Reinterpret the buyer and seller in the double auction as a firm that knows a worker's...

 

Transcribed Image Text:

Reinterpret the buyer and seller in the double auction as a firm that knows a worker's marginal product (m) and a worker who knows his or her outside opportunity (v), respectively. In this context, trade means that the worker is employed by the firm, and the price at which the parties trade is the worker's wage, w. If there is trade, then the firm's payoff is m - w and the worker's payoff is w; if there is no trade then the firm's payoff is zero and the worker's payoff is v. Suppose that m and v are independent and uniformly distributed on [0,1]. Consider the following alternative to the double auction: Before the parties learn their private information, they sign a contract specifying that if the worker is employed by the firm then the worker's wage will be w, but also that either side can escape from the contract at no cost. After the parties learn their types (m for the firm and v for the worker), they simultaneously announce either that they accept the wage w or reject it. If both announce accept, then trade occurs; otherwise it does not. Given an arbitrary value of w from [0,1], what is the Bayesian Nash equilibrium of this game? Draw a diagram analogous to Figure the one for the double auction showing the values of m and v for which trade occurs. Find the value of w that maximizes the sum of the players' expected payoffs. Reinterpret the buyer and seller in the double auction as a firm that knows a worker's marginal product (m) and a worker who knows his or her outside opportunity (v), respectively. In this context, trade means that the worker is employed by the firm, and the price at which the parties trade is the worker's wage, w. If there is trade, then the firm's payoff is m - w and the worker's payoff is w; if there is no trade then the firm's payoff is zero and the worker's payoff is v. Suppose that m and v are independent and uniformly distributed on [0,1]. Consider the following alternative to the double auction: Before the parties learn their private information, they sign a contract specifying that if the worker is employed by the firm then the worker's wage will be w, but also that either side can escape from the contract at no cost. After the parties learn their types (m for the firm and v for the worker), they simultaneously announce either that they accept the wage w or reject it. If both announce accept, then trade occurs; otherwise it does not. Given an arbitrary value of w from [0,1], what is the Bayesian Nash equilibrium of this game? Draw a diagram analogous to Figure the one for the double auction showing the values of m and v for which trade occurs. Find the value of w that maximizes the sum of the players' expected payoffs.

Answer rating: 100% (QA)

In this game the firm and the worker engage in a contracting process to determine whether trade employment occurs The firm knows the workers marginal ... View the full answer