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Consider the following exchange economy. There are two goods and two consumers. What is the Walrasian equilibrium of this economy?
Construct a parallel definition for input requirement sets V(y) and give a parallel result concerning the uniqueness of solutions for FCMP( w, y ).
In the spirit of proposition 7.5, give necessary and sufficient conditions on the sequence of observations being consistent with this sort of model.
What is the long-run industry supply curve? What is the intermediate-run equilibrium position? What is the new, long-run equilibrium position?
Suppose demand is given by D(p) = 400 -100p. What is the long-run equilibrium for this industry?
Demand shifts to D(:p) = 750- 150p. What is the new short-run equilibrium where the firms can vary their usage of legumes but not their usage of kapitose?
What is the general equilibrium of this economy? Assume that firms take prices as given and are profit maximizers, and consumers take prices as given.
What is the optimal fixed fee to charge if P is set at zero? What is the optimal fixed fee to charge if P = 1? What is optimal fixed fee and per-unit charge?
Suppose that demand takes the form X = p-a for a > 1. Show that the monopoly passes on more than the full cost increase to consumers.
Create and analyze a formal model that supports some (or, if you can, all) of the intuitive assertions we made.
What is the equilibrium in this case? What (if anything) would be the equilibrium if firms had Bertrand conjectures throughout?
What will be the outcome of the distribution system in part (c) if phiffle can be resold? (Assume that consumers in this economy are very savvy folks.)
Assume the monopoly charges retailers according to simple linear prices - at a price the monopoly sets. What is the optimal price for the monopoly to set?
Suppose the N firms are numbered 1, 2, ... , N, and 'they have the following sort of conjectures. What happens to price as N goes to infinity?
ne-quarter of the workers are qualified to work only in the low-wage industry. Find all of the pairs (yH , yL ) that can occur in this economy.
What fraction of the money transferred accrued to the people in each group under the old program, and what fraction accrues under the new program?
Historical Immigration Patterns and Real Wages. Draw demand and supply graphs to show what happened to wages in Europe.
Find the Nash equilibrium for any R between 0 and 10. Find the expected profits of the owner and the agent for any R.
What is the average daily output of the firm's workers? What is the average daily output of the firm's workers after the buy-out?
Also, assume that prices must be expressed in dollars and cents, so that $4.07 is an admissible price but $4.065 is not. What is the Bertrand equilibrium?
Consider again the situation described above, but now imagine that each firm sets a price, selling as many units of the good. What is the Bertrand equilibrium?
Find the Cournot equilibrium. Determine whether the price at which the goods are sold exceeds marginal cost.
Show that any risk averse expected utility maximizer will (weakly) prefer p' to p. Can you supply a general statement of principle at work in specific example?
That is, the consumer's investment problem has a well-defined solution. Even if you can't do part (a), assume its result and go on to parts (b) and (c).
Prove that if we have two risky assets with independent return distributions, all the results obtained in the text for the case of one risky asset extend.