Problem 1 [26 Points] On the market for good , two firms engage in quantity competition. They face the following market demand function: () = 120-. X denotes total output and X=x1+x2 holds, where 1 and 2 describe each firm's output level. The cost function of firm 1 is 1(1) = 201, while the cost function of firm 2 is 2(2) = 102.

a) Derive formally firm 1's reaction function. [4 Points]

b) Derive formally firm 2's reaction function. [4 Points]

c) Calculate the profit maximizing quantities for both firms and the resulting market price under Cournot competition. [4 Points]

d) Draw the reaction functions and the Cournot equilibrium into the figure below (don't forget the labeling). [4 Points]

e) Calculate firm 2's profit maximizing quantity if the two firms engage in Stackelberg competition. Assume that firm 2 sets its quantity first (Stackelberg leader). [3 Points]

f) Calculate the resulting profit maximizing quantity of firm 1 (Stackelberg follower). [1 Point] g) Calculate the equilibrium price under Stackelberg competition. [2 Points]

h) Calculate both firms' profits for both Cournot and Stackelberg competition. [4 Points]

Problem 2 [16 Points] The utility function of an employee is given by = , where C describes consumption of goods (in euros) and F describes leisure time (in hours per day). She has 24 hours per day at her disposal to allocate between work (H) and leisure, so that 24 = + . The hourly wage rate offered to her amounts to 25. a) Derive the consumption-leisure budget constraint. [3 Points]

b) Determine the slope of the budget line in the consumption-leisure space. [1 Point]

c) Calculate the marginal rate of substitution between leisure and consumption. [3 Points]

d) Calculate the utility maximizing number of hours of work per day supplied by the employee, the resulting number of leisure hours, and the resulting consumption level. [4 Points]

e) A student claims that labour supply does always increase with the hourly wage rate. Discuss this statement. [5 Points] 8/10 Problem 3 [18 Points]

A firm produces good at costs () = 0.52 + 4 + 2. When producing , the firm causes emissions which increase the costs of a neighbouring firm. These external costs amount to () = 2. The market equilibrium price of good is 20. a) Derive the private marginal cost curve PMC and the external marginal cost curve EMC. [2 Points]

b) Calculate the quantity which maximizes the firm's profit. [2 Points] c) Draw the private marginal cost curve PMC, the external marginal cost curve EMC, the equilibrium price and the profit maximizing quantity into the diagram below (don't forget the labeling). [4 Points]

d) Derive the social marginal cost curve SMC. [2 Points]

e) Calculate the socially optimal quantity '. [2 Points]

f) Draw the social marginal cost curve SMC and the socially optimal quantity ' into the diagram from problem c). Don't forget the labeling. [2 Points]

g) Assume that the government introduces a Pigouvian tax on the production of good by the firm under consideration. Determine the tax per unit of which will incentivize the profit maximizing firm to produce the socially optimal quantity. Briefly describe why the tax yields the socially optimal output level. [4 Points]

notice are are diagrams to be drawn