Exceptional Argentina Di Tella, Glaeser and Llach - Thomas Piketty

involved in social ordering that will take the country into a fight but rather to calmness.
June 24 th , 1948.
If a worker is angry, we must subtract to his utility, a term λ(π+p-w) where p is the productivity
of the worker in the firm and π is the profit the firm obtains from the other workers. This term is
just a "spite" term: when angry, the worker dislikes the firms making a profit, and he is angrier
when he contributes to those profits. What triggers anger is that the individual rejects the
hypothesis that the firm is altruistic.
In this market, firms choose wage levels (i.e. it is not a competitive market) w and get in
exchange a product of p per worker, so when total employment is E its profits are (p-w)E. If the
firm is not altruistic, that is all there is in the firms' utility (utility = profits). If the firm is
altruistic, its utility is profits plus a term that depends on the utility of the worker. The altruistic
firm has a cost of α if worker utility is lower than a certain level (this level is exogenous for this
model, but can come from learning, adaptation, history, etc). We call the threshold τ; we will set
it to be the utility the worker would obtain in a “fairly competitive” labor market (see below).
In what follows, and without loss of generality, we normalize t = 1 and all other parameters are
just “normalized by t”. This normalization is completely general. We also assume (without loss
of generality) that the number of workers is n=1.
Equilibrium
We will analyze a signaling game, in which firms, when choosing a wage level, signal their type.
An equilibrium in this setting is a triplet [e(w,x;μ),w(θ);μ(w)] where:
• e(⋅) is an "employment" decision strategy (the same for all workers; we are looking at
symmetric equilibria) as a function of wage, tastes x (or distance) and beliefs μ (of whether the
firm is altruistic or not) into {0,1}, where a=1 means "work" and a=0 means "don't work";
• w(⋅) is a function that maps types into wages (one wage for each type; the same function for
all firms);
• μ(⋅) is a function that maps wages into [0,1], such that μ(w) is a number that represents the
probability that the worker assigns to the firm being altruistic.
• e is optimal given x,w and μ; w is optimal given e (and other firms playing w); μ is consistent
(it is derived from Bayes' rule whenever possible).
We will focus on equilibria where beliefs are of the sort “I reject the firm is altruistic iff its wage
w is such that w < w* ” for some w* (it may be a target wage). We are ruling out (for example)
equilibria in which the worker rejects that the firm is altruistic if the firm pays a wage w > w*
(i.e. the worker comes to believe the firm is selfish even if it is paying a wage above the “target”