenity is given by: ; = 200 . The winning applicant may charge any price they choose. The CEO of your firm has asked you to calculate how much to spend on lobbying in an attempt to secure this contract?

question 4 : Game theory

a. Consider the following payoff matrix for a game. Does either player have a dominant strategy? Is there a Nash equilibrium/equilibria? Explain your answer.

Player A Player B

Left Right

top 5,5 1,6

bottom 6,1 2,2

b. Reconsider the payoff matrix in (a) and sketch the payoff matrix as a game tree, assuming player A is the first mover. Using backwards induction, solve your game tree. Explain your answer.