(25 pts) A consumer likes to have a good in quantity that is equal to the quantity consumed of other good. More of any of the goods alone doesn’t improve utility. a. (2 pts) What types of goods are these? Represent her preferences using the − for and the − for b (4 pts) Give an example of a pair of goods that have the relationship you stated in a (e.g. coffees and donuts in a given period of time). c (6 pts) Call the price of the first good and the price of the second good. Suppose that the consumer has a monthly income Derive the equations for: 1) the demand of 2) the demand of 3) the Engel curve of , 4) the Engel curve of . Explain intuitively the meaning of each. d (6 pts) Choose any numbers you like for and Fix = 100 At the prices you have chosen, what are the demands for and ? Next, raise the price leaving and unchanged What are the demands for and now? Graph both equilibriums. e (5 pts) Describe the substitution and the income effects corresponding to d. f (2 pts) Label your indifference curves. How does the utility change? 2
(25 pts.) We have obtained the cost function of a firm (under given imput prices) as () = ()+() in a problem with and imperfect substitutes. a (2 pts) What are () and ()? What do they mean? b (5 pts) How we compute () and () from the graphical equilibrium solution to ( + ) s.t. = ( ) (only cite the two equations that we use with imperfect substitutes, no need to solve). c (5 pts) Suppose we know that the equilibrium with = = 1 gives () = () = Compute () and d (6 pts) It happens that the wage increases to = 2 and somebody inmediately claims: “ is now 3” Is this calculation right? If it is wrong explain why. e (7 pts) Explain graphically the effect of a raise in the wage on () and (). 3 3 (25 pts) Electricity supply in a geographical area depends on a monopolist. The cost function of the monopolist is () = + The fixed costs are due to the cost of the distribution grid and marginal cost is a production cost. a (3 pts). Draw the and curves of the monopolist and explain if we are facing a “natural monopoly” technology and why. b (3 pts). Demand is = 1 − What would the monopolist say if the area regulator asks it to produce and sell at ? Illustrate the problem with a diagram c. (3 pts) Suppose that regulator accepts a price that gives no extra profits. What is this price? Show the equation that you will use to compute it (do not compute anything). d. (3 pts) Illustrate graphically solution c. Is the price above ? Does this imply a welfare loss with respect to solution b? If so, graph the loss. e. (4 pts) Regulator thinks that is better to apply a “two-part tariff” solution. What is a two-part tariff? What would be the optimal parts of the solution with identical consumers? f. (4 pts) Write an equality that shows that welfare under a two part tariff solution equals welfare under solution b. What is the distributional change? Government of the area decides now to take in charge distribution with a state owned firm and have two competing firms producing electricity so we will have = 1 + 2. Firms cost functions are = for = 1 2 and they compete as Cournot players. g (5 pts). Compute and represent in a diagram the reaction functions of both oligopolists. Explain the meaning of the intercepts. 4 4 (25 pts). The figure represents the variation of the profits of two firms (firm 1 and firm 2) according to the level of some action. Firm 1 chooses There is no market for . a) (3 pts) In words, what does 1 mean? On the graph 1 decreases in and becomes negative. Why do you think this is the case? b) (4 pts) What is the line that represents 2 (notice that the graphical representation draws − 2 with a solid line)? Recall firm 2 doesn’t control Tell why 2 represents an externality and what type of externality. c) (5 pts) Give an example of a firm taking an action that can be illustrated as in the figure (e.g. an apicultor plants flowers and the beauty of the view attracts tourists to a close hotel). d) (3 pts) Label the competitive equilibrium on the graph. What is the profit maximization condition for firm 1? Explain what this means intuitively. e) (4 pts) The optimal solution happens when 1 + 2 = 0 Describe how you can easily obtain this condition from maximization (no math necessary). Label the optimal equilibrium on the graph. f) (3 pts) Does the optimal solution imply bigger or smallr level of than in the competitive equilibrium? Explain intuitively why in terms of your example. g) (3 pts) The value − suggests a solution to the non-optimality of the competitive equilibrium. What kind of solution is (quotas, fiscal, negociation)? Explain how it works. 5
