Consumer likes
- (25 pts) A consumer likes to have a good in quantity ï that is equal to
the quantity ï‚ 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 ï¸ âˆ’ ï¡ï¸ï©ï³ for ï and the ï¹ âˆ’ ï¡ï¸ï©ï³ for ï‚
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 ï°ïthe price of the first good and ï°ï‚ the price of the second
good. Suppose that the consumer has a monthly income ï™ï€º Derive the equations
for: 1) the demand of ï 2) the demand of ï‚ 3) the Engel curve of ï, 4) the
Engel curve of ï‚. Explain intuitively the meaning of each.
d (6 pts) Choose any numbers you like for ï°ï and ï°ï‚ Fix ï™ = 100 At the
prices you have chosen, what are the demands for ï and ï‚? Next, raise the
price ï°ï leaving ï°ï‚ and ï™ unchanged What are the demands for ï and ï‚
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 ïƒ(ï‘) = ï·ïŒ(ï‘)+ï²ï‹(ï‘) in a problem with ïŒ and ï‹ imperfect
substitutes.
a (2 pts) What are ïŒ(ï‘) and ï‹(ï‘)? What do they mean?
b (5 pts) How we compute ïŒ(ï‘) and ï‹(ï‘) from the graphical equilibrium
solution to ï ï©ï® (ï·ïŒ + ï²ï‹) s.t. ï‘ = ï†(ï‹ï€» ïŒ) (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 ï· = ï² = 1 gives
ïŒ(ï‘) = ï‹(ï‘) = ï‘ Compute ïƒ(ï‘) and ïïƒï€º
d (6 pts) It happens that the wage increases to ï· = 2 and somebody inmediately claims: "ïïƒ 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 ïŒ(ï‘) and
ï‹(ï‘).
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3 (25 pts) Electricity supply in a geographical area depends on a monopolist.
The cost function of the monopolist is ïƒ(ï‘) = ï† + ï£ï‘ The fixed costs are due
to the cost of the distribution grid and marginal cost is a production cost.
a (3 pts). Draw the ïïƒ and ïïƒ curves of the monopolist and explain if we
are facing a "natural monopoly" technology and why.
b (3 pts). Demand is ï‘ = 1 − ï°ï€º What would the monopolist say if the
area regulator asks it to produce and sell at ïïƒ? 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 ïïƒ? 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
ïŽ 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 ï‘ = ï±1 + ï±2. Firms cost functions are ïƒï© = ï£ï±ï© for ï© = 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.
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4 (25 pts). The figure represents the variation of the profits of two firms
(firm 1 and firm 2) according to the level ïº of some action. Firm 1 chooses ïºï€º
There is no market for ïº.
a) (3 pts) In words, what does ï€ï‚¼1
ï€ïº mean? On the graph ï€ï‚¼1
ï€ïº decreases in ïº
and becomes negative. Why do you think this is the case?
b) (4 pts) What is the line that represents ï€ï‚¼2
ï€ïº (notice that the graphical
representation draws − ï€ï‚¼2
ï€ïº with a solid line)? Recall firm 2 doesn’t control ïºï€º
Tell why ï€ï‚¼2
ï€ïº represents an externality and what type of externality.
c) (5 pts) Give an example of a firm taking an action ïº 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 ï€ï‚¼1
ï€ïº + ï€ï‚¼2
ï€ïº = 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 ïº than in
the competitive equilibrium? Explain intuitively why in terms of your example.
g) (3 pts) The value âˆ’ï³ suggests a solution to the non-optimality of the
competitive equilibrium. What kind of solution is (quotas, fiscal, negociation)?
Explain how it works.
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