Our first step is to find the necessary conditions under which a wage *w*
^{o} is part of a pooling equilibrium, in which workers attain their target level of utility. Consider a firm which maximizes profits in a deviation from a pooling equilibrium with wage *w*
^{o} (we are not including a utility cost of the deviating firm, since we assume for the time being that the equilibrium is such that workers attain their target utility level *τ*). If the firm increases its wage, workers wonʼt be angry. In that case, labor supply is given by the sum of all (unit) supplies of workers who are closer to the deviating firm than the two types of workers (one to each side) who are indifferent between working for the firm we are analyzing and working for its neighbor:

$$w - s - x = w^{\text{o}} - s - (b - x) \Leftrightarrow S = 2x = b + w - w^{\text{o}} .$$

Profits are then

$$(p - w)(b + w - w^{\text{o}} ).$$

When the firm maximizes this expression, we obtain an optimal wage of

$$w = \frac{{p + w^{ \circ } - b}}{2}.$$

For the firm not to want to deviate from *w*
^{o}, it must be the case that this optimal wage is lower than *w*
^{o}, or equivalently

$$w = \frac{{p + w^{ \circ } - b}}{2} \le w^{ \circ} \Leftrightarrow p - b \le w^{ \circ } .$$

(1)

In other words, if the oligopoly wage is too low, the firms are better off increasing their wage, and so workers will not punish them (by getting angry). If the firm lowers its wage, consumers become angry, and labor supply is given by the condition that

$$w - s - x - \lambda (p - w) = w^{ \circ } - s - \left( {b - x} \right) \Leftrightarrow S = b + (1 + \lambda )w - \lambda p - w^{ \circ } .$$

In that case, profits are

$$(p - w)\left( {b + \left( {1 + \lambda } \right)w - \lambda p - w^{ \circ } } \right).$$

For the firm not to want to deviate and offer the optimal wage in this deviation,

$$w = \frac{{w^{ \circ } - b + p\left( {1 + 2\lambda } \right)}}{{2\left( {1 + \lambda } \right)}} \Rightarrow \pi = \frac{{\left( {b - w^{ \circ } + p} \right)^{2} }}{4(1 + \lambda )}$$

it must be the case that profits in the equilibrium are larger than these deviation profits. Formally,

$$\left( {p - w^{ \circ } } \right)b \ge \frac{{\left( {b - w^{ \circ } + p} \right)^{2} }}{4(1 + \lambda )} \Rightarrow w^{ \circ } \le p - b\left[ {1 + 2\lambda - 2\,\sqrt {\lambda (1 + \lambda )} } \right].$$

(2)

Notice that when *λ* = 0 (the standard Salop case), we obtain from (1) and (2)

$$w^{\text{o}} = p\, - \,b.$$

Equations (1) and (2) provide two constraints to the equilibrium wage *w*
^{o}. The third and final restriction is that for a given *τ*, as we decrease the number of firms, the wage must also increase to achieve the target utility. Worker utility (in a pooling equilibrium with wage *w*
^{o}) is the number of firms, 1/*b*, times the total utility of workers hired by each firm:

$$\frac{2}{b} \int_{0}^{\frac{b}{2}} {(w^{ \circ } - s - x)} {\text{d}}x = w^{ \circ } - s - \frac{b}{4}$$

This utility is larger than *τ* if and only if

$$w^{ \circ } - s - \frac{b}{4} \ge \tau \Leftrightarrow w^{ \circ } \ge \tau + s + \frac{b}{4}$$

(3)

We now present one important result: as competition decreases (enough), anger is more likely. The following proposition shows that as competition decreases, a pooling equilibrium is less likely. But since pooling equilibria have no anger, and separating equilibria do (in expected terms there will be some selfish firms), when pooling equilibria disappear, anger appears.

###
**Proposition 1**

*There is a critical n* such that for all n′* *>* *n* *≥* *n*, the set of pooling wages is smaller when there are n firms than when there are n′. That is, as competition decreases, anger is more likely.*

###
*Proof*

Define *b** so that Eqs. (3) and (1) hold with equality and are equated:

$$\tau + s + \frac{{b^{*} }}{4} = p - b^{*} \Leftrightarrow b^{*} = \frac{4}{5}\left( {p - s - \tau } \right).$$

Let *n** = *1/b**. For *b** > *b* the set of equilibrium wages is increasing in *b* (decreasing in *n*) because: Eq. (3) is not binding; the slope of (2) is smaller (in absolute value) than the slope of (1).□

The plot below illustrates the three constraints on *w*
^{o} imposed by Eqs. 1–3. The wage *w*
^{o} must lie between the two loci with negative slopes (the flatter one is Eq. 2 and the steeper, 1) which arise from the firms’ incentives not to deviate. The wage must also lie above the positively sloped constraint (Eq. 3 that arises from the condition that fewer firms imply higher wages if workers are to obtain their target utilities).

Next, we present another relevant result, connecting the productivity of firms, the rise in anger and the possible subsequent regulation. This result provides a potential explanation for why people in less developed countries do not like capitalism. If productivity is lower and more volatile in LDCs, that would explain why capitalists and capitalism are not popular.

###
**Proposition 2**

*When productivity decreases, or when it becomes more volatile, anger is more likely.*

###
*Proof*

When productivity decreases, the two loci of Eqs. (2) and (1) move downwards by the amount of the decrease in productivity. Since Eq. (3) is unchanged, the set of pooling equilibrium wages shrinks.

A larger volatility in productivities makes it more likely that a low (pooling breaking) cost will happen, and then the selfish firms will reveal themselves as such, and anger will arise. □

An interesting point to note is that higher variability in productivity in LDCs could be the consequence of higher regulations to begin with: firms in sectors with a comparative advantage could have higher worker productivities, while firms in protected sectors lower productivities (even considering government regulations to protect them). In a sense, then, Peronism, by introducing distortions, generates anger towards capitalists and perpetuates the beliefs that Peronism fostered.

The next result illustrates another obvious feature of the rise in anger: when for some exogenous reason workers become “captive” of one particular firm, anger is more likely. The mechanism is as one would expect: when workerʼs labor elasticity of supply decreases, local monopolies have an incentive to lower wages. The temptation may be large enough that an anger-triggering wage decrease may be profitable. In countries with concentrated industries, like Argentina, and with little inter-industry mobility, workers do not have mobility, and so elasticity of supply is lower.

We model this increase in captivity by changing the cost of re-converting to another industry, while keeping rivalʼs wages fixed. The reason for this assumption is simple: if it is suddenly harder for workers employed in firm *i* to work in firm *i* − 1 or *i* + 1, those firms will keep their wages fixed: if they did not wish to attract the marginal worker before the change in re-conversion costs, they donʼt want to after, so there is no incentive to raise wages; if firm *i*-1 did not want to lower its wage before the change in costs, they donʼt want to do so after, since the incentives of the marginal worker working for them have not changed. As will become transparent in the proof, an equivalent way of modeling this is assuming that the two neighbors of the firm being analyzed move farther away, as if there had been a decrease in the number of firms.

###
**Proposition 3**

*Assume that, for a given parameter configuration, there is a pooling equilibrium with a wage of w*
^{o}
*. If the cost of re-converting to firms i* *−* *1 or i* *+* *1 increases from 1 to t* *>* *1, but the cost to firm i remains constant, the firm’s incentives to decrease its wage increase. There is a threshold t* such that if t* *≥* *t*, firm i lowers its wage and workers become angry.*

###
*Proof*

When the cost of converting to firms *i* − 1 and *i* + 1 increases to *t*, the supply faced by firm *i* (after an anger-triggering decrease in wage) and its profits, are

$$S = 2\frac{{w^{ \circ } - w + \left( {w - p} \right)\lambda + bt}}{t + 1} \Rightarrow \pi = (p - w)2\frac{{w^{ \circ } - w + \left( {w - p} \right)\lambda + bt}}{t + 1}$$

and the optimal wage and profit are

$$w = \frac{p - w + 2p\lambda - bt}{{2\left( {\lambda + 1} \right)}} \Rightarrow \pi = \frac{{\left( {p - w^{ \circ } + bt} \right)^{2} }}{{2\left( {\lambda + 1} \right)\left( {t + 1} \right)}}.$$

Notice that in the equation for the optimal wage, an increase in *t* is equivalent to an increase in *b*: a fall in the number of firms. For large enough *t*, these profits exceed the oligopoly profit, and the firm lowers its wage, causing anger. QED

In the above proposition we have assumed that workers continue to make inferences based on the equilibrium prior to the shock. Although one could argue that a new equilibrium (one with fewer firms or with higher *t*) should be the benchmark, we believe that keeping the old equilibrium beliefs is also plausible. In addition, the case of fewer firms also leads to more anger, as established by Proposition 1.

The previous proposition may be particularly relevant for the rise of Peronism and Peronist beliefs. In a time of rising speed of technological change, the cost of re-converting to other industries also rises. Hence, we may view the ascent of Perón as a consequence of the increasing exploitation by firms that had gained more power over their workers.

Any wage *w*
^{o} in the range determined by Eqs. (1) and (2) can be part of a pooling equilibrium if we choose τ or α appropriately. Note that if the firm is altruistic and it lowers its wage enough, there could be a utility cost of providing workers with a very low level of utility. Since we found necessary conditions, we focused only on the incentives of the selfish firm. When we want to build an equilibrium with a wage *w*
^{o} within the range we have just identified, we need to take into account this utility cost for the altruistic firm. But choosing *τ* or *α* low enough, any one of these wages is part of an equilibrium. We do not elaborate, because the construction is simple.