By Stephen F. LeRoy
This publication introduces graduate scholars in economics to the subfield of economic economics. It stresses the hyperlink among monetary economics and equilibrium thought, devoting much less recognition to merely monetary themes equivalent to valuation of derivatives. when you consider that scholars frequently locate this hyperlink challenging to understand, the remedy goals to make the relationship specific and transparent in each one level of the exposition. Emphasis is put on certain learn of two-date types, simply because just about all of the most important rules in monetary economics might be constructed within the two-date surroundings. The research is meant to be related in rigor to the easiest paintings in microeconomics; while, the authors offer sufficient dialogue and examples to make the tips without problems comprehensible.
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Econometrica, 55:1403–18, 1987. 1 Introduction So far we have assumed that agents can trade without explicit portfolio restrictions, meaning that they can choose any portfolio provided that the resulting consumption satisfies the agent’s restriction on admissible consumptions (for example, positivity). In particular, the only limits on short selling were those implied by restrictions on consumption, if any were imposed. Short sales restrictions and transaction costs are an important feature of realworld security markets.
Suppose that there are two securities and that short selling of security 2 is restricted. 3, then there is no limited or unlimited arbitrage portfolio. 1, then there is no unlimited arbitrage portfolio, but the portfolios in the shaded region are limited arbitrages. These portfolios involve a long position in security 1 and a short position in security 2. As the figure suggests, the set of security prices excluding unlimited arbitrage is larger than the set of prices excluding arbitrage. 1 The arbitrage indicated by portfolios in the shaded region is implemented via a short sale of security 2.
We conjecture that portfolio allocation (0, −1, 1) for agent 1 and (0, 1, −1) for agent 2 and security prices p1 = 3/4, and p2 = p3 = 1/2 are an equilibrium under the assumed short sales restrictions. 9) hold for both agents in the conjectured equilibrium with the Lagrange multiplier λ equal to 1. The portfolio (0, −1, 1) generates the consumption plan (2, 1) for agent 1; consequently, the vector of marginal utilities equals (1/4, 1/2). 9) holds with equality for these securities. Multiplying the payoffs of security 1 by agent 1’s marginal utilities and summing over states, 1/4 · 1 + 1/2 · 1, we obtain p1 = 3/4.