Reference no: EM133147561
Suppose that the demand side of the oil market consists of two consumers (think of them as countries or sectors of an economy, such as transportation and manufacturing), with the following demand functions:
Consumer 1: Q1 = 500 - 10P
Consumer 2: Qez= 1000-20P.
where Qui and Qaz represent the quantities of oil demanded by each of the consumers.
a. Determine the inverse market demand function for oil.
b. Graph and label the market demand curve for oil (with price on vertical axis)
Now suppose that the market price of oil is $20.
c. What is the market quantity demanded at this price
d. What is the total benefit to consumers in the market at this quantity?
e. What is the consumer surplus in the market at this quantity and price?
Consider the market for full-sized sport-utility vehicles (SUVs). Suppose the following equations describe market demand and market supply for these vehicles:
Inverse Demand Function: P = 177.500- Qdm Inverse Supply Function: P = 2,500+ 0.25 Qm, where Qu and Qm represent the market quantity demanded and supplied, respectively.
a. Determine the market equilibrium price and quantity and denote them by Pe and Qo. Show your answer both graphically and mathematically.
b. Calculate the economic surplus at this equilibrium. Show your answer mathematically as well as indicate the corresponding area on the graph.
Suppose that demand for the services of a durable good in a given period of time is represented by the inverse demand curve pt = 1000 -qt ; where qt is the quantity of the durable whose services are consumed. Suppose the marginal cost of providing the good is zero and that there are two time periods. Let a< 1 denote the discount factor used by both consumers and firms (recall: if i is the discount rate, the discount factor is a = 1 /(1+i ). Find the profit-maximizing prices, quantities, and profits (all as functions of a) for
a. A monopolist that leases the good (i.e., each period, sells 1 period's use of the good)
b. A monopolist that cannot lease and cannot commit in period 1 to the price that it will set in period 2
c. A monopolist that cannot lease but can commit in period 1 to the price that it will set in period 2.
Now suppose that a= 1 and that the monopolist has the option to either (i) produce the durable good (at zero marginal cost) and price without commitment, or (ii) produce a non-durable version of the good (one lasting only one period) at a marginal cost of c.
d. For what values of c will a monopolist that cannot lease choose to produce the nondurable good?
e. For what values of c will a monopolist that can lease choose to produce the nondurable good?
f. What would be the merits of a government policy banning leasing in this case
Consider a market with inverse demand P = a - 2Q. Firms have no fixed cost and constant marginal cost c.
a. Derive expressions for industry price, quantity, profit, and the Lerner index (price-cost margin) if this market is served by a monopolist.
b. Derive expressions for the Nash equilibrium industry price, quantity, profit, and the Lerner index if the market is served by Cournot duopolists. Compare these to your answers in part a.
c. Do the same thing for the case in which the market is served by Bertrand duopolists.
d. If the duopolists could choose whether to compete by choosing prices simultaneously or by choosing quantities simultaneously, which would they prefer? Which would consumers prefer? Which is more efficient?
e. What will firm profits be in Nash equilibrium if there are n identical Cournot competitors?
Now consider the game
L R
U (5; 5) (10; 0)
D (0; 10) (0;0).
a. Argue that if there is a mixed strategy Nash equilibrium in which player 1 (the row player) is randomizing between the actions U and D, player 1 must be indifferent between these two actions.
b. Use this observation to derive the probabilities with which player 2 must be randomizing in his equilibrium strategy.
c. Following the same logic, derive the probabilities with which player 1 must be randomizing in the mixed strategy Nash equilibrium.
Consider a continuous-time, complete markets economy consisting of two agent types, one with log preferences (γ = 1), and one with constant relative risk aversion greater than one (γ > 1). Assume aggregate consumption follows a geometric brownian motion dC/ C = µdt + σdB
(a) Write down the planner's problem that characterizes the optimal (and equilibrium) allocation of consumption to the two agent types.
(b) Prove that the share of the γ > 1 agent converges to zero.
(c) Briefly discuss how this outcome would be supported in a competitive equilibrium with asset trade. Explain intuitively why the log agent eventually dominates.
(d) Now suppose both agent types have log preferences, but one of the agent types fears model misspecification, and so computes 'robust' consumption/portfolio policies, as in Hansen & Sargent. Suppose the entropy penalty is scaled as in Maenhout (2004). Re-do the previous analysis to show that the robust agent ultimately 'disappears' from the economy. Again, explain this result intuitively.