WORKING 

 PAPERS

Job Insecurity isn’t Always Efficient

David J. Balan

Dan Hanner

WORKING PAPER NO. 305

September 2010

___________________________________________________________________________

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______________________________________________________________________________

BUREAU OF ECONOMICS

FEDERAL TRADE COMMISSION

WASHINGTON, DC 20580
1

Job Insecurity isn’t Always Efficient*

David J. Balan 

Dan Hanner 

Bureau of Economics 

Federal Trade Commission 

dbalan@ftc.gov 

dhanner@ftc.gov 

September, 2010 

Abstract: Workers value job security. If at least some workers value it enough, then it is efficient for at least some firms to adopt policies in which they commit (implicitly or explicitly) not 

to dismiss employees except for “just-cause,” as opposed to policies in which employers are free 

to dismiss employees “at-will.” In this paper, we develop a simple model in which the equilibrium distribution of workers between just-cause firms and at-will firms is not generally efficient: 

there can be inefficiently many workers in just-cause firms or inefficiently few. If there are inefficiently few, then a tax or even a ban on at-will firms can be welfare-improving. 

 

*

 We are grateful to Patrick DeGraba and Daniel Hosken, and to participants at the 2006 NEUDC conference for 

helpful comments on an earlier and much different version of this paper. The views expressed in this paper are those 

of the authors and do not represent the views of the Federal Trade Commission or of any individual Commissioner. 
2

I. Introduction:

 Workers value job security. Specifically, they value protection against the possibility that 

they will lose their job because their skills have become obsolete or have ceased to be a good 

match for their employer. If at least some workers value job security highly enough, then it is efficient for at least some firms to adopt policies in which they commit, implicitly or explicitly, not 

to dismiss employees except for “just-cause,” in contrast to policies in which employers are free 

to dismiss employees “at-will.” This is true even though just-cause firms have lower average 

output, which they do because workers remain at their jobs even when their skills become obsolete, and also because some just-cause workers exploit the greater opportunity to shirk afforded 

by just-cause protection. Just-cause firms can simply offer a correspondingly lower wage, which 

some workers will accept. There is a tradeoff, and the reduced output can be the (efficient) price 

paid for increased job security. 

 The main purpose of this paper is to investigate whether the market efficiently allocates 

workers to just-cause jobs vs. at-will jobs, and how policy interventions impact total welfare. We 

show that the unregulated allocation of workers is not generally welfare-maximizing. This is due 

to the presence of externalities: a non-shirker who joins a just-cause firm raises average output 

(and hence the wage) for all other just-cause workers, but does not internalize this effect and so 

is more reluctant to join a just-cause firm than would be efficient. A shirker who joins a justcause firm has the opposite (also not internalized) effect on wages, and so is inefficiently eager 

to join a just-cause firm. A policy that encourages just-cause employment will cause some nonshirkers (of whom inefficiently few join just-cause firms) and some shirkers (of whom inefficiently many join just-cause firms) to switch to just-cause firms, and we show that in some circumstances this can be welfare-improving. 
3

 To see why this is so, consider the effect of a tax on at-will firms, which would have the effect of moving some workers from at-will to just-cause firms. Infra-marginal workers who 

choose at-will firms even with the tax will be worse off by the amount of the tax (assuming their 

labor supply elasticity is zero), but this loss will be exactly offset by the government’s gain from 

tax receipts. Infra-marginal workers who choose just-cause firms even without the tax will be affected by it only insofar as it affects the wage that prevails in just-cause firms: an increase in the 

just-cause wage is necessary and sufficient to make them better off. We show that if workers are 

paid as part of a class or group, the just-cause wage may increase or decrease as a result of the 

tax. Marginal workers who switch from at-will to just-cause jobs as a result of the tax will be 

made strictly worse off if the just-cause wage decreases or stays the same, as these are workers 

who preferred at-will to just-cause employment absent the tax. This group can only be made better off by a tax if it causes a sufficiently large increase in the just-cause wage. In sum, an increase in the just-cause wage is necessary for the tax to increase total welfare, and a sufficiently 

large increase in that wage guarantees it. 

 The ideal policy would be to set the tax (or the subsidy if the market allocation contained too 

few at-will workers instead of too many1

) that achieves the welfare-maximizing allocation of 

workers. If setting the tax at the optimal level is not practically possible, then it becomes worth 

asking whether a ban on all at-will firms (which can be thought of as a sufficiently high tax) can 

increase welfare even though it will cause there to be inefficiently many just-cause firms. We 

show that a ban can increase or decrease total welfare relative to the unregulated equilibrium. 

 A key assumption of the model is that in just-cause firms the pay difference between shirkers 

and non-shirkers must be smaller than the difference in their productivity. If this were not the 

 

1

 We focus on potentially welfare-improving taxes on AW firms rather than subsidies because it is policies that encourage just-cause protections, not those that discourage them, that are actually proposed. 
4

case (i.e., if workers were paid their marginal products), then the externalities described above 

would not be present and the unregulated equilibrium would be efficient. Moreover, for justcause protection to be meaningful, it must limit firms’ ability not only to fire workers, but also to 

cut the wages of workers who the firm would like to be rid of. We assume complete wage compression in just-cause firms.2

 

II. Previous Literature:

 It is often argued that employment protections lead to inefficient allocation of resources because firms cannot destroy jobs that have lost their productive value. Furthermore, if job destruction is difficult, it may lead to less job creation and higher unemployment (Lazear (1990), 

Ljungqvist and Sargent (1998)). But there are also a number of papers that develop models in 

which employment protection can increase aggregate output. Bertola (2004) shows that requiring 

risk-neutral firms to insure risk-averse employees against negative income shocks can enhance 

aggregate output if job switching is costly. The idea is that job switching is likely to be efficient 

precisely when current income is low, but that is when risk-averse workers are least willing to 

pay the job-switching costs. Similarly MacLeod & Nakavachara (2007) argue that just-cause 

employment laws can, under certain conditions, provide workers with better incentives to make 

relationship-specific investments. In Levine (1991) just-cause employment laws can increase aggregate output by limiting worker shirking. 

 Even if job protection laws reduce employment or aggregate output, it does not necessarily 

mean that they are economically inefficient. If workers suffer disutility from job insecurity, then 

the welfare harm from some reduction in output can be overbalanced by greater security. Pissarides (2001) points out that most models of employment protection ignore this, and hence rule 

 

2

 See Section II below for a discussion of the empirical evidence on wage compression. 
5

out the most natural reason why such protections would exist in the first place. He shows that 

severance payments and advance notice requirements can serve as a form of efficient insurance 

for risk-averse employees, though the mechanism in his model differs from ours. Blanchard & 

Tirole (2008) also argue that worker risk-aversion means that layoffs have a social cost that is 

not internalized by firms, but they argue that forcing firms to pay a layoff tax to internalize this 

cost is superior to just-cause protection. We do not take a position on the relative effectiveness of 

alternative government interventions. Instead we focus solely on just-cause protection, which 

appears to be the relevant policy question in some cases. Moreover, the basic intuition that we 

develop in this paper may be applicable in other situations where workers and firms bargain over 

job characteristics, and where the outcome of such bargaining can be sub-optimal. See the discussion in Section V below for such an example. 

 Like the majority of this literature, our model acknowledges that just-cause protection results 

in some workers remaining in their firms even when their skills become obsolete or are no longer 

a good match. Another key element of our model is that some workers are “shirkers” who will 

shirk if they work in just-cause firms. The only other paper we know of that focuses on the impact of shirking is Levine (1991). In Levine’s model, at-will firms must pay efficiency wages to 

induce effort, which results in equilibrium unemployment. This inefficiency can be mitigated by 

having workers post performance bonds which they forfeit if they are fired for shirking. But 

workers will be unwilling to post such bonds with at-will employers for fear that the employers 

will fire them and appropriate the bond even if they don’t shirk. Since just-cause firms, by assumption, credibly commit not to do this, they can make more use of bonds and so need to rely 

less heavily on efficiency wages (which cause equilibrium unemployment) to induce effort. On 

the other hand, some workers in just-cause firms will shirk. Levine shows that there are parame-
6

ter values for which total employment, and hence total welfare (in the Levine paper there is no 

disutility from avoiding job insecurity, so welfare depends only on employment), is higher if all 

firms are just-cause firms. 

Levine then shows that there are parameter values for which total welfare is higher if all 

firms are just-cause firms, but for which an individual just-cause firm could not survive, as a single just-cause firm will attract a disproportionate number of shirkers. This result depends on the 

assumption that there is some cost (Levine calls it a “mobility” cost) associated with working for 

the single just-cause employer that shirkers will be more willing to pay than non-shirkers. 

Our paper is similar to Levine’s in that there is adverse selection of shirkers into just-cause 

jobs. But our mechanism is simpler and we think more general. We do not rely upon efficiency 

wages, performance bonds, or mobility costs. Rather our model is driven by the fact that individual job choice decisions involve externalities for other workers in the job class. Also, our model 

allows for the possibility of a welfare-improving tax on at-will firms instead of a complete ban. 

In Section IV below we show an example in which a small tax on at-will firms is welfareincreasing relative to the unregulated equilibrium, but a full ban is not. 

Just-cause protection would have little effect if firms could radically cut workers’ wages 

rather than firing them outright. Furthermore, as discussed above significant wage compression 

is necessary for our model to work. We assume that all workers in just-cause firms earn the same 

wage. There is a substantial literature on wage compression in firms. Government and union jobs 

have significant wage compression that may impact wage dispersion in the entire economy (DiNardo, Fortin, & Lemieux (1996)). But wage compression has been empirically documented in 

other job settings (Baker, Gibbs, & Holmstrom (1994), Frank (1984)). Pay compression may 

persist because differences in pay for the same job can lead to morale problems, and because 
7

workers may accept within-firm status as a reward for hard work even if not paid their full marginal product (Campbell & Kamlani (1997), Frank (1984)). 

III. Model Setup:

A. Sectors. 

There are two sectors in the economy, similar to those in Bulow & Summers (1986). In “primary” sector firms production is complex, and workers are only productive if their skills are current (and if they don’t shirk). Primary sector workers whose skills are current (and who don’t 

shirk) produce output equal to η, while primary sector workers whose skills are obsolete produce 

zero.3

 In the “secondary” sector production is simple, and all workers produce an output of θ (if 

they don’t shirk).4 That is, workers in the secondary sector produce less than primary sector 

workers whose skills are current, but more than primary sector workers whose skills are obsolete. 

B. Firms. 

There are two types of primary sector firms. “At-will” (AW) firms can fire workers for having obsolete skills or for shirking. “Just-Cause” (JC) firms commit not to fire workers for having 

obsolete skills, so working for a JC firm represents a form of insurance against having one’s 

skills lose their value. But JC firms can only fire workers for shirking if they can prove to a third 

party that the shirking took place. We assume that shirking can always be detected, but that it is 

too costly to prove, so shirkers in JC firms are not fired. So in equilibrium there are no termina-

 

3

 An equivalent alternative to skills becoming obsolete is for a worker and a firm to cease to be a good match. 4

 We assume that it is not worthwhile for primary sector firms to try to match with old workers. This means that no 

fired worker will get another job in the primary sector. It also means that no old non-shirker will quit a JC firm and 

join an AW firm, even if their skills are not obsolete. 
8

tions in either type of firm. In JC firms, not even shirkers can be fired, and in AW firms, the 

threat of being fired gives even shirkers the incentive to work hard. 

 Following Levine (1991), we assume that JC firms cannot cut the wages of those workers 

known to be shirkers: all JC workers are paid the same wage.5

 Secondary sector jobs require no 

skill and are always available, so no secondary-sector worker would have any reason to accept a 

lower wage in exchange for job security, which means that all secondary sector firms are AW

firms and no secondary sector workers shirk. All firms employ constant returns to scale 

production technologies, so firms can be of any size, and all firms operate in perfectly 

competitive product markets and earn zero profits, so all output is paid out as wages. 

C. Workers and Wages. 

A “non-shirker” is defined as a worker who will never shirk, and a “shirker” as a worker who 

will shirk if he or she can get away with it. That is, non-shirkers never shirk regardless of which 

type of firm they are in, whereas shirkers shirk in JC firms but not in AW firms. 

All workers live for two periods: young and old. Each young worker is endowed with up-todate skills and joins a primary sector firm. With probability ρ the worker’s skills remain current 

when old, and with probability (1-ρ) they become obsolete. In JC firms workers with obsolete 

skills cannot be fired, and they do not quit as long as utility in the JC firm is higher than utility in 

the secondary sector. In AW firms, these workers are fired and forced into the secondary sector. 

This lack of job security in AW firms is a source of disutility, due either to risk-aversion or to the 

negative psychological effect of being fired. In the numerical examples in this paper, we focus 

 

5

 To approximate wage compression, we could model a scenario where shirkers are paid somewhat less than nonshirkers, but not their actual marginal product, and not enough to discourage shirking behavior. For simplicity in exposition, we assume the shirker and non-shirker wages are not only similar, but identical. See Section II for a discussion of the empirical literature on wage compression. 
9

only on the risk-aversion effect. For a worker i, this disutility is represented by αi which has (for 

both shirkers and non-shirkers) a probability distribution function f(α) with support [α

MIN,αMAX]. 

This distribution is the same for shirkers and for non-shirkers. 

 A worker in an AW firm earns η with certainty when young. When old, that worker faces a 

gamble (skills may or may not turn out to be obsolete) with an expected value of ρη + (1-ρ)θ. 

The risk associated with this gamble is the source of disutility from job insecurity. Let X represent the certainty equivalent, the amount of guaranteed money that would make a worker equally 

well-off as the gamble, and let αi be the difference between ρη + (1-ρ)θ and X. Using a Constant 

Relative Risk Aversion utility function for wages U(w) = (w

1-σ

-1)/(1-σ), a worker i’s expected 

wage utility from the gamble is U(w) = ρ(η

1-σi

-1)/(1-σi) + (1-ρ)(θ 1-σi-1)/(1-σi), and the certainty equivalent is X = ((1-σi)U(w) +1)1/(1-σi )

. This gives us the following expression for αi: 

(1)  

1

1 1 1 (1 ) ( 1) (1 )( 1) 1 i i i i                  

 There is a mass of non-shirkers of measure NS N and a mass of shirkers of measure S N . The 

mass of non-shirkers who join JC firms ( NS NJC ) is equal to NS N times the fraction of non-shirkers 

for whom NS i  , where NS  is the (endogenous) threshold level ofi above which a non-shirker 

prefers a JC firm to an AW firm. Similarly, the mass of shirkers who join JC firms ( S NJC ) is equal 

to the total mass of shirkers S N times the fraction of shirkers for whom S i  , where S  is defined analogously to NS  . 

Since no one (including shirkers) shirks in AW firms, the wage in primary sector AW firms is 

equal to η, and the wage in secondary sector firms (all of which are AW firms) is equal to θ. We 

assume that η > θ > e, so that output is greater in the primary sector than in secondary sector (if 

skills are not obsolete), and that exerting effort is always efficient, even in the secondary sector. 
10

Utility is linear and additively separable in expected wages, disutility from exerting effort, and 

disutility from lacking job security. The lifetime utility UAW of a worker who joins a primary sector AW firm when young (ignoring discounting) is: 

(2) (1 ) 2 U e AW i         

 Let wJC be the wage in JC firms. The lifetime utility NS UJC of a non-shirker who joins a JC

firm when young is: 

(3) 2 2 NS U we JC JC  

The lifetime utility S UJC of a shirker who joins a JC firm when young is: 

(4) 2 S U w JC JC 

Note that (3) and (4) only differ by 2e, which is the disutility cost of effort that is borne by nonshirkers but not by shirkers. 

 Shirkers in JC firms all shirk and produce zero output, so all output in JC firms is produced 

by non-shirkers. Half of the non-shirkers are young and produce output of η. The other half are 

old, and a proportion r of them also produce η. The rest of the old non-shirkers produce zero. So 

the average output of a non-shirker in a JC firm is( )/2    . The JC wage wJC is equal to: 

(5) 

( ) 2 2

() ()

MAX

NS

MAX MAX

NS S

NS NS

JC

JC NS S

JC JC NS S

N fd N

w

N N

N fdN fd





 

 

     

  

 

  





 

Total output in a JC firm is equal to the average non-shirker output times NS NJC , which according 

to our wage compression assumption is divided equally among all NS S N N JC JC  JC workers. 
11

D. Thresholds. 

Recall that the threshold level of the disutility from lacking job security above which nonshirkers prefer JC firms to AW firms is called α

NS, and that the corresponding threshold for 

shirkers is called α

S

. 

Lemma 1: 2 S NS    e

Proof: A non-shirker is indifferent between the two sectors if: 

(6) 2 2 (1 ) 2 (1 ) 2 NS NS we e w JC                    JC 

A shirker is indifferent between the two sectors if: 

 (7) 2 (1 ) 2 (1 ) 2 2 S S w e we JC                    JC

 

These expressions only implicitly define α

NS and αS

 because wJC depends on the thresholds. 

Nevertheless, it is immediate that (6) and (7) differ by 2e. ■

 The α

NS threshold level in (6) is the difference in the expected wage for a non-shirker who 

chooses an at-will firm and one who chooses a just-cause firm. The α

S

 threshold in (7) is the 

difference in the expected wage minus the effort cost that shirkers only bear if they choose an atwill firm. So the only difference between shirkers and non-shirkers is that shirkers in JC firms 

get 2e more utility than do non-shirkers. The fact that NS S   means that the fraction of nonshirkers who join JC firms must be (weakly) smaller than the fraction of shirkers who do so:6

working in a JC firm is always more attractive to a shirker than it is to an otherwise equivalent 

non-shirker. 

 

6

 This will be true even if the two distributions are not identical, as long as the disutility from job insecurity is not 

too much greater among shirkers than it is among non-shirkers. 
12

E. Equilibrium. 

 A combination{ , ,} NS S N Nw JC JC JC is an equilibrium if equations (5) – (7) are satisfied. Rearranging terms in equation (6) shows that the number of non-shirkers that will join JC firms at wage 

wJC is determined by the distribution of αi. Similarly, the number of shirkers that will join JC

firms at wage wJC is determined by the distribution of αi and Equation (7). Notice that for any 

wJC, there is a specific combination of non-shirkers and shirkers that will be attracted to join JC

firms. This means, for example, that it is not possible for a firm to choose to attract 20 nonshirkers and 0 shirkers. 

 Depending on the distribution of αi, there may be mass points at multiple levels, equations 

(5) – (7) may be satisfied at multiple points { , ,} NS S N Nw JC JC JC and there may be multiple stable 

equilibria. The general model with an unrestricted αi suggests that policy changes can have almost any impact. But if we restrict the distribution of αi to have nice properties (such as continuity, convexity, etc.), we can say more about the equilibrium. 

 For example, if αi is distributed continuously and uniformly, equations (6) and (7) define an 

increasing piece-wise linear relationship between wJC and the number of non-shirkers and of 

shirkers. Based on the labor availability 0, 0 NS NS S S N N NN    JC JC , Figure 1 shows the set of 

attainable labor market combinations{ , NS S N N JC JC }for any wJC.

7

 For ease of exposition, call this set 

of attainable combinations curve A. There are three line segments in curve A. At very low 

wages, as wJC increases the number of shirkers attracted to the firm is increasing, but no nonshirkers would work for a JC firm. Then, as wJC increases into the middle range, a specific posi-

 

7

 The parameters underlying Figures 1 and 2 were chosen to produce clear pictures and have no particular significance. 
13

tive combination 0, 0 NS S N N JC JC   is attracted to the firm. Then, once all shirkers are at JC firms, 

as wJC increases further, only the number of non-shirkers is increasing. 

Figure 1 

 Equation (5) represents the fact that the JC wage must be equal to average output. It can be 

graphed as a curve in the same three-dimensional space as Figure 1. An equilibrium exists when 

equation (5) crosses curve A, as indicated in Figure 2. 

Figure 2 

 There is always at least one crossing point because Equation (5) crosses curve A at the origin, where no just-cause firms operate. Along the first line segment of curve A, equation (5) is 
14

below curve A. In this segment, 0 NS NJC  and by equation (5), 0 wJC  . Starting in the middle 

segment, when 0 NS NJC  , it is possible for equation (5) to cross curve A from below, and then 

possibly again from above. 

Lemma 2: If αi is distributed continuously and uniformly, for the attainable labor combinations 

in the middle segment of curve A in Figure 1, equation (5) is increasing and strictly concave. If 

equation (5) is increasing and strictly concave in the middle segment, and if curve A is increasing and linear in the middle segment, there are zero to two crossing points. 

Proof: See appendix. 

Proposition 1: If αi is distributed continuously and uniformly, there is at most one stable equilibrium other than 0, 0, 0 NS S N Nw JC JC JC   .

8

Proof: As noted above, equation (5) starts out below curve A, so the first crossing point must be 

from below. But this is not a stable equilibrium. To see why, suppose that a small number of additional workers join JC firms, such that they reach a point on the line somewhere above the 

equilibrium. When the curve crosses the line from below, this causes the JC wage to increase to 

a level above that represented by the line (i.e., above the wage necessary to make those extra 

workers want to join JC firms), which means that other workers would want to follow the first 

ones and switch to JC firms as well, moving even further away from the equilibrium. If equation 

(5) does not cross curve A a second time, this instability will lead to an equilibrium where 

, NS NS S S N NN N JC JC   . 

If equation (5) does cross curve A a second time, this time from above, this crossing point will be 

a stable equilibrium, because moving up the line will generate a wage below that represented by 

the line, and so below the wage necessary to make those workers want to stay in JC firms, which 

pushes back towards the equilibrium. ■

 We view the equilibrium at 0, 0, 0 NS S N Nw JC JC JC    as less interesting because it tends to 

have lower welfare than the other stable equilibrium. (If there are no JC firms operating, it is eas-

 

8

 This proposition is not fully general. This is because we are ignoring the third line segment where all the shirkers 

are in the just-cause firms. The slope of equation (5) jumps up when we stop following it along the middle segment 

and start following it along the third segment. Because of this jump, it is possible to have a third and fourth crossing 

point. The third crossing point would be from below and would not be stable. The fourth crossing point may be stable, but in that equilibrium all shirkers are in JC firms so there is no shirking cost from moving additional workers to 

JC firms. This makes it is trivial to show that a tax or ban can be beneficial. Therefore, we focus on the second 

crossing point in the middle line segment in the main discussion in this paper. 
15

ier to show that a ban or tax on AW work can be beneficial.) The , NS NS S S N NN N JC JC   case is 

also less interesting because there is no impact from a policy towards JC employment. Therefore, 

in the remainder of the paper, we focus on situations with the intermediate equilibrium characterized as the second crossing point between equation (5) and the middle segment of curve A.

9

IV. Results:

A. Effect on the JC Wage of a Tax on AW Firms. 

 We consider the effect of a per-worker tax τ on primary-sector AW firms. Equations (6) and 

(7) show that as the wage differential between AW and JC jobs falls, the thresholds NS  and S 

also fall.10 Lemma 1 shows that NS  and S  must always differ by 2e, which means that the tax 

must cause the two thresholds to decrease by the same amount, which we call Δ. The tax will 

cause some marginal workers to switch from AW to JC firms, which will change the wage in JC

firms from wJC to ' wJC , which is equal to: 

(8) '

( ) 2

() ()

MAX

NS

MAX MAX

NS S

NS

JC

NS S

N fd

w

N fdN fd





 

 

   

  



 









 

Lemma 3: ' wJC can be greater or less thanwJC . When αi is distributed uniformly, ' w w JC JC  . When 

αi is distributed on the U-quadratic distribution, there are parameter values such that ' w w JC JC  . 

Proof: The first statement is immediate from comparing (5) and (8). The second and third 

statements are proven in the appendix. ■

 

9

 While we have assumed αi is distributed uniformly, there are other distributions of αi such that there will be only 

one stable equilibrium for reasons similar to those discussed above. 

10 If the tax was also levied on secondary-sector AW firms, the welfare effects would be unchanged, as the loss to the 

secondary-sector workers would be exactly offset by the gain to the government. 
16

 The effect on the JC wage of a tax on AW firms depends on whether the tax causes the proportion of non-shirkers in JC firms to increase or decrease, which in turn is determined by 

whether the proportion of non-shirkers among those who switch from AW to JC firms as a result 

of the tax is larger or smaller than the proportion of non-shirkers among infra-marginal JC workers. This can go either way, because in the presence of wage compression, individual job choices 

have external effects. Each non-shirker who switches to a JC firm raises the proportion of nonshirkers among JC workers, and so raises the wage for all JC workers. Similarly each shirker 

lowers the JC wage, but neither takes this into account when deciding which type of firm to work 

in. A tax on AW firms will cause some non-shirkers to switch and increase the wage, and some 

shirkers to switch and lower it. The net effect depends on the composition of the group of 

switchers relative to the composition of infra-marginal JC workers, which in turn depends on the 

distribution of αi. 

B. Total Welfare Effects of a Tax or a Ban on At-Will Firms. 

In this section we consider the effect on total social welfare of a tax on AW firms, and also of 

a complete ban on AW firms, which we model simply as a tax large enough that no primary sector firms choose to be an AW firm. Total welfare adds up the utility for all agents in the economy, including the utility from the work effort that shirkers in JC firms are spared. If effort 

saved through shirking were excluded in the welfare calculation, then a tax or a ban would be 

less likely to be welfare improving, as then the lost output from moving shirkers into JC firms 

would not be partially offset by the fact that those shirkers were spared the disutility of effort. 

Proposition 2: A tax τ on AW firms may increase or decrease total welfare, and a ban on AW employment may increase or decrease total welfare. 
17

Proof: A tax τ reduces the real wage of infra-marginal AW workers by τ. This is a direct transfer 

from those workers to the government, and so has no effect on total welfare. The effect of the tax 

on infra-marginal JC workers is: 

(9) ' ' 2( ) ( ) 2( ) ( )

MAX MAX

NS S

NS S N w wf d N w wf d JC JC JC JC

 

 

      

The sign of this effect depends only on the sign of ' w w JC JC  , which Lemma 3 shows can be positive or negative. The effect on marginal workers is: 

(10)         ' ' 2 (1 ) (1 ) ( ) 2 (1 ) (1 ) ( )

NS S

NS S

NS S N w fdN w fd JC JC

 

 

         

 

          

A worker (shirker or non-shirker) who switches from an AW firm to a JC firm gains the JC wage 

(for two periods), and also gains αi because that worker no longer experiences the disutility of 

job insecurity. That worker loses the expected wage in the AW firm. The net effect is negative if ' w w JC JC  , because these marginal workers preferred to work in AW firms when the JC wage 

waswJC . So a strictly positive JC wage increase is necessary for this group to be made better off. 

The net effect of the tax is the sum of (9) and (10). Below we show by numerical examples that 

this can be positive or negative. 

The total welfare effect of a ban on AW employment is: 

(11) (1 ) (1 ) () () 2 22

NS S

MIN MIN

NS S N fdN fd

 

 

         

                     

In the case of a ban, there are no infra-marginal AW workers, there are only infra-marginal JC

workers and switchers. All switchers (both shirkers and non-shirkers) who were in AW firms before the ban gain αi. The other effects of the ban are simply its effects on total output. For nonshirkers, the ban negatively effects total output because a fraction (1-ρ)/2 of them will be old 

workers with obsolete skills who will remain in a primary sector JC firm and produce zero instead of joining a secondary sector firm and producing θ, as they would have done if they had 

joined primary sector AW firms when young. For shirkers, there will be a larger loss in output, 

equal to their total expected output in a primary sector AW firm. Below we show with numerical 

examples that the expression in (11) can be positive or negative. ■

 

 Figures 3-5 graphically illustrate how welfare changes in response to changes in the tax on 

AW firms. The x-axis represents the size of the tax, and the y-axis represents utility. Moving from 

left to right, as the tax τ on AW employment increases, this lowers the wage in AW firms, causing 
18

workers to switch to JC firms. At the far right is a tax high enough that it amounts to a ban on 

AW firms. In Figure 3, the parameter values are as follows. The labor productivity variables are 

set at η=3, and θ=1: secondary sector work is less productive than primary sector work as long as 

the worker’s skills are not obsolete. The probability r is set at .98, so most workers’ skills do not 

become obsolete when they are old. The effort cost is set at a fairly low level of e=0.1. And 5% 

of workers are shirkers, /( ) S S NS NNN =.05. The distribution of σi is chosen so that the disutility of job insecurity αi is distributed uniformly on [α

MIN,αMAX] = [0,1.51]. As described in Section III.C above, α

MAX corresponds to the most risk-averse agent (σi = 10), and αMIN corresponds 

to the least risk-averse agent (σi = 0). 

 To interpret Figure 3, start at the unregulated equilibrium. Because αi is distributed uniformly, each incremental increase in τ causes a constant number of workers to switch from AW

to JC firms, a constant proportion of which are non-shirkers. The skills of some of these switching non-shirkers will become obsolete when they are old, but they will nevertheless remain in JC

firms and produce zero instead of switching to the secondary sector and producing θ, as they 

would have done had they joined an AW firm when young. This is a marginal social cost caused 

by the tax. Another marginal social cost of the tax comes from the fact that some of the switchers 

are shirkers. These switching shirkers did not shirk in their old AW firms (nobody shirks in AW

firms), but they do shirk in their new JC firms. The sum of these two costs is represented by the 

dots in Figure 3. This marginal social cost curve jumps discretely down at the level of τ such that 

all shirkers are in JC firms. Once all shirkers are in JC firms, the only cost of moving additional 

workers to JC firms is the marginal cost of obsolete skills. 

 The tax also has a social benefit against which these social costs must be traded off, which is 

that the workers who switch from AW to JC firms are spared the disutility of lacking job security. 
19

The marginal benefit of an incremental increase in τ (represented by the triangles in Figure 3) is 

the marginal disutility from job insecurity that the workers no longer experience. This is downward-sloping because the marginal workers that are induced to switch as τ increases have successively lower disutility of job insecurity, and it is linear because αi is distributed uniformly. The 

slope of this line changes at the tax rate such that all shirkers are in JC firms, because there are 

fewer total switching workers for a given increase in τ. But because shirkers are only 5% of the 

marginal workers, and because shirkers’ disutility values are near zero near the jump point, the 

change in slope is very minor. This kink is more noticeable when shirkers make up a greater proportion of the marginal workers.11

 Total social welfare is represented by the filled squares in Figure 3. Note that this is not on 

the same scale as the other lines and curves in the figure, as it represents total utility and the others represent components of marginal utility. They are presented together in the same figure to illustrate how the relationships between the marginal social costs and benefits affect total welfare. 

Starting at the unregulated equilibrium and moving to the right, at first an increase in τ causes total welfare to increase because the workers who move from AW firms to JC firms as a result have 

high disutility from job insecurity. But at certain point the marginal benefit of the tax becomes 

smaller than the marginal cost and total welfare begins to fall. When τ becomes high enough that 

all shirkers are in JC firms, the total marginal cost drops discretely and falls below the marginal 

benefit, and total welfare discretely increases. But the marginal benefit continues to fall as τ increases, and eventually it once again falls below the total marginal cost and so total welfare starts 

to fall. For the parameter values represented by Figure 3, a tax on JC firms high enough that no 

AW firms exist (which is equivalent to a total ban on AW firms) causes welfare to increase rela-

 

11 A property of the uniform distribution is that the proportion of shirkers among switchers is the same as their proportion in the population. 
20

tive to the unregulated equilibrium. But a ban is not the first-best policy, because a smaller (but 

still positive) tax results in welfare that is even higher. A ban “overshoots” the optimum, eliminating all AW firms when the optimal number of such firms is positive. 

 In Figure 3, the probability that skills become obsolete was set at a low level (r=.98). Figure 

4 displays what happens if the parameter values are the same as in Figure 3 except that the probability a worker’s skills become obsolete is higher (r=.94). This causes the marginal social cost 

due to skill obsolescence to increase, which pushes the total welfare curve downward. In this 

case a ban on AW employment makes society worse off relative to the unregulated equilibrium, 

though the welfare-maximizing level of τ is still positive. 

 In Figure 5 we return to the parameter values in Figure 3, but we make one change. In Figures 3 and 4 we let σi be distributed on [0,10] in such a way that αi is distributed uniformly on 

[α

MIN, αMAX]. In Figure 5 we let σi be distributed uniformly on [0,10]. Since, as described in Section III.C above, αi is a non-linear function of σi, in this figure the distribution of αi will not be 

uniform. There is no specific name for the distribution of αi in this case, but it is similar to the Uquadratic distribution discussed in the appendix. Specifically, this distribution has more mass in 

its tails. 

 There are several differences between Figure 5 and the previous figures. First, because of the 

mass in the tails, for each unit increase in the tax on AW firms, more workers are moved to JC

firms, and so the cost of obsolete skills is increasing. Second, without a uniform distribution of 

αi, an increase in the tax does not move over a fixed proportion of shirkers. In this example, for 

each unit increase in the tax on AW firms, an increasing proportion of shirkers are moved to JC

firms, so that the marginal social cost due to shirking is increasing. Third, the marginal social 

gain is also not linear: for each unit tax increase there is an increasing number of marginal work-
21

ers but because disutility values are still falling, the net result is a decreasing but non-linear marginal social benefit curve. Overall in Figure 5, a positive tax on AW firms attracts more shirkers 

to the JC firms, which makes it difficult for a ban or a tax on AW firms to be welfare-improving. 

Specifically, for the parameter values represented by Figure 5, any tax on AW firms will lower 

welfare. 

C. Necessary Conditions for a Tax on AW firms to be Welfare-Increasing. 

 In the above examples, we show that a tax or a ban on AW firms can either increase or decrease total welfare. In this sub-section, we show some necessary conditions for a ban to be welfare-increasing. 

Corollary to Proposition 2: A necessary condition for a tax to increase total welfare is 

that ' w w JC JC  . 

Proof: The proof to Proposition 2 showed that: (i) the effect of a tax on infra-marginal AW

workers is exactly offset by the effect on the government; (ii) the effect on infra-marginal JC

workers has the same sign as the JC wage change; and (iii) the effect on marginal switchers is 

negative if ' w w JC JC  . Thus ' w w JC JC  is a necessary condition for a tax on AW employment to be 

welfare-increasing. ■

 The condition that ' w w JC JC  is necessary for a tax on AW firms to be welfare-increasing. So 

an empirically-based prediction that a proposed tax would make the JC wage go down would be 

sufficient to conclude without further analysis that such a policy would reduce welfare. While 

the ' w w JC JC  condition is necessary, it is not sufficient. For example in Figures 3 and 4, the fact 

that αi is distributed uniformly means that the JC wage always gets higher the higher the tax (see 

Lemma 3), yet there are still some levels of τ that result lower welfare than in the unregulated 

equilibrium. We do not have a general sufficient condition for a tax on AW firms to be welfareincreasing. But we observe that both infra-marginal JC workers and marginal switchers are better 
22

off the higher the JC wage, and no one is worse off. So in principle there is always a JC wage 

increase large enough that it would guarantee that a tax would improve total welfare. An 

empirically-based prediction of a JC wage increase would not by itself indicate that it was large 

enough to cause the tax to be welfare-increasing. The predicted wage increase would have to be 

larger than the critical wage increase derived from the model. 

 Another necessary condition is for a tax on AW firms to increase total welfare is that αi must 

vary across workers. To see why, suppose that αi were equal to a constant ( ) for all workers 

(shirkers and non-shirkers). 

Proposition 3: If αi =  for all workers, then a tax or a ban on AW firms cannot be welfareimproving. 

Proof: If all workers started out in JC firms, then obviously a tax or on AW firms would have no 

effect, so the interesting case is where at least some workers are start out in AW firms. Lemma 1 

shows that all else equal shirkers get more utility from working in a JC firm than non-shirkers 

do. Since all shirkers are identical and all non-shirkers are identical, the only possible scenarios 

are: (i) all non-shirkers start out in AW firms and all shirkers are indifferent between JC and AW

firms and so choose randomly; (ii) all shirkers start out in JC firms and all non-shirkers are indifferent and choose randomly; and (iii) all workers of both types start out in AW firms. Case (i) is 

not possible, as in that case the only workers in JC firms are shirkers, and so wJC will be equal to 

zero, which violates the assumption that η > e. Case (ii) cannot be a stable equilibrium, as a single additional non-shirker joining a JC firm would increase wJC, breaking the indifference and 

causing all the other non-shirkers to follow. So Case (iii) is the only relevant one, and the only 

relevant policy is a tax high enough to cause all workers to switch from AW to JC firms (i.e., a 

ban).12

Since JC firms are more attractive to shirkers than to otherwise equivalent non-shirkers, the requirement for the policy to be effective is that it must cause all non-shirkers to want to switch 

from AW to JC firms. When all workers are in JC firms, the JC wage will be at its highest possible level MAX

wJC . 

(12) 2

NS

MAX

JC NS S

N

w

N N

  

 

 

12 This is the scenario considered in Levine (1991). 
23

Firms will only offer that wage if they believe that their workforce will have the same proportion 

of shirkers as in the general population. An AW ban guarantees that this will be the case. But an 

individual JC firm can also offer a wage MAX

wJC and guarantee itself the population proportion of 

shirkers. The reason is that all workers prefer JC firms at that wage, and so an individual firm 

could guarantee itself the population proportion of shirkers simply by hiring at random from the 

applicant pool. Since the market generates the same outcome that a ban would, the ban cannot be 

welfare improving. ■

 Proposition 3 holds because the applicant pool for firms that pay a wage of MAX

wJC contains the 

population proportion of shirkers. This will not be the case if there is some costly action that can 

be taken to increase the chances of getting a JC job. Shirkers will be more willing to bear that 

cost and so the applicant pool will consist disproportionately of shirkers. A “mobility” cost that 

shirkers are prepared to bear and non-shirkers are not is what drives the result in Levine (1991), 

in which a ban on AW firms can be welfare-improving even though in that model all workers are 

assumed to be identical apart from whether or not they are shirkers. 

D. Distributional Effects of a Total Welfare-Increasing Tax on AW firms. 

 A tax on AW firms that increases total welfare will not affect all workers equally. This is the 

subject of the following two propositions. 

Proposition 4: All else equal a tax on AW firms that increases total welfare makes workers with 

the lowest values of αi worse off, workers with the highest values αi better off, and has an intermediate and ambiguous effect on workers with intermediate values of αi. 

Proof: Workers with the lowest values of αi are infra-marginal AW workers, who are directly 

made worse off by the tax. The Corollary to Proposition 2 shows that for a tax or a ban on AW

firms to increase total welfare, it must cause wJC to increase. Since the workers with the highest 

values of αi are infra-marginal JC workers, any total welfare increasing tax must raise their wage 

and makes them better off. Workers with intermediate values of αi switch from AW to JC firms 

as a result of the tax. These workers are made better off if the tax causes wJC to increase by 

enough. But if they do benefit it will be by less than the infra-marginal JC workers, as they 

preferred to work in AW firms at the pre-tax wage. Similarly, if they are made worse off, it will 

be by less than the infra-marginal AW workers. ■
24

Proposition 5: All else equal, a tax on AW firms that increases total welfare benefits shirkers 

more than non-shirkers. 

Proof: Proposition 4 shows that a tax that increases total welfare always benefits infra-marginal 

JC workers, has intermediate and ambiguous effects on marginal switchers, and always harms 

infra-marginal AW workers. Lemma 1 shows that NS S   , which means that shirkers will be 

more concentrated among the groups that benefit more from the tax. ■

V. Discussion:

In the above analysis, the proportion of shirkers in the population was assumed to be exogenous. But it is possible that the desire of a worker to shirk depends on the firm‘s reputation for 

how it treats employees and/or that worker’s attitude towards the employer, which may in turn be 

affected by the worker’s treatment at the hands of past employers. That is, there may be some 

workers who only want to shirk if they believe that their employer is not loyal to them. 

If this is the case, then firms will have an incentive to treat their workers better and thereby 

generate good will if the number of workers who wish to shirk only at a non-loyal employer is 

sufficiently large. But there may be external effects that cause firms to under-invest in loyalty. 

For example, if workers are mobile, then a firm that invests in loyalty in one period may not be 

able to enjoy the benefits of it in a future period. Also, it may be the case that gestures of loyalty 

involve industry-wide economies of scale,13 so it is only worthwhile if a sufficiently large number of other firms are doing it, which will be the case if such gestures are mandatory. 

If these conditions hold, the argument for a tax (or a ban) becomes stronger: if more workers 

having the experience of working in JC firms reduces the number of shirkers in the economy, 

and if individual firms do not realize the full benefit of bringing this about, then the benefits of a 

tax are greater. Recall that a tax achieves reduced aggregate disutility from job insecurity at the 

cost of more aggregate shirking and job mismatch. To the extent that a tax also has a dynamic ef-
25

fect of reducing the desire to shirk, the case for it becomes stronger. In other words, forcing employers to act loyal may lead to a better equilibrium in which fewer workers are required to endure job insecurity and in which fewer workers shirk. 

Even in cases where a tax on at-will firms improves welfare, it would be difficult to actually 

identify the optimal tax. A better alternative, if possible, would be to find technological or other 

means that make it easier to distinguish low productivity due to shirking from low productivity 

due to skill obsolescence. If shirking could be clearly identified in a provable way, then firms 

would be able to fire shirkers while still keeping their “just-cause” commitments to non-shirkers, 

which would be an unambiguous improvement. 

The basic idea of this paper can be applied to other settings as well. For example, some firms 

in some poor countries lock workers in their factories in order to prevent theft. The tradeoff in 

that case (workers bearing the disutility of being locked in vs. the economic cost of theft) is similar to the tradeoff in this paper (workers bearing the disutility of job insecurity vs. the economic 

cost of shirking and job mismatch). As in this paper, it is possible to show that the market equilibrium is not necessarily optimal, and so a tax or a ban on firms that lock their factories could be 

welfare-improving.14

VI. Conclusions:

In this paper we emphasize the tradeoff between maximizing output and reducing workers’ 

exposure to negative exogenous shocks to their productivity. A policy that shifts workers from 

at-will to just-cause jobs will generate some job security benefits, but will also lead to more 

shirking and to more misallocated workers. The paper models a scenario in which externalities 

 13 An example may be promising that workers will be dealt with by trained Human Resource professionals, which is 

only possible if enough firms do it to support specialized HR training programs. 
26

arising from individual job choice decisions cause adverse selection of shirkers into just-cause 

jobs, so that there can fewer such jobs than is socially optimal. This raises the possibility that a 

tax or a ban on at-will firms can be welfare-improving. 

 Even a tax or a ban that increases total welfare will not improve welfare for all agents in the 

economy. It will benefit those workers who value job security the most, harm those workers who 

value it the least, and have intermediate and ambiguous effect on those in the middle. It will also 

tend to benefit shirkers more than non-shirkers. 

 14 A draft of an earlier version of this paper that focuses on locked factories is available from upon request. 
27

References:

Baker, George, Gibbs, Michael, and Holmstrom, Bengt. “The Internal Economics of the Firm: 

Evidence from Personnel Data.” Quarterly Journal of Economics 109 (1994): 881-919.

Bertola, Giuseppe. “A Pure Theory of Job Security and Labour Income Risk.” Review of Economic Studies 71 (2004): 43-61. 

Blanchard, Olivier J., and Tirole, Jean. “The Joint Design of Unemployment Insurance and Employment Protection: A First Pass.” Journal of the European Economic Association 6 (2008): 45-

77. 

Bulow, Jeremy I., and Summers, Lawrence H. “A Theory of Dual Labor Markets with Application to Industrial Policy, Discrimination, and Keynesian Unemployment.” Journal of Labor Economics 4 (1986): 376-414. 

Blanchard, Olivier J., and Tirole, Jean. “Redesigning the Employment Protection System.” De 

Economist 152 (2004): 1-20. 

Campbell, C. M., III and Kamlani, K. S. “The Reasons for Wage Rigidity: Evidence from a Survey of Firms.” Quarterly Journal of Economics 112 (1997): 759-789. 

DiNardo, John, Fortin, Nicole, and Lemieux, Thomas “Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach.” Econometrica 64 (1996): 1001-

1044. 

Frank, R. H. “Are Workers Paid their Marginal Product?” American Economic Review 74 

(1984): 549-571. 

Levine, David I. “Just-Cause Employment Policies in the Presence of Worker Adverse Selection.” Journal of Labor Economics 9 (1991): 294-305. 

Ljungqvist, Lars, and Thomas J. Sargent, “The European Unemployment Dilemma.” Journal of 

Political Economy 106 (1998): 514-550 

MacLeod, W. Bentley., and Voraprapa, Nakavachara. “Can Wrongful Discharge Law Enhance 

Employment?” Economic Journal 117 (2007): F218-F278. 

Pissarides, Christopher A. “Employment Protection.” Labour Economics 8 (2001): 131-59. 
28

Appendix 

Proof of Lemma 2:

For the uniform distribution, the middle segment of curve A is from{ , ,} NS S N Nw JC JC JC

max

max min

2 (1 ) {0, , } 2

S eN     

 

  

 to

max min min

max min

[( ) 2 ] (1 ) 2 { ,, } 2

NS eN e S N       

 

     

 , and the relationship between the two 

types of labor is max min

2 S S

S NS

JC JC NS

eN N N N

  N

   . Substituting this into equation (5), we get: 

(A1) 

max min

2

2

NS

JC

JC S S

NS NS

JC JC NS

N

w

eN N N N

N

 

 

       

  

This allows us to take derivatives following along the middle line segment. The first and second 

derivatives are: 

(A2) 

max min

2

max min

2 ( )

2 2 1

S

S S

NS

NS JC

eN

eN N N

N

 

 

 

 

              

 (A3) 

max min

3

max min

2 1 ()

2 1

S S

NS

S S

NS

NS JC

N eN

N

eN N N

N

 

 

 

 

      

              

Since all parameters are positive and non-zero, it is apparent that the first derivative is positive 

and the second derivative is strictly negative. Thus as we move along the attainable choices of 

labor, equation (5) is increasing and strictly concave. And as we moved along the attainable 

choices of labor, the middle segment of curve A was increasing and linear. Thus it follows that 

equation (5) crosses the middle segment of curve A at zero to two points. ■

Proof of Lemma 3, Uniform Distribution: 

Let αi be distributed U[a,b] for both shirkers and non-shirkers, and let NS S b a     . At the 

unregulated equilibrium, the proportion of non-shirkers among the workers in JC firms is: 
29

(A4) 

1

( )

1 1 ( )

NS

NS S

b

NS

NS NS

b b NS S NS NS S S

NS S

N d

b a N b

bN N N N N dN d

ba ba



 





 

 

    

  



 

As guaranteed by Lemma 1, this proportion is less than the population proportion of nonshirkers. The tax causes both thresholds to decrease by Δ. The mass of non-shirkers who switch 

from AW to JC firms as a result is: 

(A5) 1 1

NS NS

b b NS

NS NS N N dN d

ba ba ba  

 



       

The mass of shirkers who switch from AW to JC firms is: 

(A6) 1 1

S S

b b S

S S N N dN d

ba ba ba  

 



       

The proportion of non-shirkers among switchers is: 

(A7) 

NS

NS S

N

N N

The uniform distribution guarantees that the proportion of non-shirkers among the marginal 

switchers will be equal to the population proportion of non-shirkers. It is straightforward to show 

that (A7) must be greater than (A4). ■

Proof of Lemma 3, U-Quadratic Distribution: 

For a tax to make the JC wage decrease, the proportion of non-shirkers among marginal 

switchers must be smaller than the proportion among infra-marginal JC workers. Let αi be 

distributed U-quadratic on [a,b] for both shirkers and non-shirkers,15 and let NS S b a     . 

Choose parameter values such that ( )/2 NS   a b . At the unregulated equilibrium, the 

proportion of non-shirkers among the workers in JC firms is: 

(A8)  

2

2

3 3

2 2

3

2

2 2

( )

( ) 64 () ()

( )

b

NS

a b NS

b b S

NS S NS

ab ab e

N x yd

N

N ba e N x yd N x yd N

b a

 

 



  



  

   



 

 

15 The pdf of the U-quadratic distribution is x(α–y)2

, where x = 12/(b–a)

3

 and y = (a+b)/2. 
30

As guaranteed by Lemma 1, this proportion is less than the population proportion of nonshirkers. The tax causes both thresholds to decrease by Δ. The mass of non-shirkers who switch 

from AW to JC firms as a result is: 

(A9) 

3

2 2

3

2 2

4 () () ( )

b b NS

NS NS

ab ab

N N x yd N x yd b a

 

  

     

The mass of shirkers who switch from AW to JC firms is: 

 (A10)   2 2

2 2

3

2 2

2 2

4 12 6

() () ( )

S b b

S S

ab ab e e

N ee

N x yd N x yd b a

      

       

The proportion of non-shirkers among switchers is: 

(A11) 

2

2 2 ( ) (12 6 )

NS

NS S S

N

N N Nee



   

If b = 1, a = 0, e = 1/8, Δ = 1⁄4, 95 NS N  , and 5 S N  , then (A11) is smaller than (A8), and so the 

tax makes the JC wage decrease. ■
Utils

Marginal Social Gain Marginal Social Cost To

Figure 3

Unregulated Equilibrium

Subsidy on At Will

Tax on At Will

Note: There are two y-axis scales, one in Marginal Utils and one in Total Utils 
Utils

Marginal Social Gain Marginal Social Cost To

Figure 4

Unregulated Equilibrium

Subsidy on At Will

Tax on At Will

Note: There are two y-axis scales, one in Marginal Utils and one in Total Utils 
Utils

Marginal Social Gain Marginal Social Cost To

Figure 5

Unregulated Equilibrium

Subsidy on At Will

Tax on At Will

Note: There are two y-axis scales, one in Marginal Utils and one in Total Utils